afex/0000755000176200001440000000000013607773464011216 5ustar liggesusersafex/NAMESPACE0000644000176200001440000000357713607674774012455 0ustar liggesusers# Generated by roxygen2: do not edit by hand S3method(afex_plot,afex_aov) S3method(afex_plot,default) S3method(afex_plot,merMod) S3method(afex_plot,mixed) S3method(anova,afex_aov) S3method(anova,mixed) S3method(nice,afex_aov) S3method(nice,anova) S3method(nice,mixed) S3method(print,afex_aov) S3method(print,mixed) S3method(print,nice_table) S3method(summary,afex_aov) S3method(summary,mixed) export(afex_options) export(afex_plot) export(all_fit) export(aov.car) export(aov4) export(aov_4) export(aov_car) export(aov_ez) export(compare.2.vectors) export(ems) export(ez.glm) export(interaction_plot) export(lmer) export(lmer_alt) export(mixed) export(nice) export(nmkbw) export(oneway_plot) export(round_ps) export(set_default_contrasts) export(set_deviation_contrasts) export(set_effects_contrasts) export(set_sum_contrasts) export(set_treatment_contrasts) export(test_levene) export(test_sphericity) importFrom(car,Anova) importFrom(lme4,findbars) importFrom(lme4,getME) importFrom(lme4,glmer) importFrom(lme4,glmerControl) importFrom(lme4,isGLMM) importFrom(lme4,isREML) importFrom(lme4,lmerControl) importFrom(lme4,nobars) importFrom(lmerTest,lmer) importFrom(methods,as) importFrom(methods,is) importFrom(parallel,clusterApplyLB) importFrom(parallel,clusterCall) importFrom(parallel,clusterEvalQ) importFrom(parallel,clusterExport) importFrom(reshape2,dcast) importFrom(stats,"contrasts<-") importFrom(stats,aggregate) importFrom(stats,anova) importFrom(stats,as.formula) importFrom(stats,coef) importFrom(stats,formula) importFrom(stats,logLik) importFrom(stats,model.frame) importFrom(stats,model.matrix) importFrom(stats,optim) importFrom(stats,p.adjust) importFrom(stats,qt) importFrom(stats,sd) importFrom(stats,setNames) importFrom(stats,symnum) importFrom(stats,t.test) importFrom(stats,terms) importFrom(stats,update) importFrom(stats,wilcox.test) importFrom(stats,xtabs) importFrom(utils,packageVersion) afex/data/0000755000176200001440000000000013351525342012111 5ustar liggesusersafex/data/md_15.1.rda0000644000176200001440000000071413351525342013647 0ustar liggesusersUN@4ţGOM֓|֖n&MJ)+|@\`c4jDo盝ٙnG>c S1jXUȲ.^`Lm&6c5ac@NLAY\|0oG>y//,YH<78NA Hc O-yF;8<öd9s0K[fG] mJBhEABP% j2v+m{oZقDAECrI%hșI):XW w`/kɵnaB:y:Sk欟Sqݻ Iɬ:m}($3s?)]BZv{ɥ"\7I6mcN@4.X{S]\1ksxC K.CO9CZ<*kWeafex/data/obk.long.rda0000644000176200001440000000132613351525342014314 0ustar liggesusersYn@yC"B,#>UBذ$NpvʶF>e]7L_b7:bK'̝w{⯟!M)RȋG!g2]'y(9  +J (+)DO`mu^t+ ܥ5"&qD SoI#>FMZj(VDZ:)4uowCϗ?Uy< /{c&+݌Vz Csi@$o &صac +[A[g_װd~׃sQ =4>ʟMꈈt_r]0v+1c-.WU{̧t!m2v8Nt';v..P0_8<`7Շc;^sKS{_%>]T\\ \ǣiOZi)ס<ڹ[ʥ8(vz>ppE?vO4Q>~ڗN }ދT%;tt&(a` 4J/1)\؁j+IUϏƵf&Q١E,&nX;#%afex/data/md_16.4.rda0000644000176200001440000000063613351525342013656 0ustar liggesusersBZh91AY&SYLb7@@y-A51f$` #@1j4oT44D%OTfi &@h#И0LQG4DRllx@ꋯܫF(Kus!2HCtEQnn{3]}]W:ލhX`,q,`՝e{m=7pԦ.AhC7II=~ ) J9]!!wX#Ґ`I#H@B`@f4G[hhK'*eТ/%"ŭ~(hUTDR$"L?9}H\%! vh6c_m*7 H$c%^O*l~e;?ܑN$6<afex/data/md_16.1.rda0000644000176200001440000000045713351525342013654 0ustar liggesusersK0ߒnsQۮ"lvЃ =&`˧fɰY|K_WyJgxs._ȈcSI0bԧWƨRo2P.[dAA\1b29,*iBֲ[;Dܚteo_ WjY)?Kv;y枽I6VKcc'. 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Fk D BCUMpvQaŹg ^=:DIeՅxEPr|B1#PQ(sն"䴰DaSկzZBBs=SfsYPQk[6o"ɓrմîb W󲳶c(k[VהWnBI% ̏N7 :`^< P\=d:`Tf-#P! *=aR7ykF7Ypo]1x S  =훏!fJH>8%Ǻqb ArM"-Q{1~h <0ff>|$I$I$I$I$I$I%79ku+]a g%>IZ1` `0(*´B3E XI!4QKA$J_bȅBZ-Q!j[MD TZ$9nHZxhFb[%5bn 7hқW{1\%>٨ֵ4jZ4PmAm|q fEs 0` $C$I $H3I$0kZPkZAÂB|:!,yeb-[%2YH}VN|!U Km-DU'G듛}שۗ~aAdRDBH[lZKb["bLRbɅ# e7Vdb[@m(&t$ @N 0ImWËvQ("YhCejUh b hDdXYDN 0li]:il7w^"BN44)뿅"4ip!L A5 C^Iַ$cVG87}f_WLSNh4xpTB ),U62BE7  F)„@@afex/data/md_12.1.rda0000644000176200001440000000054413351525342013645 0ustar liggesusersSNP̥MLHWM\p튝M( u' ~'%Ź)ƄI93s!{o 0Hm$b6`2yҘM ʹyҔZee3V_@s~Azn4>Li{etWᶝ<Ŕ@IuBQw{&YB>㣮/G6?d*ïafex/man/0000755000176200001440000000000013520615175011755 5ustar liggesusersafex/man/afex_plot.Rd0000644000176200001440000010540513607673767014253 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/afex_plot.R \name{afex_plot} \alias{afex_plot} \alias{afex_plot.afex_aov} \alias{afex_plot.mixed} \alias{afex_plot.merMod} \alias{afex_plot.default} \alias{interaction_plot} \alias{oneway_plot} \title{m-way Plot with Error Bars and Raw Data} \usage{ afex_plot(object, ...) \method{afex_plot}{afex_aov}( object, x, trace, panel, mapping, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ... ) \method{afex_plot}{mixed}( object, x, trace, panel, mapping, id, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ... ) \method{afex_plot}{merMod}( object, x, trace, panel, mapping, id, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ... ) \method{afex_plot}{default}( object, x, trace, panel, mapping, id, dv, data, within_vars, between_vars, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ... ) interaction_plot( means, data, mapping = c("shape", "lineytpe"), error_plot = TRUE, error_arg = list(width = 0), data_plot = TRUE, data_geom = ggplot2::geom_point, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), dodge = 0.5, legend_title, col_x = "x", col_y = "y", col_trace = "trace", col_panel = "panel", col_lower = "lower", col_upper = "upper" ) oneway_plot( means, data, mapping = "", error_plot = TRUE, error_arg = list(width = 0), data_plot = TRUE, data_geom = ggbeeswarm::geom_beeswarm, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), legend_title, col_x = "x", col_y = "y", col_panel = "panel", col_lower = "lower", col_upper = "upper" ) } \arguments{ \item{object}{\code{afex_aov}, \code{mixed}, \code{merMod} or other model object supported by \pkg{emmeans} (for further examples see: \code{vignette("afex_plot_supported_models")}).} \item{...}{currently ignored.} \item{x}{A \code{character} vector or one-sided \code{formula} specifying the factor names of the predictors displayed on the x-axis. \code{mapping} specifies further mappings for these factors if \code{trace} is missing.} \item{trace}{An optional \code{character} vector or one-sided \code{formula} specifying the factor names of the predictors connected by the same line. \code{mapping} specifies further mappings for these factors.} \item{panel}{An optional \code{character} vector or one-sided \code{formula} specifying the factor names of the predictors shown in different panels.} \item{mapping}{A \code{character} vector specifying which aesthetic mappings should be applied to either the \code{trace} factors (if \code{trace} is specified) or the \code{x} factors. Useful options are any combination of \code{"shape"}, \code{"color"}, \code{"linetype"}, or also \code{"fill"} (see examples). The default (i.e., missing) uses \code{c("shape", "linetype")} if \code{trace} is specified and \code{""} otherwise (i.e., no additional aesthetic). If specific mappings should not be applied to specific graphical elements, one can override those via the corresponding further arguments. For example, for \code{data_arg} the default is \code{list(color = "darkgrey")} which prevents that \code{"color"} is mapped onto points in the background.} \item{error}{A scalar \code{character} vector specifying on which standard error the error bars should be based. Default is \code{"model"}, which plots model-based standard errors. Further options are: \code{"none"} (or \code{NULL}), \code{"mean"}, \code{"within"} (or \code{"CMO"}), and \code{"between"}. See details.} \item{error_ci}{Logical. Should error bars plot confidence intervals (=\code{TRUE}, the default) or standard errors (=\code{FALSE})?} \item{error_level}{Numeric value between 0 and 1 determing the width of the confidence interval. Default is .95 corresponding to a 95\% confidence interval.} \item{error_arg}{A \code{list} of further arguments passed to \code{\link[ggplot2]{geom_errorbar}}, which draws the errorsbars. Default is \code{list(width = 0)} which suppresses the vertical bars at the end of the error bar.} \item{data_plot}{\code{logical}. Should raw data be plotted in the background? Default is \code{TRUE}.} \item{data_geom}{Geom \code{function} used for plotting data in background. The default (missing) uses \code{\link[ggplot2]{geom_point}} if \code{trace} is specified, otherwise \code{\link[ggbeeswarm]{geom_beeswarm}}. See examples fo further options.} \item{data_alpha}{numeric \code{alpha} value between 0 and 1 passed to \code{data_geom}. Default is \code{0.5} which correspond to semitransparent data points in the background such that overlapping data points are plotted darker.} \item{data_arg}{A \code{list} of further arguments passed to \code{data_geom}. Default is \code{list(color = "darkgrey")}, which plots points in the background in grey.} \item{point_arg, line_arg}{A \code{list} of further arguments passed to \code{\link[ggplot2]{geom_point}} or \code{\link[ggplot2]{geom_line}} which draw the points and lines in the foreground. Default is \code{list()}. \code{line_arg} is only used if \code{trace} is specified.} \item{emmeans_arg}{A \code{list} of further arguments passed to \code{\link[emmeans]{emmeans}}. Of particular importance for ANOVAs is \code{model}, see \code{\link{afex_aov-methods}}.} \item{dodge}{Numerical amount of dodging of factor-levels on x-axis. Default is \code{0.5}.} \item{return}{A scalar \code{character} specifying what should be returned. The default \code{"plot"} returns the \pkg{ggplot2} plot. The other option \code{"data"} returns a list with two \code{data.frame}s containing the data used for plotting: \code{means} contains the means and standard errors for the foreground, \code{data} contains the raw data in the background.} \item{factor_levels}{A \code{list} of new factor levels that should be used in the plot. The name of each list entry needs to correspond to one of the factors in the plot. Each list element can optionally be a named character vector where the name corresponds to the old factor level and the value to the new factor level. Named vectors allow two things: (1) updating only a subset of factor levels (if only a subset of levels is specified) and (2) reordering (and renaming) the factor levels, as order of names within a list element are the order that will be used for plotting. If specified, emits a \code{message} with \code{old -> new} factor levels.} \item{legend_title}{A scalar \code{character} vector with a new title for the legend.} \item{id}{An optional \code{character} vector specifying over which variables the raw data should be aggregated. Only relevant for \code{mixed}, \code{merMod}, and \code{default} method. The default (missing) uses all random effects grouping factors (for \code{mixed} and \code{merMod} method) or assumes all data points are independent. This can lead to many data points. \code{error = "within"} or \code{error = "between"} require that \code{id} is of length 1. See examples.} \item{dv}{An optional scalar \code{character} vector giving the name of the column containing the dependent variable for the \code{afex_plot.default} method. If missing, the function attempts to take it from the \code{call} slot of \code{object}. This is also used as y-axis label.} \item{data}{For the \code{afex_plot.default} method, an optional \code{data.frame} containing the raw data used for fitting the model and which will be used as basis for the data points in the background. If missing, it will be attempted to obtain it from the model via \code{\link[emmeans]{recover_data}}. For the plotting functions, a \code{data.frame} with the data that has to be passed and contains the background data points.} \item{within_vars, between_vars}{For the \code{afex_plot.default} method, an optional \code{character} vector specifying which variables should be treated as within-subjects (or repeated-measures) factors and which as between-subjects (or independen-sampels) factors. If one of the two arguments is given, all other factors are assumed to fall into the other category.} \item{means}{\code{data.frame}s used for plotting of the plotting functions.} \item{error_plot}{\code{logical}. Should error bars be plotted? Only used in plotting functions. To suppress plotting of error bars use \code{error = "none"} in \code{afex_plot}.} \item{col_y, col_x, col_trace, col_panel}{A scalar \code{character} string specifying the name of the corresponding column containing the information used for plotting. Each column needs to exist in both the \code{means} and the \code{data} \code{data.frame}.} \item{col_lower, col_upper}{A scalar \code{character} string specifying the name of the columns containing lower and upper bounds for the error bars. These columns need to exist in \code{means}.} } \value{ Returns a \pkg{ggplot2} plot (i.e., object of class \code{c("gg", "ggplot")}) unless \code{return = "data"}. } \description{ Plots results from factorial experiments. Estimated marginal means and error bars are plotted in the foreground, raw data is plotted in the background. Error bars can be based on different standard errors (e.g., model-based, within-subjects, between-subjects). Functions described here return a \pkg{ggplot2} plot object, thus allowing further customization of the plot. \code{afex_plot} is the user friendly function that does data preparation and plotting. It also allows to only return the prepared data (\code{return = "data"}). \code{interaction_plot} does the plotting when a \code{trace} factor is present. \code{oneway_plot} does the plotting when a \code{trace} factor is absent. } \details{ \code{afex_plot} obtains the estimated marginal means via \code{\link[emmeans]{emmeans}} and aggregates the raw data to the same level. It then calculates the desired confidence interval or standard error (see below) and passes the prepared data to one of the two plotting functions: \code{interaction_plot} when \code{trace} is specified and \code{oneway_plot} otherwise. \subsection{Error Bars}{Error bars provide a grahical representation of the variability of the estimated means and should be routinely added to results figures. However, there exist several possibilities which particular measure of variability to use. Because of this, any figure depicting error bars should be accompanied by a note detailing which measure the error bars shows. The present functions allow plotting of different types of confidence intervals (if \code{error_ci = TRUE}, the default) or standard errors (if \code{error_ci = FALSE}). A further complication is that readers routinely misinterpret confidence intervals. The most common error is to assume that non-overlapping error bars indicate a significant difference (e.g., Belia et al., 2005). This is rarely the case (see e.g., Cumming & Finch, 2005; Knol et al., 2011; Schenker & Gentleman, 2005). For example, in a fully between-subjects design in which the error bars depict 95\% confidence intervals and groups are of approximately equal size and have equal variance, even error bars that overlap by as much as 50\% still correspond to \emph{p} < .05. Error bars that are just touching roughly correspond to \emph{p} = .01. In the case of designs involving repeated-measures factors the usual confidence intervals or standard errors (i.e., model-based confidence intervals or intervals based on the standard error of the mean) cannot be used to gauge significant differences as this requires knowledge about the correlation between measures. One popular alternative in the psychological literature are intervals based on within-subjects standard errors/confidence intervals (e.g., Cousineau & O'Brien, 2014). These attempt to control for the correlation across individuals and thereby allow judging differences between repeated-measures condition. As a downside, when using within-subjects intervals no comparisons across between-subjects conditions or with respect to a fixed-value are possible anymore. In the case of a mixed-design, no single type of error bar is possible that allows comparison across all conditions. Likewise, for mixed models involving multiple \emph{crossed} random effects, no single set of error bars (or even data aggregation) adequately represent the true varibility in the data and adequately allows for "inference by eye". Therefore, special care is necessary in such cases. One possiblity is to avoid error bars altogether and plot only the raw data in the background (with \code{error = "none"}). The raw data in the background still provides a visual impression of the variability in the data and the precision of the mean estimate, but does not as easily suggest an incorrect inferences. Another possibility is to use the model-based standard error and note in the figure caption that it does not permit comparisons across repeated-measures factors. The following "rules of eye" (Cumming and Finch, 2005) hold, when permitted by design (i.e., within-subjects bars for within-subjects comparisons; other variants for between-subjects comparisons), and groups are approximately equal in size and variance. Note that for more complex designs ususally analyzed with mixed models, such as designs involving complicated dependencies across data points, these rules of thumbs may be highly misleading. \itemize{ \item \emph{p} < .05 when the overlap of the 95\% confidence intervals (CIs) is no more than about half the average margin of error, that is, when proportion overlap is about .50 or less. \item \emph{p} < .01 when the two CIs do not overlap, that is, when proportion overlap is about 0 or there is a positive gap. \item \emph{p} < .05 when the gap between standard error (SE) bars is at least about the size of the average SE, that is, when the proportion gap is about 1 or greater. \item \emph{p} < .01 when the proportion gap between SE bars is about 2 or more. } } \subsection{Implemented Standard Errors}{The following lists the implemented approaches to calculate confidence intervals (CIs) and standard errors (SEs). CIs are based on the SEs using the \emph{t}-distribution with degrees of freedom based on the cell or group size. For ANOVA models, \code{afex_plot} attempts to warn in case the chosen approach is misleading given the design (e.g., model-based error bars for purely within-subjects plots). For \code{mixed} models, no such warnings are produced, but users should be aware that all options beside \code{"model"} are not actually appropriate and have only heuristic value. But then again, \code{"model"} based error bars do not permit comparisons for factors varying within one of the random-effects grouping factors (i.e., factors for which random-slopes should be estimated). \describe{ \item{\code{"model"}}{Uses model-based CIs and SEs. For ANOVAs, the variant based on the \code{lm} or \code{mlm} model (i.e., \code{emmeans_arg = list(model = "multivariate")}) seems generally preferrable.} \item{\code{"mean"}}{Calculates the standard error of the mean for each cell ignoring any repeated-measures factors.} \item{\code{"within"} or \code{"CMO"}}{Calculates within-subjects SEs using the Cosineau-Morey-O'Brien (Cousineau & O'Brien, 2014) method. This method is based on a double normalization of the data. SEs and CIs are then calculated independently for each cell (i.e., if the desired output contains between-subjects factors, SEs are calculated for each cell including the between-subjects factors).} \item{\code{"between"}}{First aggregates the data per participant and then calculates the SEs for each between-subjects condition. Results in one SE and \emph{t}-quantile for all conditions in purely within-subjects designs.} \item{\code{"none"} or \code{NULL}}{Suppresses calculation of SEs and plots no error bars.} } For \code{mixed} models, the within-subjects/repeated-measures factors are relative to the chosen \code{id} effects grouping factor. They are automatically detected based on the random-slopes of the random-effects grouping factor in \code{id}. All other factors are treated as independent-samples or between-subjects factors. } } \examples{ # note: use library("ggplot") to avoid "ggplot2::" in the following ################################################################## ## 2-factor Within-Subject Design ## ################################################################## data(md_12.1) aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) ##--------------------------------------------------------------- ## Basic Interaction Plots - ##--------------------------------------------------------------- afex_plot(aw, x = "angle", trace = "noise") # or: afex_plot(aw, x = ~angle, trace = ~noise) afex_plot(aw, x = "noise", trace = "angle") ### For within-subject designs, using within-subject CIs is better: afex_plot(aw, x = "angle", trace = "noise", error = "within") (p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within")) ## use different themes for nicer graphs: p1 + ggplot2::theme_bw() \dontrun{ p1 + ggplot2::theme_light() p1 + ggplot2::theme_minimal() p1 + jtools::theme_apa() p1 + ggpubr::theme_pubr() ### set theme globally for R session: ggplot2::theme_set(ggplot2::theme_bw()) ### There are several ways to deal with overlapping points in the background besides alpha # 1. using the default data geom and ggplot2::position_jitterdodge afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 5, dodge.width = 0.3 ## needs to be same as dodge ), color = "darkgrey")) # 2. using ggbeeswarm::geom_beeswarm afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8, color = "darkgrey")) # 3. do not display points, but use a violinplot: ggplot2::geom_violin afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) # 4. violinplots with color: ggplot2::geom_violin afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("linetype", "shape", "fill"), data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) # 5. do not display points, but use a boxplot: ggplot2::geom_boxplot afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3)) # 6. combine points with boxplot: ggpol::geom_boxjitter afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggpol::geom_boxjitter, data_arg = list(width = 0.3)) ## hides error bars! # 7. nicer variant of ggpol::geom_boxjitter afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.3, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0)) # 8. nicer variant of ggpol::geom_boxjitter without lines afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), line_arg = list(linetype = 0), error_arg = list(size = 1.5, width = 0)) } ##--------------------------------------------------------------- ## One-Way Plots - ##--------------------------------------------------------------- afex_plot(aw, x = "angle", error = "within") ## default \dontrun{ ## with color we need larger points afex_plot(aw, x = "angle", mapping = "color", error = "within", point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) afex_plot(aw, x = "angle", error = "within", data_geom = ggpol::geom_boxjitter) ## nicer afex_plot(aw, x = "angle", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.07, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) ## we can add a line connecting the means using geom_point(aes(group = 1)): afex_plot(aw, x = "angle", error = "within") + ggplot2::geom_line(ggplot2::aes(group = 1)) ## One-way plots also supports panels: afex_plot(aw, x = "angle", panel = "noise", error = "within") ## And panels with lines: afex_plot(aw, x = "angle", panel = "noise", error = "within") + ggplot2::geom_line(ggplot2::aes(group = 1)) ## For more complicated plots it is easier to attach ggplot2: library("ggplot2") ## We can hide geoms by plotting them in transparent color and add them ## afterward to use a mapping not directly supported. ## For example, the next plot adds a line to a one-way plot with panels, but ## with all geoms in the foreground having a color conditional on the panel. afex_plot(aw, x = "angle", panel = "noise", error = "within", point_arg = list(color = "transparent"), error_arg = list(color = "transparent")) + geom_point(aes(color = panel)) + geom_linerange(aes(color = panel, ymin = lower, ymax = upper)) + geom_line(aes(group = 1, color = panel)) + guides(color = guide_legend(title = "NOISE")) ## Note that we need to use guides explicitly, otherwise the legend title would ## be "panel". legend_title does not work in this case. ##--------------------------------------------------------------- ## Other Basic Options - ##--------------------------------------------------------------- ## relabel factor levels via factor_levels (with message) afex_plot(aw, x = "noise", trace = "angle", factor_levels = list(angle = c("0°", "4°", "8°"), noise = c("Absent", "Present"))) ## factor_levels allows named vectors which enable reordering the factor levels ### and renaming subsets of levels: afex_plot(aw, x = "noise", trace = "angle", factor_levels = list( angle = c(X8 = "8°", X4 = "4°", X0 = "0°"), noise = c(present = "Present") ) ) ## Change title of legend afex_plot(aw, x = "noise", trace = "angle", legend_title = "Noise Condition") ## for plots with few factor levels, smaller dodge might be better: afex_plot(aw, x = "angle", trace = "noise", dodge = 0.25) ################################################################# ## 4-factor Mixed Design ## ################################################################# data(obk.long, package = "afex") a1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") ## too difficult to see anything afex_plot(a1, ~phase*hour, ~treatment) + ggplot2::theme_light() ## better afex_plot(a1, ~hour, ~treatment, ~phase) + ggplot2::theme_light() ## even better and different model-based standard errors afex_plot(a1, ~hour, ~treatment, ~phase, dodge = 0.65, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 0.2, dodge.width = 0.65 ## needs to be same as dodge ), color = "darkgrey"), emmeans_arg = list(model = "multivariate")) + ggplot2::theme_classic() # with color instead of linetype to separate trace factor afex_plot(a1, ~hour, ~treatment, ~phase, mapping = c("shape", "color"), dodge = 0.65, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 0.2, dodge.width = 0.65 ## needs to be same as dodge )), emmeans_arg = list(model = "multivariate")) + ggplot2::theme_light() # only color to separate trace factor afex_plot(a1, ~hour, ~treatment, ~phase, mapping = "color", dodge = 0.65, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 0.2, dodge.width = 0.65 ## needs to be same as dodge )), emmeans_arg = list(model = "multivariate")) + ggplot2::theme_classic() ## plot involving all 4 factors: afex_plot(a1, ~hour, ~treatment, ~gender+phase, dodge = 0.65, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 0.2, dodge.width = 0.65 ## needs to be same as dodge ), color = "darkgrey"), emmeans_arg = list(model = "multivariate")) + ggplot2::theme_bw() ##--------------------------------------------------------------- ## Different Standard Errors Available - ##--------------------------------------------------------------- ## purely within-design cbind( afex_plot(a1, ~phase, ~hour, error = "model", return = "data")$means[,c("phase", "hour", "y", "SE")], multivariate = afex_plot(a1, ~phase, ~hour, emmeans_arg = list(model = "multivariate"), error = "model", return = "data")$means$error, mean = afex_plot(a1, ~phase, ~hour, error = "mean", return = "data")$means$error, within = afex_plot(a1, ~phase, ~hour, error = "within", return = "data")$means$error, between = afex_plot(a1, ~phase, ~hour, error = "between", return = "data")$means$error) ## mixed design cbind( afex_plot(a1, ~phase, ~treatment, error = "model", return = "data")$means[,c("phase", "treatment", "y", "SE")], multivariate = afex_plot(a1, ~phase, ~treatment, emmeans_arg = list(model = "multivariate"), error = "model", return = "data")$means$error, mean = afex_plot(a1, ~phase, ~treatment, error = "mean", return = "data")$means$error, within = afex_plot(a1, ~phase, ~treatment, error = "within", return = "data")$means$error, between = afex_plot(a1, ~phase, ~treatment, error = "between", return = "data")$means$error) } ################################################################## ## Mixed Models ## ################################################################## data("Machines", package = "MEMSS") m1 <- mixed(score ~ Machine + (Machine|Worker), data=Machines) pairs(emmeans::emmeans(m1, "Machine")) # contrast estimate SE df t.ratio p.value # A - B -7.966667 2.420850 5 -3.291 0.0481 # A - C -13.916667 1.540100 5 -9.036 0.0007 # B - C -5.950000 2.446475 5 -2.432 0.1253 ## Default (i.e., model-based) error bars suggest no difference between Machines. ## This contrasts with pairwise comparisons above. afex_plot(m1, "Machine") ## Impression from within-subject error bars is more in line with pattern of differences. afex_plot(m1, "Machine", error = "within") \dontrun{ data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### following model should take less than a minute to fit: mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ (task||item), fhch, method = "S", expand_re = TRUE) ## way too many points in background: afex_plot(mrt, "stimulus", "frequency", "task") ## better to restrict plot of data to one random-effects grouping variable afex_plot(mrt, "stimulus", "frequency", "task", id = "id") ## when plotting data from a single random effect, different error bars are possible: afex_plot(mrt, "stimulus", "frequency", "task", id = "id", error = "within") afex_plot(mrt, "stimulus", "frequency", "task", id = "id", error = "mean") ## compare visual impression with: pairs(emmeans::emmeans(mrt, c("stimulus", "frequency"), by = "task")) ## same logic also possible for other random-effects grouping factor afex_plot(mrt, "stimulus", "frequency", "task", id = "item") ## within-item error bars are misleading here. task is sole within-items factor. afex_plot(mrt, "stimulus", "frequency", "task", id = "item", error = "within") ## CIs based on stanard error of mean look small, but not unreasonable given results. afex_plot(mrt, "stimulus", "frequency", "task", id = "item", error = "mean") ### compare distribution of individual data for different random effects: ## requires package cowplot p_id <- afex_plot(mrt, "stimulus", "frequency", "task", id = "id", error = "within", dodge = 0.7, data_geom = ggplot2::geom_violin, mapping = c("shape", "fill"), data_arg = list(width = 0.7)) + ggplot2::scale_shape_manual(values = c(4, 17)) + ggplot2::labs(title = "ID") p_item <- afex_plot(mrt, "stimulus", "frequency", "task", id = "item", error = "within", dodge = 0.7, data_geom = ggplot2::geom_violin, mapping = c("shape", "fill"), data_arg = list(width = 0.7)) + ggplot2::scale_shape_manual(values = c(4, 17)) + ggplot2::labs(title = "Item") ### see: https://cran.r-project.org/package=cowplot/vignettes/shared_legends.html p_comb <- cowplot::plot_grid( p_id + ggplot2::theme_light() + ggplot2::theme(legend.position="none"), p_item + ggplot2::theme_light() + ggplot2::theme(legend.position="none") ) legend <- cowplot::get_legend(p_id + ggplot2::theme(legend.position="bottom")) cowplot::plot_grid(p_comb, legend, ncol = 1, rel_heights = c(1, 0.1)) ##---------------------------------------------------------------- ## Support for lme4::lmer - ##---------------------------------------------------------------- Oats <- nlme::Oats ## afex_plot does currently not support implicit nesting: (1|Block/Variety) ## Instead, we need to create the factor explicitly Oats$VarBlock <- Oats$Variety:Oats$Block Oats.lmer <- lmer(yield ~ Variety * factor(nitro) + (1|VarBlock) + (1|Block), data = Oats) afex_plot(Oats.lmer, "nitro", "Variety") afex_plot(Oats.lmer, "nitro", panel = "Variety") ################################################################## ## Default Method works for Models Supported by emmeans ## ################################################################## ## lm warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks) afex_plot(warp.lm, "tension") afex_plot(warp.lm, "tension", "wool") ## poisson glm ins <- data.frame( n = c(500, 1200, 100, 400, 500, 300), size = factor(rep(1:3,2), labels = c("S","M","L")), age = factor(rep(1:2, each = 3)), claims = c(42, 37, 1, 101, 73, 14)) ins.glm <- glm(claims ~ size + age + offset(log(n)), data = ins, family = "poisson") afex_plot(ins.glm, "size", "age") ## binomial glm adapted from ?predict.glm ldose <- factor(rep(0:5, 2)) numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16) sex <- factor(rep(c("M", "F"), c(6, 6))) SF <- numdead/20 ## dv should be a vector, no matrix budworm.lg <- glm(SF ~ sex*ldose, family = binomial, weights = rep(20, length(numdead))) afex_plot(budworm.lg, "ldose") afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! afex_plot(budworm.lg, "ldose", "sex", data_arg = list(size = 4, color = "red")) ## nlme mixed model data(Oats, package = "nlme") Oats$nitro <- factor(Oats$nitro) oats.1 <- nlme::lme(yield ~ nitro * Variety, random = ~ 1 | Block / Variety, data = Oats) afex_plot(oats.1, "nitro", "Variety", data = Oats) afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block") afex_plot(oats.1, "nitro", data = Oats) afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")) afex_plot(oats.1, "nitro", data = Oats, id = "Block") } } \references{ Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers Misunderstand Confidence Intervals and Standard Error Bars. \emph{Psychological Methods}, 10(4), 389-396. https://doi.org/10.1037/1082-989X.10.4.389 Cousineau, D., & O'Brien, F. (2014). Error bars in within-subject designs: a comment on Baguley (2012). \emph{Behavior Research Methods}, 46(4), 1149-1151. https://doi.org/10.3758/s13428-013-0441-z Cumming, G., & Finch, S. (2005). Inference by Eye: Confidence Intervals and How to Read Pictures of Data. \emph{American Psychologist}, 60(2), 170-180. https://doi.org/10.1037/0003-066X.60.2.170 Knol, M. J., Pestman, W. R., & Grobbee, D. E. (2011). The (mis)use of overlap of confidence intervals to assess effect modification. \emph{European Journal of Epidemiology}, 26(4), 253-254. https://doi.org/10.1007/s10654-011-9563-8 Schenker, N., & Gentleman, J. F. (2001). On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals. \emph{The American Statistician}, 55(3), 182-186. https://doi.org/10.1198/000313001317097960 } afex/man/md_16.1.Rd0000644000176200001440000000357413351525342013320 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/md_16.1-data.R \docType{data} \encoding{UTF-8} \name{md_16.1} \alias{md_16.1} \title{Data 16.1 / 10.9 from Maxwell & Delaney} \format{A data.frame with 24 rows and 3 variables.} \source{ Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 } \usage{ md_16.1 } \description{ Hypothetical Reaction Time Data for 2 x 3 Perceptual Experiment: Example data for chapter 12 of Maaxwell and Delaney (2004, Table 12.1, p. 574) in long format. Has two within.subjects factors: angle and noise. } \details{ Description from pp. 829: As brief background, the goal of the study here is to examine the extent to which female and male clinical psychology graduate student trainees may assign different severity ratings to clients at initial intake. Three female and 3 male graduate students are randomly selected to participate and each is randomly assigned four clients with whom to do an intake interview, after which each clinical trainee assigns a severity rating to each client, producing the data shown in Table 16.1. Note that I changed the labeling of the id slightly, so that they are now labeled from 1 to 6. Furthermore, I changed the contrasts of sex to \code{contr.treatment} to replicate the exact results of Table 16.3 (p. 837). } \examples{ ### replicate results from Table 16.3 (Maxwell & Delaney, 2004, p. 837) data(md_16.1) # original results need treatment contrasts: (mixed1_orig <- mixed(severity ~ sex + (1|id), md_16.1, check.contrasts=FALSE)) summary(mixed1_orig$full.model) # p-values stay the same with afex default contrasts (contr.sum), # but estimates and t-values for the fixed effects parameters change. (mixed1 <- mixed(severity ~ sex + (1|id), md_16.1)) summary(mixed1$full.model) } \keyword{dataset} afex/man/md_12.1.Rd0000644000176200001440000000520513351525342013305 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/md_12.1-data.R \docType{data} \encoding{UTF-8} \name{md_12.1} \alias{md_12.1} \title{Data 12.1 from Maxwell & Delaney} \format{A data.frame with 60 rows and 4 variables.} \source{ Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 } \usage{ md_12.1 } \description{ Hypothetical Reaction Time Data for 2 x 3 Perceptual Experiment: Example data for chapter 12 of Maaxwell and Delaney (2004, Table 12.1, p. 574) in long format. Has two within.subjects factors: angle and noise. } \details{ Description from pp. 573: Suppose that a perceptual psychologist studying the visual system was interested in determining the extent to which interfering visual stimuli slow the ability to recognize letters. Subjects are brought into a laboratory and seated in front of a tachistoscope. Subjects are told that they will see either the letter T or the letter I displayed on the screen. In some trials, the letter appears by itself, but in other trials, the target letter is embedded in a group of other letters. This variation in the display constitutes the first factor, which is referred to as noise. The noise factor has two levels?absent and present. The other factor varied by the experimenter is where in the display the target letter appears. This factor, which is called angle, has three levels. The target letter is either shown at the center of the screen (i.e., 0° off-center, where the subject has been instructed to fixate), 4° off-center or 8° off-center (in each case, the deviation from the center varies randomly between left and right). Table 12.1 presents hypothetical data for 10 subjects. As usual, the sample size is kept small to make the calculations easier to follow. The dependent measure is reaction time (latency), measured in milliseconds (ms), required by a subject to identify the correct target letter. Notice that each subject has six scores, one for each combination of the 2 x 3 design. In an actual perceptual experiment, each of these six scores would itself be the mean score for that subject across a number of trials in the particular condition. Although "trials" could be used as a third within-subjects factor in such a situation, more typically trials are simply averaged over to obtain a more stable measure of the individual's performance in each condition. } \examples{ data(md_12.1) # Table 12.5 (p. 578): aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), args.return=list(correction = "none", es = "none")) } \keyword{dataset} afex/man/mixed.Rd0000644000176200001440000010265713607673671013400 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mixed.R \encoding{UTF-8} \name{mixed} \alias{mixed} \alias{lmer_alt} \title{p-values for fixed effects of mixed-model via lme4::lmer()} \usage{ mixed( formula, data, type = afex_options("type"), method = afex_options("method_mixed"), per_parameter = NULL, args_test = list(), test_intercept = FALSE, check_contrasts = afex_options("check_contrasts"), expand_re = FALSE, all_fit = FALSE, set_data_arg = afex_options("set_data_arg"), progress = TRUE, cl = NULL, return = "mixed", sig_symbols = afex_options("sig_symbols"), ... ) lmer_alt(formula, data, check_contrasts = FALSE, ...) } \arguments{ \item{formula}{a formula describing the full mixed-model to be fitted. As this formula is passed to \code{lmer}, it needs at least one random term.} \item{data}{\code{data.frame} containing the data. Should have all the variables present in \code{fixed}, \code{random}, and \code{dv} as columns.} \item{type}{type of test on which effects are based. Default is to use type 3 tests, taken from \code{\link{afex_options}}.} \item{method}{character vector indicating which methods for obtaining p-values should be used: \code{"KR"} corresponds to the Kenward-Roger approximation for degrees of freedom (only LMMs), \code{"S"} corresponds to the Satterthwaite approximation for degrees of freedom (via \code{\link{lmerTest}}, only LMMs), \code{"PB"} calculates p-values based on parametric bootstrap, \code{"LRT"} calculates p-values via the likelihood ratio tests implemented in the \code{anova} method for \code{merMod} objects (only recommended for models with many [i.e., > 50] levels for the random factors). The default (currently \code{"KR"}) is taken from \code{\link{afex_options}}. For historical compatibility \code{"nested-KR"} is also supported which was the default KR-method in previous versions.} \item{per_parameter}{\code{character} vector specifying for which variable tests should be run for each parameter (instead for the overall effect). Can be useful e.g., for testing ordered factors. Uses \code{\link{grep}} for selecting parameters among the fixed effects so regular expressions (\code{\link{regex}}) are possible. See Examples.} \item{args_test}{\code{list} of arguments passed to the function calculating the p-values. See Details.} \item{test_intercept}{logical. Whether or not the intercept should also be fitted and tested for significance. Default is \code{FALSE}. Only relevant if \code{type = 3}.} \item{check_contrasts}{\code{logical}. Should contrasts be checked and (if necessary) changed to \code{"contr.sum"}? See Details. The default (\code{"TRUE"}) is taken from \code{\link{afex_options}}.} \item{expand_re}{logical. Should random effects terms be expanded (i.e., factors transformed into numerical variables) before fitting with \code{(g)lmer}? Allows to use "||" notation with factors.} \item{all_fit}{logical. Should \code{\link{all_fit}} be used to fit each model with each available optimization algorithm and the results that provided the best fit in each case be used? Warning: This can dramatically increase the optimization time. Adds two new attributes to the returned object designating which algorithm was selected and the log-likelihoods for each algorithm. Note that only warnings from the initial fit are emitted during fitting. The warnings of the chosen models are emitted when printing the returned object.} \item{set_data_arg}{\code{logical}. Should the data argument in the slot \code{call} of the \code{merMod} object returned from \code{lmer} be set to the passed data argument? If \code{FALSE} (currently the default) the name will be \code{data}. \code{TRUE} may be helpful when fitted objects are used afterwards (e.g., compared using \code{anova} or when using the \code{effects} package, see examples). \pkg{emmeans} functions appear to work better with \code{FALSE}. Default is given by afex_options("set_data_arg").} \item{progress}{if \code{TRUE}, shows progress with a text progress bar and other status messages during estimation} \item{cl}{A vector identifying a cluster; used for distributing the estimation of the different models using several cores (if seveal models are calculated). See examples. If \code{ckeck_contrasts = TRUE}, mixed sets the current contrasts (\code{getOption("contrasts")}) at the nodes. Note this does \emph{not} distribute calculation of p-values (e.g., when using \code{method = "PB"}) across the cluster. Use \code{args_test} for this.} \item{return}{the default is to return an object of class \code{"mixed"}. \code{return = "merMod"} will skip the calculation of all submodels and p-values and simply return the full model estimated with \code{lmer} (note that somewhat unintuiviely, the returned object can either be of class \code{"lmerModLmerTest"} or of class \code{"merMod"}, depending on the value of \code{\link{afex_options}}\code{("lmer_function")}). Can be useful in combination with \code{expand_re = TRUE} which allows to use "||" with factors. \code{return = "data"} will not fit any models but just return the data that would have been used for estimating the model (note that the data is also part of the returned object).} \item{sig_symbols}{Character. What should be the symbols designating significance? When entering an vector with \code{length(sig.symbol) < 4} only those elements of the default (\code{c(" +", " *", " **", " ***")}) will be replaced. \code{sig_symbols = ""} will display the stars but not the \code{+}, \code{sig_symbols = rep("", 4)} will display no symbols. The default is given by \code{afex_options("sig_symbols")}.} \item{...}{further arguments (such as \code{weights}, \code{family}, or \code{control}) passed to \code{\link{lmer}}/\code{\link{glmer}}. Note that additional data (e.g., \code{weights}) need to be passed fully and not only by name (e.g., \code{weights = df$weights} and not \code{weights = weights}).} } \value{ An object of class \code{"mixed"} (i.e., a list) with the following elements: \enumerate{ \item \code{anova_table} a data.frame containing the statistics returned from \code{\link[pbkrtest]{KRmodcomp}}. The \code{stat} column in this data.frame gives the value of the test statistic, an F-value for \code{method = "KR"} and a chi-square value for the other two methods. \item \code{full_model} the \code{"lmerModLmerTest"} or \code{"merMod"} object returned from estimating the full model. Use \code{\link{afex_options}}\code{("lmer_function")} for setting which function for estimation should be used. The possible options are \code{"lmerTest"} (the default returning an object of class \code{"lmerModLmerTest"}) and \code{"lme4"} returning an object of class (\code{"merMod"}). Note that in case a \code{family} argument is present an object of class \code{"glmerMod"} is always returned. \item \code{restricted_models} a list of \code{"g/lmerMod"} (or \code{"lmerModLmerTest"}) objects from estimating the restricted models (i.e., each model lacks the corresponding effect) \item \code{tests} a list of objects returned by the function for obtaining the p-values. \item \code{data} The data used for estimation (i.e., after excluding missing rows and applying expand_re if requested). \item \code{call} The matched call. } It also has the following attributes, \code{"type"} and \code{"method"}. And the attributes \code{"all_fit_selected"} and \code{"all_fit_logLik"} if \code{all_fit=TRUE}. Two similar methods exist for objects of class \code{"mixed"}: \code{print} and \code{anova}. They print a nice version of the \code{anova_table} element of the returned object (which is also invisibly returned). This methods omit some columns and nicely round the other columns. The following columns are always printed: \enumerate{ \item \code{Effect} name of effect \item \code{p.value} estimated p-value for the effect } For LMMs with \code{method="KR"} or \code{method="S"} the following further columns are returned (note: the Kenward-Roger correction does two separate things: (1) it computes an effective number for the denominator df; (2) it scales the statistic by a calculated amount, see also \url{http://stackoverflow.com/a/25612960/289572}): \enumerate{ \item \code{F} computed F statistic \item \code{ndf} numerator degrees of freedom (number of parameters used for the effect) \item \code{ddf} denominator degrees of freedom (effective residual degrees of freedom for testing the effect), computed from the Kenward-Roger correction using \code{pbkrtest::KRmodcomp} \item \code{F.scaling} scaling of F-statistic computing from Kenward-Roger approximation (only printed if \code{method="nested-KR"}) } For models with \code{method="LRT"} the following further columns are returned: \enumerate{ \item \code{df.large} degrees of freedom (i.e., estimated paramaters) for full model (i.e., model containing the corresponding effect) \item \code{df.small} degrees of freedom (i.e., estimated paramaters) for restricted model (i.e., model without the corresponding effect) \item \code{chisq} 2 times the difference in likelihood (obtained with \code{logLik}) between full and restricted model \item \code{df} difference in degrees of freedom between full and restricted model (p-value is based on these df). } For models with \code{method="PB"} the following further column is returned: \enumerate{ \item \code{stat} 2 times the difference in likelihood (obtained with \code{logLik}) between full and restricted model (i.e., a chi-square value). } Note that \code{anova} can also be called with additional mixed and/or \code{merMod} objects. In this casethe full models are passed on to \code{anova.merMod} (with \code{refit=FALSE}, which differs from the default of \code{anova.merMod}) which produces the known LRT tables. The \code{summary} method for objects of class \code{mixed} simply calls \code{\link{summary.merMod}} on the full model. If \code{return = "merMod"} (or when invoking \code{lmer_alt}), an object of class \code{"lmerModLmerTest"} or of class \code{"merMod"} (depending on the value of \code{\link{afex_options}}\code{("lmer_function")}), as returned from \code{g/lmer}, is returned. The default behavior is to return an object of class \code{"lmerModLmerTest"} estimated via \code{\link[lmerTest]{lmer}}. } \description{ Estimates mixed models with \pkg{lme4} and calculates p-values for all fixed effects. The default method \code{"KR"} (= Kenward-Roger) as well as \code{method="S"} (Satterthwaite) support LMMs and estimate the model with \code{\link[lmerTest]{lmer}} and then pass it to the \code{\link[lmerTest]{lmerTest}} \code{anova} method (or \code{\link[car]{Anova}}). The other methods (\code{"LRT"} = likelihood-ratio tests and \code{"PB"} = parametric bootstrap) support both LMMs (estimated via \code{\link[lme4]{lmer}}) and GLMMs (i.e., with \code{family} argument which invokes estimation via \code{\link[lme4]{glmer}}) and estimate a full model and restricted models in which the parameters corresponding to one effect (i.e., model term) are withhold (i.e., fixed to 0). Per default tests are based on Type 3 sums of squares. \code{print}, \code{nice}, \code{anova}, and \code{summary} methods for the returned object of class \code{"mixed"} are available. \code{summary} invokes the default \pkg{lme4} summary method and shows parameters instead of effects. \code{lmer_alt} is simply a wrapper for mixed that only returns the \code{"lmerModLmerTest"} or \code{"merMod"} object and correctly uses the \code{||} notation for removing correlations among factors. This function otherwise behaves like \code{g/lmer} (as for \code{mixed}, it calls \code{glmer} as soon as a \code{family} argument is present). Use \code{\link{afex_options}}\code{("lmer_function")} to set which function for estimation should be used. This option determines the class of the returned object (i.e., \code{"lmerModLmerTest"} or \code{"merMod"}). } \details{ For an introduction to mixed-modeling for experimental designs see our chapter (\href{http://singmann.org/download/publications/singmann_kellen-introduction-mixed-models.pdf}{Singmann & Kellen, in press}) or Barr, Levy, Scheepers, & Tily (2013). Arguments for using the Kenward-Roger approximation for obtaining p-values are given by Judd, Westfall, and Kenny (2012). Further introductions to mixed-modeling for experimental designs are given by Baayen and colleagues (Baayen, 2008; Baayen, Davidson & Bates, 2008; Baayen & Milin, 2010). Specific recommendations on which random effects structure to specify for confirmatory tests can be found in Barr and colleagues (2013) and Barr (2013), but also see Bates et al. (2015). \subsection{p-value Calculations}{ When \code{method = "KR"} (the default, implemented via \code{\link[pbkrtest]{KRmodcomp}}), the Kenward-Roger approximation for degrees-of-freedom is calculated using \code{\link[lmerTest]{lmerTest}} (if \code{test_intercept=FALSE}) or \code{\link[car]{Anova}} (if \code{test_intercept=TRUE}), which is only applicable to linear-mixed models (LMMs). The test statistic in the output is an F-value (\code{F}). A similar method that requires less RAM is \code{method = "S"} which calculates the Satterthwaite approximation for degrees-of-freedom via \code{\link[lmerTest]{lmerTest}} and is also only applicable to LMMs. \code{method = "KR"} or \code{method = "S"} provide the best control for Type 1 errors for LMMs (Luke, 2017). \code{method = "PB"} calculates p-values using parametric bootstrap using \code{\link[pbkrtest]{PBmodcomp}}. This can be used for linear and also generalized linear mixed models (GLMMs) by specifying a \code{\link[stats]{family}} argument to \code{mixed}. Note that you should specify further arguments to \code{PBmodcomp} via \code{args_test}, especially \code{nsim} (the number of simulations to form the reference distribution) or \code{cl} (for using multiple cores). For other arguments see \code{\link[pbkrtest]{PBmodcomp}}. Note that \code{REML} (argument to \code{[g]lmer}) will be set to \code{FALSE} if method is \code{PB}. \code{method = "LRT"} calculates p-values via likelihood ratio tests implemented in the \code{anova} method for \code{"merMod"} objects. This is the method recommended by Barr et al. (2013; which did not test the other methods implemented here). Using likelihood ratio tests is only recommended for models with many levels for the random effects (> 50), but can be pretty helpful in case the other methods fail (due to memory and/or time limitations). The \href{http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html}{lme4 faq} also recommends the other methods over likelihood ratio tests. } \subsection{Implementation Details}{ For methods \code{"KR"} and \code{"S"} type 3 and 2 tests are implemented as in \code{\link[car]{Anova}}. For all other methods, type 3 tests are obtained by comparing a model in which only the tested effect is excluded with the full model (containing all effects). For method \code{"nested-KR"} (which was the default in previous versions) this corresponds to the (type 3) Wald tests given by \code{car::Anova} for \code{"lmerMod"} models. The submodels in which the tested effect is excluded are obtained by manually creating a model matrix which is then fitted in \code{"lme4"}. Type 2 tests are truly sequential. They are obtained by comparing a model in which the tested effect and all higher oder effect (e.g., all three-way interactions for testing a two-way interaction) are excluded with a model in which only effects up to the order of the tested effect are present and all higher order effects absent. In other words, there are multiple full models, one for each order of effects. Consequently, the results for lower order effects are identical of whether or not higher order effects are part of the model or not. This latter feature is not consistent with classical ANOVA type 2 tests but a consequence of the sequential tests (and \href{https://stat.ethz.ch/pipermail/r-sig-mixed-models/2012q3/018992.html}{I didn't find a better way} of implementing the Type 2 tests). This \strong{does not} correspond to the (type 2) Wald test reported by \code{car::Anova}. If \code{check_contrasts = TRUE}, contrasts will be set to \code{"contr.sum"} for all factors in the formula if default contrasts are not equal to \code{"contr.sum"} or \code{attrib(factor, "contrasts") != "contr.sum"}. Furthermore, the current contrasts (obtained via \code{getOption("contrasts")}) will be set at the cluster nodes if \code{cl} is not \code{NULL}. } \subsection{Expand Random Effects}{ \code{expand_re = TRUE} allows to expand the random effects structure before passing it to \code{lmer}. This allows to disable estimation of correlation among random effects for random effects term containing factors using the \code{||} notation which may aid in achieving model convergence (see Bates et al., 2015). This is achieved by first creating a model matrix for each random effects term individually, rename and append the so created columns to the data that will be fitted, replace the actual random effects term with the so created variables (concatenated with +), and then fit the model. The variables are renamed by prepending all variables with rei (where i is the number of the random effects term) and replacing ":" with "_by_". \code{lmer_alt} is simply a wrapper for \code{mixed} that is intended to behave like \code{lmer} (or \code{glmer} if a \code{family} argument is present), but also allows the use of \code{||} with factors (by always using \code{expand_re = TRUE}). This means that \code{lmer_alt} per default does not enforce a specific contrast on factors and only returns the \code{"lmerModLmerTest"} or \code{"merMod"} object without calculating any additional models or p-values (this is achieved by setting \code{return = "merMod"}). Note that it most likely differs from \code{g/lmer} in how it handles missing values so it is recommended to only pass data without missing values to it! One consequence of using \code{expand_re = TRUE} is that the data that is fitted will not be the same as the passed data.frame which can lead to problems with e.g., the \code{predict} method. However, the actual data used for fitting is also returned as part of the \code{mixed} object so can be used from there. Note that the \code{set_data_arg} can be used to change whether the \code{data} argument in the call to \code{g/lmer} is set to \code{data} (the default) or the name of the data argument passed by the user. } } \note{ When \code{method = "KR"}, obtaining p-values is known to crash due too insufficient memory or other computational limitations (especially with complex random effects structures). In these cases, the other methods should be used. The RAM demand is a problem especially on 32 bit Windows which only supports up to 2 or 3GB RAM (see \href{https://CRAN.R-project.org/bin/windows/base/rw-FAQ.html}{R Windows FAQ}). Then it is probably a good idea to use methods "S", "LRT", or "PB". \code{"mixed"} will throw a message if numerical variables are not centered on 0, as main effects (of other variables then the numeric one) can be hard to interpret if numerical variables appear in interactions. See Dalal & Zickar (2012). Per default \code{mixed} uses \code{\link[lmerTest]{lmer}}, this can be changed to \code{\link[lme4]{lmer}} by calling: \code{afex_options(lmer_function = "lme4")} Formulas longer than 500 characters will most likely fail due to the use of \code{\link{deparse}}. Please report bugs or unexpected behavior by opening a guthub issue: \url{https://github.com/singmann/afex/issues} } \examples{ ################################## ## Simple Examples (from MEMSS) ## ################################## data("Machines", package = "MEMSS") # simple model with random-slopes for repeated-measures factor m1 <- mixed(score ~ Machine + (Machine|Worker), data=Machines) m1 # suppress correlation among random effect parameters with expand_re = TRUE m2 <- mixed(score ~ Machine + (Machine||Worker), data=Machines, expand_re = TRUE) m2 ## compare: summary(m1)$varcor summary(m2)$varcor # for wrong solution see: # summary(lmer(score ~ Machine + (Machine||Worker), data=Machines))$varcor # follow-up tests library("emmeans") # package emmeans needs to be attached for follow-up tests. (emm1 <- emmeans(m1, "Machine")) pairs(emm1, adjust = "holm") # all pairwise comparisons con1 <- list( c1 = c(1, -0.5, -0.5), # 1 versus other 2 c2 = c(0.5, -1, 0.5) # 1 and 3 versus 2 ) contrast(emm1, con1, adjust = "holm") # plotting emmip(m1, ~Machine, CIs = TRUE) emmip(m2, ~Machine, CIs = TRUE) \dontrun{ ####################### ### Further Options ### ####################### ## Multicore: require(parallel) (nc <- detectCores()) # number of cores cl <- makeCluster(rep("localhost", nc)) # make cluster # to keep track of what the function is doindg redirect output to outfile: # cl <- makeCluster(rep("localhost", nc), outfile = "cl.log.txt") data("Machines", package = "MEMSS") ## There are two ways to use multicore: # 1. Obtain fits with multicore: mixed(score ~ Machine + (Machine|Worker), data=Machines, cl = cl) # 2. Obtain PB samples via multicore: mixed(score ~ Machine + (Machine|Worker), data=Machines, method = "PB", args_test = list(nsim = 50, cl = cl)) # better use 500 or 1000 ## Both ways can be combined: # 2. Obtain PB samples via multicore: mixed(score ~ Machine + (Machine|Worker), data=Machines, cl = cl, method = "PB", args_test = list(nsim = 50, cl = cl)) #### use all_fit = TRUE and expand_re = TRUE: data("sk2011.2") # data described in more detail below sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) require(optimx) # uses two more algorithms sk2_aff_b <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE) attr(sk2_aff_b, "all_fit_selected") attr(sk2_aff_b, "all_fit_logLik") # considerably faster with multicore: clusterEvalQ(cl, library(optimx)) # need to load optimx in cluster sk2_aff_b2 <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE, cl=cl) attr(sk2_aff_b2, "all_fit_selected") attr(sk2_aff_b2, "all_fit_logLik") stopCluster(cl) } ################################################### ## Replicating Maxwell & Delaney (2004) Examples ## ################################################### \dontrun{ ### replicate results from Table 15.4 (Maxwell & Delaney, 2004, p. 789) data(md_15.1) # random intercept plus random slope (t15.4a <- mixed(iq ~ timecat + (1+time|id),data=md_15.1)) # to also replicate exact parameters use treatment.contrasts and the last level as base level: contrasts(md_15.1$timecat) <- contr.treatment(4, base = 4) (t15.4b <- mixed(iq ~ timecat + (1+time|id),data=md_15.1, check_contrasts=FALSE)) summary(t15.4a) # gives "wrong" parameters extimates summary(t15.4b) # identical parameters estimates # for more examples from chapter 15 see ?md_15.1 ### replicate results from Table 16.3 (Maxwell & Delaney, 2004, p. 837) data(md_16.1) # original results need treatment contrasts: (mixed1_orig <- mixed(severity ~ sex + (1|id), md_16.1, check_contrasts=FALSE)) summary(mixed1_orig$full_model) # p-value stays the same with afex default contrasts (contr.sum), # but estimates and t-values for the fixed effects parameters change. (mixed1 <- mixed(severity ~ sex + (1|id), md_16.1)) summary(mixed1$full_model) # data for next examples (Maxwell & Delaney, Table 16.4) data(md_16.4) str(md_16.4) ### replicate results from Table 16.6 (Maxwell & Delaney, 2004, p. 845) # Note that (1|room:cond) is needed because room is nested within cond. # p-value (almost) holds. (mixed2 <- mixed(induct ~ cond + (1|room:cond), md_16.4)) # (differences are dut to the use of Kenward-Roger approximation here, # whereas M&W's p-values are based on uncorrected df.) # again, to obtain identical parameter and t-values, use treatment contrasts: summary(mixed2) # not identical # prepare new data.frame with contrasts: md_16.4b <- within(md_16.4, cond <- C(cond, contr.treatment, base = 2)) str(md_16.4b) # p-value stays identical: (mixed2_orig <- mixed(induct ~ cond + (1|room:cond), md_16.4b, check_contrasts=FALSE)) summary(mixed2_orig$full_model) # replicates parameters ### replicate results from Table 16.7 (Maxwell & Delaney, 2004, p. 851) # F-values (almost) hold, p-values (especially for skill) are off (mixed3 <- mixed(induct ~ cond + skill + (1|room:cond), md_16.4)) # however, parameters are perfectly recovered when using the original contrasts: mixed3_orig <- mixed(induct ~ cond + skill + (1|room:cond), md_16.4b, check_contrasts=FALSE) summary(mixed3_orig) ### replicate results from Table 16.10 (Maxwell & Delaney, 2004, p. 862) # for this we need to center cog: md_16.4b$cog <- scale(md_16.4b$cog, scale=FALSE) # F-values and p-values are relatively off: (mixed4 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b)) # contrast has a relatively important influence on cog (mixed4_orig <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, check_contrasts=FALSE)) # parameters are again almost perfectly recovered: summary(mixed4_orig) } ########################### ## Full Analysis Example ## ########################### \dontrun{ ### split-plot experiment (Singmann & Klauer, 2011, Exp. 2) ## between-factor: instruction ## within-factor: inference & type ## hypothesis: three-way interaction data("sk2011.2") # use only affirmation problems (S&K also splitted the data like this) sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) # set up model with maximal by-participant random slopes sk_m1 <- mixed(response ~ instruction*inference*type+(inference*type|id), sk2_aff) sk_m1 # prints ANOVA table with nicely rounded numbers (i.e., as characters) nice(sk_m1) # returns the same but without printing potential warnings anova(sk_m1) # returns and prints numeric ANOVA table (i.e., not-rounded) summary(sk_m1) # lmer summary of full model # same model but using Satterthwaite approximation of df # very similar results but faster sk_m1b <- mixed(response ~ instruction*inference*type+(inference*type|id), sk2_aff, method="S") nice(sk_m1b) # identical results as: anova(sk_m1$full_model) # suppressing correlation among random slopes: # very similar results, but significantly faster and often less convergence warnings. sk_m2 <- mixed(response ~ instruction*inference*type+(inference*type||id), sk2_aff, expand_re = TRUE) sk_m2 ## mixed objects can be passed to emmeans library("emmeans") # however, package emmeans needs to be attached first # recreates basically Figure 4 (S&K, 2011, upper panel) # only the 4th and 6th x-axis position are flipped emmip(sk_m1, instruction~type+inference) # use lattice instead of ggplot2: emm_options(graphics.engine = "lattice") emmip(sk_m1, instruction~type+inference) emm_options(graphics.engine = "ggplot") # reset options # set up reference grid for custom contrasts: # this can be made faster via: emm_options(lmer.df = "Kenward-Roger") # set df for emmeans to KR # emm_options(lmer.df = "Satterthwaite") # the default # emm_options(lmer.df = "asymptotic") # the fastest, no df (rg1 <- emmeans(sk_m1, c("instruction", "type", "inference"))) # set up contrasts on reference grid: contr_sk2 <- list( ded_validity_effect = c(rep(0, 4), 1, rep(0, 5), -1, 0), ind_validity_effect = c(rep(0, 5), 1, rep(0, 5), -1), counter_MP = c(rep(0, 4), 1, -1, rep(0, 6)), counter_AC = c(rep(0, 10), 1, -1) ) # test the main double dissociation (see S&K, p. 268) contrast(rg1, contr_sk2, adjust = "holm") # only plausibility effect is not significant here. } #################### ## Other Examples ## #################### \dontrun{ # use the obk.long data (not reasonable, no random slopes) data(obk.long) mixed(value ~ treatment * phase + (1|id), obk.long) # Examples for using the per.parameter argument # note, require method = "nested-KR", "LRT", or "PB" # also we use custom contrasts data(obk.long, package = "afex") obk.long$hour <- ordered(obk.long$hour) contrasts(obk.long$phase) <- "contr.sum" contrasts(obk.long$treatment) <- "contr.sum" # tests only the main effect parameters of hour individually per parameter. mixed(value ~ treatment*phase*hour +(1|id), per_parameter = "^hour$", data = obk.long, method = "nested-KR", check_contrasts = FALSE) # tests all parameters including hour individually mixed(value ~ treatment*phase*hour +(1|id), per_parameter = "hour", data = obk.long, method = "nested-KR", check_contrasts = FALSE) # tests all parameters individually mixed(value ~ treatment*phase*hour +(1|id), per_parameter = ".", data = obk.long, method = "nested-KR", check_contrasts = FALSE) # example data from package languageR: # Lexical decision latencies elicited from 21 subjects for 79 English concrete nouns, # with variables linked to subject or word. data(lexdec, package = "languageR") # using the simplest model m1 <- mixed(RT ~ Correct + Trial + PrevType * meanWeight + Frequency + NativeLanguage * Length + (1|Subject) + (1|Word), data = lexdec) m1 # Mixed Model Anova Table (Type 3 tests, KR-method) # # Model: RT ~ Correct + Trial + PrevType * meanWeight + Frequency + NativeLanguage * # Model: Length + (1 | Subject) + (1 | Word) # Data: lexdec # Effect df F p.value # 1 Correct 1, 1627.73 8.15 ** .004 # 2 Trial 1, 1592.43 7.57 ** .006 # 3 PrevType 1, 1605.39 0.17 .68 # 4 meanWeight 1, 75.39 14.85 *** .0002 # 5 Frequency 1, 76.08 56.53 *** <.0001 # 6 NativeLanguage 1, 27.11 0.70 .41 # 7 Length 1, 75.83 8.70 ** .004 # 8 PrevType:meanWeight 1, 1601.18 6.18 * .01 # 9 NativeLanguage:Length 1, 1555.49 14.24 *** .0002 # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1 # Fitting a GLMM using parametric bootstrap: require("mlmRev") # for the data, see ?Contraception gm1 <- mixed(use ~ age + I(age^2) + urban + livch + (1 | district), method = "PB", family = binomial, data = Contraception, args_test = list(nsim = 10)) ## note that nsim = 10 is way too low for all real examples! } \dontrun{ ##################################### ## Interplay with effects packages ## ##################################### data("Machines", package = "MEMSS") # simple model with random-slopes for repeated-measures factor m1 <- mixed(score ~ Machine + (Machine|Worker), data=Machines, set_data_arg = TRUE) ## necessary for it to work! library("effects") Effect("Machine", m1$full_model) # not correct: # Machine effect # Machine # A B C # 59.65000 52.35556 60.32222 # compare: emmeans::emmeans(m1, "Machine") # Machine emmean SE df asymp.LCL asymp.UCL # A 52.35556 1.680711 Inf 49.06142 55.64969 # B 60.32222 3.528546 Inf 53.40640 67.23804 # C 66.27222 1.806273 Inf 62.73199 69.81245 ## necessary to set contr.sum globally: set_sum_contrasts() Effect("Machine", m1$full_model) # Machine effect # Machine # A B C # 52.35556 60.32222 66.27222 plot(Effect("Machine", m1$full_model)) } } \references{ Baayen, R. H. (2008). \emph{Analyzing linguistic data: a practical introduction to statistics using R}. Cambridge, UK; New York: Cambridge University Press. Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. \emph{Journal of Memory and Language}, 59(4), 390-412. doi:10.1016/j.jml.2007.12.005 Baayen, R. H., & Milin, P. (2010). Analyzing Reaction Times. \emph{International Journal of Psychological Research}, 3(2), 12-28. Barr, D. J. (2013). Random effects structure for testing interactions in linear mixed-effects models. \emph{Frontiers in Quantitative Psychology and Measurement}, 328. doi:10.3389/fpsyg.2013.00328 Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. \emph{Journal of Memory and Language}, 68(3), 255-278. doi:10.1016/j.jml.2012.11.001 Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015). \emph{Parsimonious Mixed Models}. arXiv:1506.04967 [stat]. Retrieved from \url{http://arxiv.org/abs/1506.04967} Dalal, D. K., & Zickar, M. J. (2012). Some Common Myths About Centering Predictor Variables in Moderated Multiple Regression and Polynomial Regression. \emph{Organizational Research Methods}, 15(3), 339-362. doi:10.1177/1094428111430540 Judd, C. M., Westfall, J., & Kenny, D. A. (2012). Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem. \emph{Journal of Personality and Social Psychology}, 103(1), 54-69. doi:10.1037/a0028347 Luke, S. (2017). Evaluating significance in linear mixed-effects models in R. \emph{Behavior Research Methods}. \url{https://doi.org/10.3758/s13428-016-0809-y} Maxwell, S. E., & Delaney, H. D. (2004). \emph{Designing experiments and analyzing data: a model-comparisons perspective.} Mahwah, N.J.: Lawrence Erlbaum Associates. } \seealso{ \code{\link{aov_ez}} and \code{\link{aov_car}} for convenience functions to analyze experimental deisgns with classical ANOVA or ANCOVA wrapping \code{\link[car]{Anova}}. see the following for the data sets from Maxwell and Delaney (2004) used and more examples: \code{\link{md_15.1}}, \code{\link{md_16.1}}, and \code{\link{md_16.4}}. } \author{ Henrik Singmann with contributions from \href{http://stackoverflow.com/q/11335923/289572}{Ben Bolker and Joshua Wiley}. } afex/man/sk2011.2.Rd0000644000176200001440000001067413351525342013333 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/sk2011.2-data.R \docType{data} \encoding{UTF-8} \name{sk2011.2} \alias{sk2011.2} \title{Data from Singmann & Klauer (2011, Experiment 2)} \format{A data.frame with 2268 rows and 9 variables.} \source{ Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. Thinking & Reasoning, 17(3), 247-281. doi:10.1080/13546783.2011.572718 } \usage{ sk2011.2 } \description{ Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and type of the problem. Problem type consistent of three levels: prological problems (i.e., problems in which background knowledge suggested to accept valid but reject invalid conclusions), neutral problems (i.e., in which background knowledge suggested to reject all problems), and counterlogical problems (i.e., problems in which background knowledge suggested to reject valid but accept invalid conclusions). } \details{ This data set contains 63 participants in contrast to the originally reported 56 participants. The additional participants were not included in the original studies as they did not meet the inclusion criteria (i.e., no students, prior education in logic, or participated in a similar experiment). The IDs of those additional participants are: 7, 8, 9, 12, 17, 24, 30. The excluded participant reported in the paper has ID 16. content has the following levels (C = content/conditional):\cr 1 = Wenn eine Person in ein Schwimmbecken gefallen ist, dann ist sie nass.\cr 2 = Wenn ein Hund Flöhe hat, dann kratzt er sich hin und wieder.\cr 3 = Wenn eine Seifenblase mit einer Nadel gestochen wurde, dann platzt sie.\cr 4 = Wenn ein Mädchen Geschlechtsverkehr vollzogen hat, dann ist es schwanger.\cr 5 = Wenn eine Pflanze ausreichend gegossen wird, dann bleibt sie grün.\cr 6 = Wenn sich eine Person die Zähne putzt, dann bekommt sie KEIN Karies.\cr 7 = Wenn eine Person viel Cola trinkt, dann nimmt sie an Gewicht zu.\cr 8 = Wenn eine Person die Klimaanlage angeschaltet hat, dann fröstelt sie.\cr 9 = Wenn eine Person viel lernt, dann wird sie in der Klausur eine gute Note erhalten. } \examples{ data("sk2011.2") ## remove excluded participants: sk2_final <- droplevels(sk2011.2[!(sk2011.2$id \%in\% c(7, 8, 9, 12, 16, 17, 24, 30)),]) str(sk2_final) ## Table 2 (inference = problem): aov_ez("id", "response", sk2_final[sk2_final$what == "affirmation",], between = "instruction", within = c("inference", "type"), anova_table=list(es = "pes")) aov_ez("id", "response", sk2_final[sk2_final$what == "denial",], between = "instruction", within = c("inference", "type"), anova_table=list(es = "pes")) # Recreate Figure 4 (corrected version): sk2_aff <- droplevels(sk2_final[sk2_final$what == "affirmation",]) sk2_aff$type2 <- factor(sk2_aff$inference:sk2_aff$type, levels = c("MP:prological", "MP:neutral", "MP:counterlogical", "AC:counterlogical", "AC:neutral", "AC:prological")) a1_b <- aov_ez("id", "response", sk2_aff, between = "instruction", within = c("type2")) sk2_den <- droplevels(sk2_final[sk2_final$what == "denial",]) sk2_den$type2 <- factor(sk2_den$inference:sk2_den$type, levels = c("MT:prological", "MT:neutral", "MT:counterlogical", "DA:counterlogical", "DA:neutral","DA:prological")) a2_b <- aov_ez("id", "response", sk2_den, between = "instruction", within = c("type2")) if (requireNamespace("emmeans")) { emmeans::emmip(a1_b,instruction~type2, ylim = c(0, 100)) emmeans::emmip(a2_b,instruction~type2, ylim = c(0, 100)) } } \keyword{dataset} afex/man/all_fit.Rd0000644000176200001440000000700213607673671013670 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/allFit.R \name{all_fit} \alias{all_fit} \alias{nmkbw} \title{Refit \code{lmer} model using multiple optimizers} \usage{ all_fit( m, meth_tab = cbind(optimizer = rep(c("bobyqa", "Nelder_Mead", "optimx", "nloptwrap", "nmkbw"), c(1, 1, 2, 2, 1)), method = c("", "", "nlminb", "L-BFGS-B", "NLOPT_LN_NELDERMEAD", "NLOPT_LN_BOBYQA", "")), verbose = TRUE, maxfun = 1e+06, ... ) nmkbw(fn, par, lower, upper, control) } \arguments{ \item{m}{a fitted model with \code{lmer}} \item{meth_tab}{a matrix (or data.frame) with columns - method the name of a specific optimization method to pass to the optimizer (leave blank for built-in optimizers) - optimizer the \code{optimizer} function to use} \item{verbose}{print progress messages?} \item{maxfun}{number of iterations to allow for the optimization rountine.} \item{...}{further arguments passed to \code{\link{update.merMod}} such as \code{data}.} \item{fn}{needed for \code{dfoptim::nmkb}} \item{par}{needed for \code{dfoptim::nmkb}} \item{lower}{needed for \code{dfoptim::nmkb}} \item{upper}{needed for \code{dfoptim::nmkb}} \item{control}{needed for \code{dfoptim::nmkb}} } \value{ a list of fitted \code{merMod} objects } \description{ Attempt to re-fit a [g]lmer model with a range of optimizers. The default is to use all known optimizers for R that satisfy the requirements (do not require explicit gradients, allow box constraints), in four categories; (i) built-in (\code{minqa::bobyqa}, \code{lme4::Nelder_Mead}), (ii) wrapped via optimx (most of optimx's optimizers that allow box constraints require an explicit gradient function to be specified; the two provided here are really base R functions that can be accessed via optimx, (iii) wrapped via nloptr, (iv) \code{dfoptim::nmkb}. } \details{ Needs packages \pkg{nloptr}, \pkg{optimx}, and \code{dfoptim} to try out all optimizers. \pkg{optimx} needs to be loaded explicitly using \code{library} or \code{require} (see examples). \code{nmkbw} is a simple wrapper function for fitting models with the corresponding optimizer. It needs to be exported for \code{lme4}, but should not be called directly by the user. } \note{ Very similar to the function of the same name that is part of \pkg{lme4}. The present function will be removed eventually in favor of the \pkg{lme4} function. } \examples{ \dontrun{ # basic usage require(optimx) gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd), data = cbpp, family = binomial) gm_all <- all_fit(gm1) t(sapply(gm_all,fixef)) ## extract fixed effects sapply(gm_all,logLik) ## log-likelihoods sapply(gm_all,getME,"theta") ## theta parameters !sapply(gm_all,inherits,"try-error") ## was fit OK? ## for GLMMs: require("mlmRev") # for data gm1 <- mixed(use ~ age*urban + (1 | district), family = binomial, data = Contraception, method = "LRT") gm_all <- all_fit(gm1$full_model) sapply(gm_all,logLik) ## use allFit in combination with expand.re = TRUE data("sk2011.2") # see example("mixed") sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk_m2 <- mixed(response ~ instruction*inference*type+(inference*type||id), sk2_aff, expand_re = TRUE) sk_m2 sk_m2_allFit <- all_fit(sk_m2$full_model) sk_m2_allFit # all fits fail sk_m2_allFit <- all_fit(sk_m2$full_model, data = sk_m2$data) # works t(sapply(sk_m2_allFit,fixef)) sapply(sk_m2_allFit,logLik) } } \seealso{ slice, slice2D in the bbmle package } \author{ Ben Bolker, minor changes by Henrik Singmann } afex/man/set_sum_contrasts.Rd0000644000176200001440000000152613351525342016025 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/set_contrasts.R \name{set_sum_contrasts} \alias{set_sum_contrasts} \alias{set_deviation_contrasts} \alias{set_effects_contrasts} \alias{set_treatment_contrasts} \alias{set_default_contrasts} \title{Set global contrasts} \usage{ set_sum_contrasts() set_deviation_contrasts() set_effects_contrasts() set_default_contrasts() set_treatment_contrasts() } \value{ nothing. These functions are called for their side effects to change the global options. } \description{ These functions are simple wrappers to set contrasts globally via \code{options(contrasts = ...)}. } \details{ \code{set_deviation_contrasts} and \code{set_effects_contrasts} are wrappers for \code{set_sum_contrasts}. Likewise, \code{set_default_contrasts} is a wrapper to \code{set_treatment_contrasts()}. } afex/man/fhch2010.Rd0000644000176200001440000000702013351525342013454 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/fhch2010-data.R \docType{data} \encoding{UTF-8} \name{fhch2010} \alias{fhch2010} \title{Data from Freeman, Heathcote, Chalmers, & Hockley (2010)} \format{A \code{data.frame} with 13,222 obs. of 9 variables: \describe{ \item{id}{participant id, \code{factor}} \item{task}{\code{factor} with two levels indicating which task was performed: \code{"naming"} or \code{"lexdec"}} \item{stimulus}{\code{factor} indicating whether the shown stimulus was a \code{"word"} or \code{"nonword"}} \item{density}{\code{factor} indicating the neighborhood density of presented items with two levels: \code{"low"} and \code{"high"}. Density is defined as the number of words that differ from a base word by one letter or phoneme.} \item{frequency}{\code{factor} indicating the word frequency of presented items with two levels: \code{"low"} (i.e., words that occur less often in natural language) and \code{"high"} (i.e., words that occur more often in natural language).} \item{length}{\code{factor} with 3 levels (4, 5, or 6) indicating the number of characters of presented stimuli.} \item{item}{\code{factor} with 600 levels: 300 words and 300 nonwords} \item{rt}{response time in seconds} \item{log_rt}{natural logarithm of response time in seconds} \item{correct}{boolean indicating whether or not the response in the lexical decision task was correct or incorrect (incorrect responses of the naming task are not part of the data).} }} \source{ Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. Journal of Memory and Language, 62(1), 1-18. http://doi.org/10.1016/j.jml.2009.09.004 } \usage{ fhch2010 } \description{ Lexical decision and word naming latencies for 300 words and 300 nonwords presented in Freeman, Heathcote, Chalmers, and Hockley (2010). The study had one between-subjects factors, \code{"task"} with two levels (\code{"naming"} or \code{"lexdec"}), and four within-subjects factors: \code{"stimulus"} type with two levels (\code{"word"} or \code{"nonword"}), word \code{"density"} and word \code{"frequency"} each with two levels (\code{"low"} and \code{"high"}) and stimulus \code{"length"} with three levels (4, 5, and 6). } \details{ In the lexical-decision condition (N = 25), subjects indicated whether each item was a word or a nonword, by pressing either the left (labeled word) or right (labeled nonword) outermost button on a 6-button response pad. The next study item appeared immediately after the lexical decision response was given. In the naming condition (N = 20), subjects were asked to name each item aloud, and items remained on screen for 3 s. Naming time was recorded by a voice key. Items consisted of 300 words, 75 in each set making up a factorial combination of high and low density and frequency, and 300 nonwords, with equal numbers of 4, 5, and 6 letter items in each set. } \examples{ data("fhch2010") str(fhch2010) a1 <- aov_ez("id", "log_rt", fhch2010, between = "task", within = c("density", "frequency", "length", "stimulus")) nice(a1) if (requireNamespace("emmeans")) { emmeans::emmip(a1, frequency~length|task+stimulus) emmeans::emmip(a1, frequency~density|task+stimulus) } \dontrun{ a2 <- aov_ez("id", "rt", fhch2010, between = "task", within = c("density", "frequency", "length", "stimulus")) nice(a2) if (requireNamespace("emmeans")) { emmeans::emmip(a2, frequency~length|task+stimulus) emmeans::emmip(a2, frequency~density|task+stimulus) } } } \keyword{dataset} afex/man/afex-package.Rd0000644000176200001440000000216513607673671014577 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/afex-package.R \docType{package} \name{afex-package} \alias{afex} \alias{afex-package} \title{\packageTitle{afex} Maintainer: \packageMaintainer{afex}} \description{ \packageDescription{afex} } \details{ The DESCRIPTION file: \packageDESCRIPTION{afex} } \seealso{ Useful links: \itemize{ \item \url{http://afex.singmann.science/} \item \url{https://github.com/singmann/afex} \item Report bugs at \url{https://github.com/singmann/afex/issues} } } \author{ \strong{Maintainer}: Henrik Singmann \email{singmann+afex@gmail.com} (\href{https://orcid.org/0000-0002-4842-3657}{ORCID}) Authors: \itemize{ \item Ben Bolker \item Jake Westfall \item Frederik Aust (\href{https://orcid.org/0000-0003-4900-788X}{ORCID}) \item Mattan S. Ben-Shachar } Other contributors: \itemize{ \item Søren Højsgaard [contributor] \item John Fox [contributor] \item Michael A. Lawrence [contributor] \item Ulf Mertens [contributor] \item Jonathon Love [contributor] \item Russell Lenth [contributor] \item Rune Haubo Bojesen Christensen [contributor] } } afex/man/md_15.1.Rd0000644000176200001440000000632413351525342013313 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/md_15.1-data.R \docType{data} \encoding{UTF-8} \name{md_15.1} \alias{md_15.1} \title{Data 15.1 / 11.5 from Maxwell & Delaney} \format{A data.frame with 48 rows and 4 variables.} \source{ Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 766 } \usage{ md_15.1 } \description{ Hypothetical IQ Data from 12 children at 4 time points: Example data for chapter 11/15 of Maxwell and Delaney (2004, Table 15.1, p. 766) in long format. Has two one within-subjects factor: time. } \details{ Description from pp. 534: The data show that 12 subjects have been observed in each of 4 conditions. To make the example easier to discuss, let's suppose that the 12 subjects are children who have been observed at 30, 36, 42, and 48 months of age. In each case, the dependent variable is the child's age-normed general cognitive score on the McCarthy Scales of Children's Abilities. Although the test is normed so that the mean score is independent of age for the general population, our 12 children may come from a population in which cognitive abilities are either growing more rapidly or less rapidly than average. Indeed, this is the hypothesis our data allow us to address. In other words, although the sample means suggest that the children's cognitive abilities are growing, a significance test is needed if we want to rule out sampling error as a likely explanation for the observed differences. To replicate the results in chapter 15 several different contrasts need to be applied, see Examples. \code{time} is time in months (centered at 0) and \code{timecat} is the same as a categorical variable. } \examples{ ### replicate results from Table 15.2 to 15.6 (Maxwell & Delaney, 2004, pp. 774) data(md_15.1) ### ANOVA results (Table 15.2) aov_4(iq ~ timecat + (timecat|id),data=md_15.1, anova_table=list(correction = "none")) ### Table 15.3 (random intercept only) # we need to set the base level on the last level: contrasts(md_15.1$timecat) <- contr.treatment(4, base = 4) # "Type 3 Tests of Fixed Effects" (t15.3 <- mixed(iq ~ timecat + (1|id),data=md_15.1, check.contrasts=FALSE)) # "Solution for Fixed Effects" and "Covariance Parameter Estimates" summary(t15.3$full.model) ### make Figure 15.2 plot(NULL, NULL, ylim = c(80, 140), xlim = c(30, 48), ylab = "iq", xlab = "time") plyr::d_ply(md_15.1, plyr::.(id), function(x) lines(as.numeric(as.character(x$timecat)), x$iq)) ### Table 15.4, page 789 # random intercept plus slope (t15.4 <- mixed(iq ~ timecat + (1+time|id),data=md_15.1, check.contrasts=FALSE)) summary(t15.4$full.model) ### Table 15.5, page 795 # set up polynomial contrasts for timecat contrasts(md_15.1$timecat) <- contr.poly # fit all parameters separately (t15.5 <- mixed(iq ~ timecat + (1+time|id), data=md_15.1, check.contrasts=FALSE, per.parameter="timecat")) # quadratic trend is considerably off, conclusions stay the same. ### Table 15.6, page 797 # growth curve model (t15.6 <- mixed(iq ~ time + (1+time|id),data=md_15.1)) summary(t15.6$full.model) } \author{ R code for examples written by Ulf Mertens and Henrik Singmann } \keyword{dataset} afex/man/md_16.4.Rd0000644000176200001440000000501613351525342013314 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/md_16.4-data.R \docType{data} \encoding{UTF-8} \name{md_16.4} \alias{md_16.4} \title{Data 16.4 from Maxwell & Delaney} \format{A data.frame with 24 rows and 3 variables.} \source{ Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 } \usage{ md_16.4 } \description{ Data from a hypothetical inductive reasoning study. } \details{ Description from pp. 841: Suppose an educational psychologist has developed an intervention to teach inductive reasoning skills to school children. She decides to test the efficacy of her intervention by conducting a randomized design. Three classrooms of students are randomly assigned to the treatment condition, and 3 other classrooms are assigned to the control. Table 16.4 shows hypothetical data collected from 29 children who participated in the study assessing the effectiveness of the intervention to increase inductive reasoning skills. We want to call your attention to several aspects of the data. First, the 15 children with condition values of 0 received the control, whereas the 14 children with condition values of 1 received the treatment. Second, 4 of the children in the control condition were students in control Classroom 1, 6 of them were students in control Classroom 2, and 5 were students in control Classroom 3. Along similar lines, 3 of the children in the treatment condition were students in treatment Classroom 1, 5 were students in treatment Classroom 2, and 6 were students in treatment Classroom 3. It is essential to understand that there are a total of six classrooms here; we have coded classroom from 1 to 3 for control as well as treatment, because we will indicate to PROC MIXED that classroom is nested under treatment. Third, scores on the dependent variable appear in the rightmost column under the variable label "induct." Note that it would make a lot more sense to change the labeling of room from 1 to 3 nested within cond to 1 to 6. However, I keep this in line with the original. The random effects term in the call to mixed is therefore a little bit uncommon.#' } \examples{ # data for next examples (Maxwell & Delaney, Table 16.4) data(md_16.4) str(md_16.4) ### replicate results from Table 16.6 (Maxwell & Delaney, 2004, p. 845) # p-values (almost) hold: (mixed2 <- mixed(induct ~ cond + (1|room:cond), md_16.4)) # (1|room:cond) is needed because room is nested within cond. } \keyword{dataset} afex/man/test_assumptions.Rd0000644000176200001440000000270413506224623015671 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/test_assumption.R \name{test_levene} \alias{test_levene} \alias{test_sphericity} \title{Assumption Tests for ANOVAs} \usage{ test_levene(afex_aov, center = mean, ...) test_sphericity(afex_aov) } \arguments{ \item{afex_aov}{\code{afex_aov} object.} \item{center}{Function to compute the center of each group; \code{mean} (the default) gives the original Levene's test.} \item{...}{passed to \code{\link[car]{leveneTest}}} } \description{ \code{test_levene} computes Levene's test for homogeneity of variances across groups via \code{car::leveneTest}. \code{test_sphericity} computes Mauchly test of sphericity via \code{car::Anova}. } \examples{ ### Setup ANOVAs data(obk.long, package = "afex") between_1 <- aov_car(value ~ treatment + Error(id), data = obk.long) between_2 <- aov_car(value ~ treatment*gender + Error(id), data = obk.long) mixed <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long) within <- aov_car(value ~ 1 + Error(id/(phase*hour)), data = obk.long) ### Levene Test for Homogeneity of Variances test_levene(between_1) test_levene(between_2) test_levene(mixed) \dontrun{ test_levene(within) ## fails } ### Mauchly Test of Sphericity \dontrun{ ## fails for between-subjects only models: test_sphericity(between_1) test_sphericity(between_2) } test_sphericity(mixed) test_sphericity(within) } \author{ Mattan S. Ben-Shachar and Henrik Singmann } afex/man/afex_aov-methods.Rd0000644000176200001440000001266513607673671015522 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/methods.afex_aov.R \name{afex_aov-methods} \alias{afex_aov-methods} \alias{anova.afex_aov} \alias{print.afex_aov} \alias{summary.afex_aov} \alias{recover_data.afex_aov} \alias{emm_basis.afex_aov} \title{Methods for afex_aov objects} \usage{ \method{anova}{afex_aov}( object, es = afex_options("es_aov"), observed = NULL, correction = afex_options("correction_aov"), MSE = TRUE, intercept = FALSE, p_adjust_method = NULL, sig_symbols = attr(object$anova_table, "sig_symbols"), ... ) \method{print}{afex_aov}(x, ...) \method{summary}{afex_aov}(object, ...) recover_data.afex_aov(object, ..., model = afex_options("emmeans_model")) emm_basis.afex_aov( object, trms, xlev, grid, ..., model = afex_options("emmeans_model") ) } \arguments{ \item{object, x}{object of class \code{afex_aov} as returned from \code{\link{aov_car}} and related functions.} \item{es}{Effect Size to be reported. The default is given by \code{afex_options("es_aov")}, which is initially set to \code{"ges"} (i.e., reporting generalized eta-squared, see details). Also supported is partial eta-squared (\code{"pes"}) or \code{"none"}.} \item{observed}{character vector referring to the observed (i.e., non manipulated) variables/effects in the design. Important for calculation of generalized eta-squared (ignored if \code{es} is not \code{"ges"}), see details.} \item{correction}{Character. Which sphericity correction of the degrees of freedom should be reported for the within-subject factors. The default is given by \code{afex_options("correction_aov")}, which is initially set to \code{"GG"} corresponding to the Greenhouse-Geisser correction. Possible values are \code{"GG"}, \code{"HF"} (i.e., Hyunh-Feldt correction), and \code{"none"} (i.e., no correction).} \item{MSE}{logical. Should the column containing the Mean Sqaured Error (MSE) be displayed? Default is \code{TRUE}.} \item{intercept}{logical. Should intercept (if present) be included in the ANOVA table? Default is \code{FALSE} which hides the intercept.} \item{p_adjust_method}{\code{character} indicating if p-values for individual effects should be adjusted for multiple comparisons (see \link[stats]{p.adjust} and details).} \item{sig_symbols}{Character. What should be the symbols designating significance? When entering an vector with \code{length(sig.symbol) < 4} only those elements of the default (\code{c(" +", " *", " **", " ***")}) will be replaced. \code{sig_symbols = ""} will display the stars but not the \code{+}, \code{sig_symbols = rep("", 4)} will display no symbols. The default is given by \code{afex_options("sig_symbols")}.} \item{...}{further arguments passed through, see description of return value for details.} \item{model}{argument for \code{\link[emmeans]{emmeans}()} and rlated functions that allows to choose on which model the follow-up tests for ANOVAs with repeated-measures factors are based. \code{"univariate"} uses the \code{aov} model and \code{"multivariate"} uses the \code{lm} model. Default given by \code{afex_options("emmeans_mode")}. Multivariate tests likely provide a better correction for violations of sphericity.} \item{trms, xlev, grid}{same as for \code{\link[emmeans]{emm_basis}}.} } \value{ \describe{ \item{\code{anova}}{Returns an ANOVA table of class \code{c("anova", "data.frame")}. Information such as effect size (\code{es}) or df-correction are calculated each time this method is called.} \item{\code{summary}}{For ANOVAs containing within-subject factors it returns the full output of the within-subject tests: the uncorrected results, results containing Greenhousse-Geisser and Hyunh-Feldt correction, and the results of the Mauchly test of sphericity (all achieved via \code{summary.Anova.mlm}). For other ANOVAs, the \code{anova} table is simply returned.} \item{\code{print}}{Prints (and invisibly returns) the ANOVA table as constructed from \code{\link{nice}} (i.e., as strings rounded nicely). Arguments in \code{...} are passed to \code{nice} allowing to pass arguments such as \code{es} and \code{correction}.} \item{\code{recover_data} and \code{emm_basis}}{Provide the backbone for using \code{\link[emmeans]{emmeans}} and related functions from \pkg{emmeans} directly on \code{afex_aov} objects by returning a \code{\link[emmeans]{emmGrid-class}} object. Should not be called directly but through the functionality provided by \pkg{emmeans}.} } } \description{ Methods defined for objects returned from the ANOVA functions \code{\link{aov_car}} et al. of class \code{afex_aov} containing both the ANOVA fitted via \code{car::Anova} and base R's \code{aov}. } \details{ Exploratory ANOVA, for which no detailed hypotheses have been specified a priori, harbor a multiple comparison problem (Cramer et al., 2015). To avoid an inflation of familywise Type I error rate, results need to be corrected for multiple comparisons using \code{p_adjust_method}. \code{p_adjust_method} defaults to the method specified in the call to \code{\link{aov_car}} in \code{anova_table}. If no method was specified and \code{p_adjust_method = NULL} p-values are not adjusted. } \references{ Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies. \emph{Psychonomic Bulletin & Review}, 1-8. doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} } afex/man/afex_options.Rd0000644000176200001440000000712213506224623014742 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/helpers.R \name{afex_options} \alias{afex_options} \title{Set/get global afex options} \usage{ afex_options(...) } \arguments{ \item{...}{One of four: (1) nothing, then returns all options as a list; (2) a name of an option element, then returns its' value; (3) a name-value pair which sets the corresponding option to the new value (and returns nothing), (4) a list with option-value pairs which sets all the corresponding arguments. The example show all possible cases.} } \value{ depends on input, see above. } \description{ Global afex options are used, for example, by \code{\link{aov_car}} (et al.) and \code{\link{mixed}}. But can be changed in each functions directly using an argument (which has precedence over the global options). } \details{ The following arguments are currently set: \itemize{ \item \code{check_contrasts} should contrasts be checked and changed to sum-to-zero contrasts? Default is \code{TRUE}. \item \code{type} type of sums-of-squares to be used for testing effects, default is 3 which reports Type 3 tests. \item \code{method_mixed}: Method used to obtain p-values in \code{\link{mixed}}, default is \code{"KR"} (which will change to \code{"LRT"} soon). (\code{mixed()} only) \item \code{es_aov}: Effect size reported for ANOVAs (see \code{\link{aov_car}}), default is \code{"ges"} (generalized eta-squared). \item \code{correction_aov}: Correction used for within-subjects factors with more than two levels for ANOVAs (see \code{\link{aov_car}} or \code{\link{nice}}), default is \code{"GG"} (Greenhouse-Geisser correction). (ANOVA functions only) \item \code{emmeans_model}: Which model should be used by \pkg{emmeans} for follow-up analysis of ANOVAs (i.e., objects pf class \code{"afex_aov"})? Default is \code{"univariate"} which uses the \code{aov} model object (if present). The other option is \code{"multivariate"} which uses the \code{lm} model object (which is an object of class \code{"mlm"} in case repeated-measures factors are present). \item \code{include_aov}: Should the \code{aov} model be included into ANOVA objects of class \code{"afex_aov"}? Setting this to \code{FALSE} can lead to considerable speed improvements. \item \code{factorize}: Should between subject factors be factorized (with note) before running the analysis? Default is \code{TRUE}. (ANOVA functions only) \item \code{sig_symbols}: Default significant symbols used for ANOVA and \code{mixed} printing. Default is\code{c(" +", " *", " **", " ***")}. \item \code{lmer_function}: Which \code{lmer} function should \code{mixed} or \code{lmer_alt} use. The default is \code{"lmerTest"} which uses \code{\link[lmerTest]{lmer}}, \code{"lme4"} is also possible which uses \code{\link[lme4]{lmer}}. Note that \code{mixed} methods \code{"KR"} and \code{"S"} only work with \code{"lmerTest"}. For the other methods, \code{"lme4"} could be minimally faster, but does not allow to use \code{lmerTest::anova()}. \item \code{return_aov}: Return value of the ANOVA functions (see \code{\link{aov_car}}), default is \code{"nice"}. } } \note{ All options are saved in the global R \code{\link{options}} with prefix \code{afex.} } \examples{ afex_options() # see all options afex_options("return_aov") #get single option aop <- afex_options() # save current options \dontrun{ # change options afex_options(return_aov = "nice") afex_options("return_aov") #get single option afex_options(return_aov = "nice", method_mixed = "LRT") afex_options("method_mixed") #get single option # do something } afex_options(aop) # reset options } afex/man/reexports.Rd0000644000176200001440000000061313351525342014275 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/reexport.R \docType{import} \name{reexports} \alias{reexports} \alias{lmer} \title{Objects exported from other packages} \keyword{internal} \description{ These objects are imported from other packages. Follow the links below to see their documentation. \describe{ \item{lmerTest}{\code{\link[lmerTest]{lmer}}} }} afex/man/ks2013.3.Rd0000644000176200001440000000735513351525342013340 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ks2013.3-data.R \docType{data} \encoding{UTF-8} \name{ks2013.3} \alias{ks2013.3} \title{Data from Klauer & Singmann (2013, Experiment 3)} \format{A data.frame with 1440 rows and 6 variables.} \source{ Klauer, K. C., & Singmann, H. (2013). Does logic feel good? Testing for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39(4), 1265-1273. http://doi.org/10.1037/a0030530 Morsanyi, K., & Handley, S. J. (2012). Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(3), 596-616. http://doi.org/10.1037/a0026099 } \usage{ ks2013.3 } \description{ Klauer and Singmann (2013) attempted to replicate an hypothesis of Morsanyi and Handley (2012) according to which individuals have an intuitive sense of logicality. Specifically, Morsanyi and Handley apparently provided evidence that the logical status of syllogisms (i.e., valid or invalid) affects participants liking ratings of the conclusion of syllogisms. Conclusions from valid syllogisms (e.g., Some snakes are poisonous. No poisonous animals are obbs. Some snakes are not obbs.) received higher liking ratings than conclusions from invalid syllogisms (e.g., No ice creams are vons. Some vons are hot. Some ice creams are not hot.). It is important to noted that in the experiments participants were simply shown the premises and conclusion in succession, they were not asked whether or not the conclusion follows or to generate their own conclusion. Their task was simply to judge how much they liked the "final" statement (i.e., the conclusion). } \details{ In their Experiment 3 Klauer and Singmann (2013) tested the idea that this finding was a consequence of the materials used and not an effect intuitive logic. More specifically, they observed that in the original study by Morsanyi and Handley (2012) a specific content always appeared with the same logical status. For example, the "ice-cream" content only ever appeared as an invalid syllogism as in the example above but never in a valid syllogism. In other words, content was perfectly confounded with logical status in the original study. To test this they compared a condition in which the logical status was confounded with the content (the "fixed" condition) with a condition in which the contents were randomly assigned to a logical status across participants (the "random" condition). For example, the ice-cream content was, across participants, equally like to appear in the invalid form as given above or in the following valid form: No hot things are vons. Some vons are ice creams. Conclusion Some ice creams are not hot. The data.frame contains the raw responses of all 60 participants (30 per condition) reported in Klauer & Singmann (2013). Each participants provided 24 responses, 12 to valid and 12 to invalid syllogisms. Furthermore, 8 syllogisms had a believable conclusion (e.g., Some ice creams are not hot.), 8 had an abstract conclusion (e.g., Some snakes are not obbs.), and 8 had an unbelievable conclusion (e.g., Some animals are not monkeys.). The number of the contents corresponds to the numbering given in Morsanyi and Handley (2012, p. 616). } \examples{ data("ks2013.3") # replicate results reported in Klauer & Singmann (2013, p. 1270) aov_ez("id", "response", ks2013.3, between = "condition", within = c("believability", "validity")) aov_ez("id", "response", subset(ks2013.3, condition == "fixed"), within = c("believability", "validity")) aov_ez("id", "response", subset(ks2013.3, condition == "random"), within = c("believability", "validity")) } \keyword{dataset} afex/man/ems.Rd0000644000176200001440000000533413351525342013033 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ems.R \name{ems} \alias{ems} \title{Expected values of mean squares for factorial designs Implements the Cornfield-Tukey algorithm for deriving the expected values of the mean squares for factorial designs.} \usage{ ems(design, nested = NULL, random = "") } \arguments{ \item{design}{A \code{formula} object specifying the factors in the design (except residual error, which is always implicitly included). The left hand side of the \code{~} is the symbol that will be used to denote the number of replications per lowest-level factor combination (I usually use "r" or "n"). The right hand side should include all fixed and random factors separated by \code{*}. Factor names should be single letters.} \item{nested}{A \code{character} vector, where each element is of the form \code{"A/B"}, indicating that the levels of factor B are nested under the levels of factor A.} \item{random}{A \code{character} string indicating, without spaces or any separating characters, which of the factors specified in the design are random.} } \value{ The returned value is a formatted table where the rows represent the mean squares, the columns represent the variance components that comprise the various mean squares, and the entries in each cell represent the terms that are multiplied and summed to form the expectation of the mean square for that row. Each term is either the lower-case version of one of the experimental factors, which indicates the number of levels for that factor, or a "1", which means the variance component for that column is contributes to the mean square but is not multiplied by anything else. } \description{ Expected values of mean squares for factorial designs Implements the Cornfield-Tukey algorithm for deriving the expected values of the mean squares for factorial designs. } \note{ Names for factors or parameters should only be of length 1 as they are simply concatenated in the returned table. } \examples{ # 2x2 mixed anova # A varies between-subjects, B varies within-subjects ems(r ~ A*B*S, nested="A/S", random="S") # Clark (1973) example # random Subjects, random Words, fixed Treatments ems(r ~ S*W*T, nested="T/W", random="SW") # EMSs for Clark design if Words are fixed ems(r ~ S*W*T, nested="T/W", random="S") } \seealso{ A detailed description with explanation of the example can be found \href{http://www.talkstats.com/showthread.php/18603-Share-your-functions-amp-code?p=82050&viewfull=1\#post82050}{elsewhere} (note that the \code{design} argument of the function described at the link behaves slightly different). Example applications of this function can be found here: \url{http://stats.stackexchange.com/a/122662/442}. } \author{ Jake Westfall } afex/man/nice.Rd0000644000176200001440000001721713607673671013205 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nice.R \encoding{UTF-8} \name{nice} \alias{nice} \alias{nice.afex_aov} \alias{nice.anova} \alias{nice.mixed} \alias{print.nice_table} \title{Make nice ANOVA table for printing.} \usage{ nice(object, ...) \method{nice}{afex_aov}( object, es = attr(object$anova_table, "es"), observed = attr(object$anova_table, "observed"), correction = attr(object$anova_table, "correction"), MSE = NULL, intercept = NULL, p_adjust_method = attr(object$anova_table, "p_adjust_method"), sig_symbols = attr(object$anova_table, "sig_symbols"), ... ) \method{nice}{anova}( object, MSE = NULL, intercept = NULL, sig_symbols = attr(object, "sig_symbols"), sig.symbols, ... ) \method{nice}{mixed}(object, sig_symbols = attr(object$anova_table, "sig_symbols"), ...) \method{print}{nice_table}(x, ...) } \arguments{ \item{object, x}{An object of class \code{"afex_aov"} (see \code{\link{aov_car}}) or of class \code{"mixed"} (see \code{\link{mixed}}) as returned from the \pkg{afex} functions. Alternatively, an object of class \code{"Anova.mlm"} or \code{"anova"} as returned from \code{\link[car]{Anova}}.} \item{...}{currently ignored.} \item{es}{Effect Size to be reported. The default is given by \code{afex_options("es_aov")}, which is initially set to \code{"ges"} (i.e., reporting generalized eta-squared, see details). Also supported is partial eta-squared (\code{"pes"}) or \code{"none"}.} \item{observed}{character vector referring to the observed (i.e., non manipulated) variables/effects in the design. Important for calculation of generalized eta-squared (ignored if \code{es} is not \code{"ges"}), see details.} \item{correction}{Character. Which sphericity correction of the degrees of freedom should be reported for the within-subject factors. The default is given by \code{afex_options("correction_aov")}, which is initially set to \code{"GG"} corresponding to the Greenhouse-Geisser correction. Possible values are \code{"GG"}, \code{"HF"} (i.e., Hyunh-Feldt correction), and \code{"none"} (i.e., no correction).} \item{MSE}{logical. Should the column containing the Mean Sqaured Error (MSE) be displayed? Default is \code{TRUE}.} \item{intercept}{logical. Should intercept (if present) be included in the ANOVA table? Default is \code{FALSE} which hides the intercept.} \item{p_adjust_method}{\code{character} indicating if p-values for individual effects should be adjusted for multiple comparisons (see \link[stats]{p.adjust} and details). The default \code{NULL} corresponds to no adjustment.} \item{sig_symbols}{Character. What should be the symbols designating significance? When entering an vector with \code{length(sig.symbol) < 4} only those elements of the default (\code{c(" +", " *", " **", " ***")}) will be replaced. \code{sig_symbols = ""} will display the stars but not the \code{+}, \code{sig_symbols = rep("", 4)} will display no symbols. The default is given by \code{afex_options("sig_symbols")}.} \item{sig.symbols}{deprecated argument, only for backwards compatibility, use \code{"sig_symbols"} instead.} } \value{ A \code{data.frame} of class \code{nice_table} with the ANOVA table consisting of characters. The columns that are always present are: \code{Effect}, \code{df} (degrees of freedom), \code{F}, and \code{p}. \code{ges} contains the generalized eta-squared effect size measure (Bakeman, 2005), \code{pes} contains partial eta-squared (if requested). } \description{ This generic function produces a nice ANOVA table for printing for objects of class. \code{nice_anova} takes an object from \code{\link[car]{Anova}} possible created by the convenience functions \code{\link{aov_ez}} or \code{\link{aov_car}}. When within-subject factors are present, either sphericity corrected or uncorrected degrees of freedom can be reported. } \details{ The returned \code{data.frame} is print-ready when adding to a document with proper methods. Either directly via \pkg{knitr} or similar approaches such as via package \pkg{xtable} (nowadays \pkg{knitr} is probably the best approach, see \href{http://yihui.name/knitr/}{here}). \pkg{xtable} converts a \code{data.frame} into LaTeX code with many possible options (e.g., allowing for \code{"longtable"} or \code{"sidewaystable"}), see \code{\link[xtable]{xtable}} and \code{\link[xtable]{print.xtable}}. See Examples. Conversion functions to other formats (such as HTML, ODF, or Word) can be found at the \href{https://CRAN.R-project.org/view=ReproducibleResearch}{Reproducible Research Task View}. The default reports generalized eta squared (Olejnik & Algina, 2003), the "recommended effect size for repeated measured designs" (Bakeman, 2005). Note that it is important that all measured variables (as opposed to experimentally manipulated variables), such as e.g., age, gender, weight, ..., must be declared via \code{observed} to obtain the correct effect size estimate. Partial eta squared (\code{"pes"}) does not require this. Exploratory ANOVA, for which no detailed hypotheses have been specified a priori, harbor a multiple comparison problem (Cramer et al., 2015). To avoid an inflation of familywise Type I error rate, results need to be corrected for multiple comparisons using \code{p_adjust_method}. \code{p_adjust_method} defaults to the method specified in the call to \code{\link{aov_car}} in \code{anova_table}. If no method was specified and \code{p_adjust_method = NULL} p-values are not adjusted. } \examples{ ## example from Olejnik & Algina (2003) # "Repeated Measures Design" (pp. 439): data(md_12.1) # create object of class afex_aov: rmd <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) rmd nice(rmd) str(nice(rmd)) # use different es: nice(rmd, es = "pes") # noise: .82 nice(rmd, es = "ges") # noise: .39 # same data other approach: rmd2 <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table=list(correction = "none", es = "none")) nice(rmd2) nice(rmd2, correction = "GG") nice(rmd2, correction = "GG", es = "ges") # exampel using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset from car. data(obk.long) # create object of class afex_aov: tmp.aov <- aov_car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long) nice(tmp.aov, observed = "gender") nice(tmp.aov, observed = "gender", sig_symbols = rep("", 4)) \dontrun{ # use package ascii or xtable for formatting of tables ready for printing. full <- nice(tmp.aov, observed = "gender") require(ascii) print(ascii(full, include.rownames = FALSE, caption = "ANOVA 1"), type = "org") require(xtable) print.xtable(xtable(full, caption = "ANOVA 2"), include.rownames = FALSE) } } \references{ Bakeman, R. (2005). Recommended effect size statistics for repeated measures designs. \emph{Behavior Research Methods}, 37(3), 379-384. doi:10.3758/BF03192707 Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies. \emph{Psychonomic Bulletin & Review}, 1-8. doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} Olejnik, S., & Algina, J. (2003). Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs. \emph{Psychological Methods}, 8(4), 434-447. doi:10.1037/1082-989X.8.4.434 } \seealso{ \code{\link{aov_ez}} and \code{\link{aov_car}} are the convenience functions to create the object appropriate for \code{nice_anova}. } \author{ The code for calculating generalized eta-squared was written by Mike Lawrence.\cr Everything else was written by Henrik Singmann. } afex/man/aov_car.Rd0000644000176200001440000006663113607673671013705 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/aov_car.R \encoding{UTF-8} \name{aov_car} \alias{aov_car} \alias{aov_4} \alias{aov_ez} \title{Convenient ANOVA estimation for factorial designs} \usage{ aov_car( formula, data, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), observed = NULL, anova_table = list(), include_aov = afex_options("include_aov"), return = afex_options("return_aov"), ... ) aov_4( formula, data, observed = NULL, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), anova_table = list(), include_aov = afex_options("include_aov"), ..., print.formula = FALSE ) aov_ez( id, dv, data, between = NULL, within = NULL, covariate = NULL, observed = NULL, fun_aggregate = NULL, transformation, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), anova_table = list(), include_aov = afex_options("include_aov"), ..., print.formula = FALSE ) } \arguments{ \item{formula}{A formula specifying the ANOVA model similar to \code{\link{aov}} (for \code{aov_car} or similar to \code{lme4:lmer} for \code{aov_4}). Should include an error term (i.e., \code{Error(id/...)} for \code{aov_car} or \code{(...|id)} for \code{aov_4}). Note that the within-subject factors do not need to be outside the Error term (this contrasts with \code{aov}). See Details.} \item{data}{A \code{data.frame} containing the data. Mandatory.} \item{fun_aggregate}{The function for aggregating the data before running the ANOVA if there is more than one observation per individual and cell of the design. The default \code{NULL} issues a warning if aggregation is necessary and uses \code{\link{mean}}. Pass \code{mean} directly to avoid the warning.} \item{type}{The type of sums of squares for the ANOVA. The default is given by \code{afex_options("type")}, which is \strong{initially set to 3}. Passed to \code{\link[car]{Anova}}. Possible values are \code{"II"}, \code{"III"}, \code{2}, or \code{3}.} \item{factorize}{logical. Should between subject factors be factorized (with note) before running the analysis. The default is given by \code{afex_options("factorize")}, which is initially \code{TRUE}. If one wants to run an ANCOVA, this needs to be set to \code{FALSE} (in which case centering on 0 is checked on numeric variables).} \item{check_contrasts}{\code{logical}. Should contrasts for between-subject factors be checked and (if necessary) changed to be \code{"contr.sum"}. See details. The default is given by \code{afex_options("check_contrasts")}, which is initially \code{TRUE}.} \item{observed}{\code{character} vector indicating which of the variables are observed (i.e, measured) as compared to experimentally manipulated. The default effect size reported (generalized eta-squared) requires correct specification of the obsered (in contrast to manipulated) variables.} \item{anova_table}{\code{list} of further arguments passed to function producing the ANOVA table. Arguments such as \code{es} (effect size) or \code{correction} are passed to either \code{anova.afex_aov} or \code{nice}. Note that those settings can also be changed once an object of class \code{afex_aov} is created by invoking the \code{anova} method directly.} \item{include_aov}{Boolean. Allows suppressing the calculation of the aov object, which is per default part of the returned \code{afex_aov} object. \code{FALSE} prevents this potentially costly calculation. Especially for designs with larger N and within-subjects factors, this is highly advisable. Follow-up analyses using \pkg{emmeans} are then always based on the multivariate or \code{lm} model.} \item{return}{What should be returned? The default is given by \code{afex_options("return_aov")}, which is initially \code{"afex_aov"}, returning an S3 object of class \code{afex_aov} for which various \link[=afex_aov-methods]{methods} exist (see there and below for more details). Other values are currently still supported for backward compatibility.} \item{...}{Further arguments passed to \code{fun_aggregate}.} \item{print.formula}{\code{aov_ez} and \code{aov_4} are wrapper for \code{aov_car}. This boolean argument indicates whether the formula in the call to \code{car.aov} should be printed.} \item{id}{\code{character} vector (of length 1) indicating the subject identifier column in \code{data}.} \item{dv}{\code{character} vector (of length 1) indicating the column containing the \strong{dependent variable} in \code{data}.} \item{between}{\code{character} vector indicating the \strong{between}-subject(s) factor(s)/column(s) in \code{data}. Default is \code{NULL} indicating no between-subjects factors.} \item{within}{\code{character} vector indicating the \strong{within}-subject(s)(or repeated-measures) factor(s)/column(s) in \code{data}. Default is \code{NULL} indicating no within-subjects factors.} \item{covariate}{\code{character} vector indicating the between-subject(s) covariate(s) (i.e., column(s)) in \code{data}. Default is \code{NULL} indicating no covariates. Please note that \code{factorize} needs to be set to \code{FALSE} in case the covariate is numeric and should be treated as such.} \item{transformation}{In \code{aov_ez}, a \code{character} vector (of length 1) indicating the name of a transformation to apply to \code{dv} before fitting the model. If missing, no transformation is applied. In \code{aov_car} and \code{aov_4}, a response transformation may be incorporated in the left-hand side of \code{formula}.} } \value{ \code{aov_car}, \code{aov_4}, and \code{aov_ez} are wrappers for \code{\link[car]{Anova}} and \code{\link{aov}}, the return value is dependent on the \code{return} argument. Per default, an S3 object of class \code{"afex_aov"} is returned containing the following slots: \describe{ \item{\code{"anova_table"}}{An ANOVA table of class \code{c("anova", "data.frame")}.} \item{\code{"aov"}}{\code{aov} object returned from \code{\link{aov}} (should not be used to evaluate significance of effects, but can be passed to \code{emmeans} for post-hoc tests).} \item{\code{"Anova"}}{object returned from \code{\link[car]{Anova}}, an object of class \code{"Anova.mlm"} (if within-subjects factors are present) or of class \code{c("anova", "data.frame")}.} \item{\code{"lm"}}{the object fitted with \code{lm} and passed to \code{Anova} (i.e., an object of class \code{"lm"} or \code{"mlm"}). Also returned if \code{return = "lm"}.} \item{\code{"data"}}{a list containing: (1) \code{long} (the possibly aggregated data in long format used for \code{aov}), \code{wide} (the data used to fit the \code{lm} object), and \code{idata} (if within-subject factors are present, the \code{idata} argument passed to \code{car::Anova}). Also returned if \code{return = "data"}.} } In addition, the object has the following attributes: \code{"dv"}, \code{"id"}, \code{"within"}, \code{"between"}, and \code{"type"}. The \link[=afex_aov-methods]{print} method for \code{afex_aov} objects (invisibly) returns (and prints) the same as if \code{return} is \code{"nice"}: a nice ANOVA table (produced by \code{\link{nice}}) with the following columns: \code{Effect}, \code{df}, \code{MSE} (mean-squared errors), \code{F} (potentially with significant symbols), \code{ges} (generalized eta-squared), \code{p}. } \description{ These functions allow convenient specification of any type of ANOVAs (i.e., purely within-subjects ANOVAs, purely between-subjects ANOVAs, and mixed between-within or split-plot ANOVAs) for data in the \strong{long} format (i.e., one observation per row). If the data has more than one observation per individual and cell of the design (e.g., multiple responses per condition), the data will by automatically aggregated. The default settings reproduce results from commercial statistical packages such as SPSS or SAS. \code{aov_ez} is called specifying the factors as character vectors, \code{aov_car} is called using a formula similar to \code{\link{aov}} specifying an error strata for the within-subject factor(s), and \code{aov_4} is called with a \pkg{lme4}-like formula (all ANOVA functions return identical results). The returned object contains the ANOVA also fitted via base R's \code{\link{aov}} which can be passed to e.g., \pkg{emmeans} for further analysis (e.g., follow-up tests, contrasts, plotting, etc.). These functions employ \code{\link[car]{Anova}} (from the \pkg{car} package) to provide test of effects avoiding the somewhat unhandy format of \code{car::Anova}. } \details{ \subsection{Details of ANOVA Specification}{ \code{aov_ez} will concatenate all between-subject factors using \code{*} (i.e., producing all main effects and interactions) and all covariates by \code{+} (i.e., adding only the main effects to the existing between-subject factors). The within-subject factors do fully interact with all between-subject factors and covariates. This is essentially identical to the behavior of SPSS's \code{glm} function. The \code{formula}s for \code{aov_car} or \code{aov_4} must contain a single \code{Error} term specifying the \code{ID} column and potential within-subject factors (you can use \code{\link{mixed}} for running mixed-effects models with multiple error terms). Factors outside the \code{Error} term are treated as between-subject factors (the within-subject factors specified in the \code{Error} term are ignored outside the \code{Error} term; in other words, it is not necessary to specify them outside the \code{Error} term, see Examples).\cr Suppressing the intercept (i.e, via \code{0 +} or \code{- 1}) is ignored. Specific specifications of effects (e.g., excluding terms with \code{-} or using \code{^}) could be okay but is not tested. Using the \code{\link{I}} or \code{\link{poly}} function within the formula is not tested and not supported! To run an ANCOVA you need to set \code{factorize = FALSE} and make sure that all variables have the correct type (i.e., factors are factors and numeric variables are numeric and centered). Note that the default behavior is to include calculation of the effect size generalized eta-squared for which \strong{all non-manipluated (i.e., observed)} variables need to be specified via the \code{observed} argument to obtain correct results. When changing the effect size to \code{"pes"} (partial eta-squared) or \code{"none"} via \code{anova_table} this becomes unnecessary. If \code{check_contrasts = TRUE}, contrasts will be set to \code{"contr.sum"} for all between-subject factors if default contrasts are not equal to \code{"contr.sum"} or \code{attrib(factor, "contrasts") != "contr.sum"}. (within-subject factors are hard-coded \code{"contr.sum"}.) } \subsection{Statistical Issues}{ \strong{Type 3 sums of squares are default in \pkg{afex}.} While some authors argue that so-called type 3 sums of squares are dangerous and/or problematic (most notably Venables, 2000), they are the default in many commercial statistical application such as SPSS or SAS. Furthermore, statisticians with an applied perspective recommend type 3 tests (e.g., Maxwell and Delaney, 2004). Consequently, they are the default for the ANOVA functions described here. For some more discussion on this issue see \href{http://stats.stackexchange.com/q/6208/442}{here}. Note that lower order effects (e.g., main effects) in type 3 ANOVAs are only meaningful with \href{http://www.ats.ucla.edu/stat/mult_pkg/faq/general/effect.htm}{effects coding}. That is, contrasts should be set to \code{\link{contr.sum}} to obtain meaningful results. This is imposed automatically for the functions discussed here as long as \code{check_contrasts} is \code{TRUE} (the default). I nevertheless recommend to set the contrasts globally to \code{contr.sum} via running \code{\link{set_sum_contrasts}}. For a discussion of the other (non-recommended) coding schemes see \href{http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm}{here}. } \subsection{Follow-Up Contrasts and Post-Hoc Tests}{ The S3 object returned per default can be directly passed to \code{emmeans::emmeans} for further analysis. This allows to test any type of contrasts that might be of interest independent of whether or not this contrast involves between-subject variables, within-subject variables, or a combination thereof. The general procedure to run those contrasts is the following (see Examples for a full example): \enumerate{ \item Estimate an \code{afex_aov} object with the function returned here. For example: \code{x <- aov_car(dv ~ a*b + (id/c), d)} \item Obtain a \code{\link[emmeans]{emmGrid-class}} object by running \code{\link[emmeans]{emmeans}} on the \code{afex_aov} object from step 1 using the factors involved in the contrast. For example: \code{r <- emmeans(x, ~a:c)} \item Create a list containing the desired contrasts on the reference grid object from step 2. For example: \code{con1 <- list(a_x = c(-1, 1, 0, 0, 0, 0), b_x = c(0, 0, -0.5, -0.5, 0, 1))} \item Test the contrast on the reference grid using \code{\link[emmeans]{contrast}}. For example: \code{contrast(r, con1)} \item To control for multiple testing p-value adjustments can be specified. For example the Bonferroni-Holm correction: \code{contrast(r, con1, adjust = "holm")} } Note that \pkg{emmeans} allows for a variety of advanced settings and simplifiations, for example: all pairwise comparison of a single factor using one command (e.g., \code{emmeans(x, "a", contr = "pairwise")}) or advanced control for multiple testing by passing objects to \pkg{multcomp}. A comprehensive overview of the functionality is provided in the accompanying vignettes (see \href{https://CRAN.R-project.org/package=emmeans}{here}). A caveat regarding the use of \pkg{emmeans} concerns the assumption of sphericity for ANOVAs including within-subjects/repeated-measures factors (with more than two levels). The current default for follow-up tests uses a univariate model (\code{model = "univariate"} in the call to \code{emmeans}), which does not adequately control for violations of sphericity. This may result in anti-conservative tests and contrasts somewhat with the default ANOVA table which reports results based on the Greenhousse-Geisser correction. An alternative is to use a multivariate model (\code{model = "multivariate"} in the call to \code{emmeans}) which should handle violations of sphericity better. The default will likely change to multivariate tests in one of the next versions of the package. Starting with \pkg{afex} version 0.22, \pkg{emmeans} is \emph{not} loaded/attached automatically when loading \pkg{afex}. Therefore, \pkg{emmeans} now needs to be loaded by the user via \code{library("emmeans")} or \code{require("emmeans")}. } \subsection{Methods for \code{afex_aov} Objects}{ A full overview over the methods provided for \code{afex_aov} objects is provided in the corresponding help page: \code{\link{afex_aov-methods}}. The probably most important ones for end-users are \code{summary}, \code{anova}, and \code{\link{nice}}. The \code{summary} method returns, for ANOVAs containing within-subject (repeated-measures) factors with more than two levels, the complete univariate analysis: Results without df-correction, the Greenhouse-Geisser corrected results, the Hyunh-Feldt corrected results, and the results of the Mauchly test for sphericity. The \code{anova} method returns a \code{data.frame} of class \code{"anova"} containing the ANOVA table in numeric form (i.e., the one in slot \code{anova_table} of a \code{afex_aov}). This method has arguments such as \code{correction} and \code{es} and can be used to obtain an ANOVA table with different correction than the one initially specified. The \code{\link{nice}} method also returns a \code{data.frame}, but rounds most values and transforms them into characters for nice printing. Also has arguments like \code{correction} and \code{es} which can be used to obtain an ANOVA table with different correction than the one initially specified. } } \section{Functions}{ \itemize{ \item \code{aov_4}: Allows definition of ANOVA-model using \code{lme4::lmer}-like Syntax (but still fits a standard ANOVA). \item \code{aov_ez}: Allows definition of ANOVA-model using character strings. }} \note{ Calculation of ANOVA models via \code{aov} (which is done per default) can be comparatively slow and produce comparatively large objects for ANOVAs with many within-subjects factors or levels. To avoid this calculation set \code{include_aov = FALSE}. You can also disable this globally with: \code{afex_options(include_aov = FALSE)} The id variable and variables entered as within-subjects (i.e., repeated-measures) factors are silently converted to factors. Levels of within-subject factors are converted to valid variable names using \code{\link{make.names}(...,unique=TRUE)}. Unused factor levels are silently dropped on all variables. Contrasts attached to a factor as an attribute are probably not preserved and not supported. The workhorse is \code{aov_car}. \code{aov_4} and \code{aov_ez} only construe and pass an appropriate formula to \code{aov_car}. Use \code{print.formula = TRUE} to view this formula. In contrast to \code{\link{aov}} \code{aov_car} assumes that all factors to the right of \code{/} in the \code{Error} term are belonging together. Consequently, \code{Error(id/(a*b))} and \code{Error(id/a*b)} are identical (which is not true for \code{\link{aov}}). } \examples{ ########################## ## 1: Specifying ANOVAs ## ########################## # Example using a purely within-subjects design # (Maxwell & Delaney, 2004, Chapter 12, Table 12.5, p. 578): data(md_12.1) aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table=list(correction = "none", es = "none")) # Default output aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) # examples using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset (car package). # Data is a split-plot or mixed design: contains both within- and between-subjects factors. data(obk.long, package = "afex") # estimate mixed ANOVA on the full design: aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long, observed = "gender") aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), observed = "gender") # the three calls return the same ANOVA table: # Anova Table (Type 3 tests) # # Response: value # Effect df MSE F ges p.value # 1 treatment 2, 10 22.81 3.94 + .20 .05 # 2 gender 1, 10 22.81 3.66 + .11 .08 # 3 treatment:gender 2, 10 22.81 2.86 .18 .10 # 4 phase 1.60, 15.99 5.02 16.13 *** .15 .0003 # 5 treatment:phase 3.20, 15.99 5.02 4.85 * .10 .01 # 6 gender:phase 1.60, 15.99 5.02 0.28 .003 .71 # 7 treatment:gender:phase 3.20, 15.99 5.02 0.64 .01 .61 # 8 hour 1.84, 18.41 3.39 16.69 *** .13 <.0001 # 9 treatment:hour 3.68, 18.41 3.39 0.09 .002 .98 # 10 gender:hour 1.84, 18.41 3.39 0.45 .004 .63 # 11 treatment:gender:hour 3.68, 18.41 3.39 0.62 .01 .64 # 12 phase:hour 3.60, 35.96 2.67 1.18 .02 .33 # 13 treatment:phase:hour 7.19, 35.96 2.67 0.35 .009 .93 # 14 gender:phase:hour 3.60, 35.96 2.67 0.93 .01 .45 # 15 treatment:gender:phase:hour 7.19, 35.96 2.67 0.74 .02 .65 # # Sphericity correction method: GG # --- # Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1 # "numeric" variables are per default converted to factors (as long as factorize = TRUE): obk.long$hour2 <- as.numeric(as.character(obk.long$hour)) # gives same results as calls before aov_car(value ~ treatment * gender + Error(id/phase*hour2), data = obk.long, observed = c("gender")) # ANCOVA: adding a covariate (necessary to set factorize = FALSE) aov_car(value ~ treatment * gender + age + Error(id/(phase*hour)), data = obk.long, observed = c("gender", "age"), factorize = FALSE) aov_4(value ~ treatment * gender + age + (phase*hour|id), data = obk.long, observed = c("gender", "age"), factorize = FALSE) aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), covariate = "age", observed = c("gender", "age"), factorize = FALSE) # aggregating over one within-subjects factor (phase), with warning: aov_car(value ~ treatment * gender + Error(id/hour), data = obk.long, observed = "gender") aov_ez("id", "value", obk.long, c("treatment", "gender"), "hour", observed = "gender") # aggregating over both within-subjects factors (again with warning), # only between-subjects factors: aov_car(value ~ treatment * gender + Error(id), data = obk.long, observed = c("gender")) aov_4(value ~ treatment * gender + (1|id), data = obk.long, observed = c("gender")) aov_ez("id", "value", obk.long, between = c("treatment", "gender"), observed = "gender") # only within-subject factors (ignoring between-subjects factors) aov_car(value ~ Error(id/(phase*hour)), data = obk.long) aov_4(value ~ (phase*hour|id), data = obk.long) aov_ez("id", "value", obk.long, within = c("phase", "hour")) ### changing defaults of ANOVA table: # no df-correction & partial eta-squared: aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, anova_table = list(correction = "none", es = "pes")) # no df-correction and no MSE aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long,observed = "gender", anova_table = list(correction = "none", MSE = FALSE)) # add p-value adjustment for all effects (see Cramer et al., 2015, PB&R) aov_ez("id", "value", obk.long, between = "treatment", within = c("phase", "hour"), anova_table = list(p_adjust_method = "holm")) ########################### ## 2: Follow-up Analysis ## ########################### # use data as above data(obk.long, package = "afex") # 1. obtain afex_aov object: a1 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), observed = "gender") library("emmeans") # package emmeans needs to be attached for follow-up tests. # 1b. plot data (per default with ggplot2): emmip(a1, gender ~ hour | treatment+phase) ## add univariate CIs: emmip(a1, gender ~ hour | treatment+phase, CIs = TRUE) ## add multivariate CIs emmip(a1, gender ~ hour | treatment+phase, CIs = TRUE, model = "multivariate") # use lattice instead of ggplot2 (which has no CIs): emm_options(graphics.engine = "lattice") emmip(a1, gender ~ hour | treatment+phase) emm_options(graphics.engine = "ggplot") # reset options # 2. obtain reference grid object (default uses univariate model): r1 <- emmeans(a1, ~treatment +phase) r1 # multivariate model may be more appropriate r1 <- emmeans(a1, ~treatment +phase, model = "multivariate") r1 # 3. create list of contrasts on the reference grid: c1 <- list( A_B_pre = c(rep(0, 6), 0, -1, 1), # A versus B for pretest A_B_comb = c(-0.5, 0.5, 0, -0.5, 0.5, 0, 0, 0, 0), # A vs. B for post and follow-up combined effect_post = c(0, 0, 0, -1, 0.5, 0.5, 0, 0, 0), # control versus A&B post effect_fup = c(-1, 0.5, 0.5, 0, 0, 0, 0, 0, 0), # control versus A&B follow-up effect_comb = c(-0.5, 0.25, 0.25, -0.5, 0.25, 0.25, 0, 0, 0) # control versus A&B combined ) # 4. test contrasts on reference grid: contrast(r1, c1) # same as before, but using Bonferroni-Holm correction for multiple testing: contrast(r1, c1, adjust = "holm") # 2. (alternative): all pairwise comparisons of treatment: emmeans(a1, "treatment", contr = "pairwise", model = "multivariate") ## set multivariate models globally: # afex_options(emmeans_model = "multivariate") ####################### ## 3: Other examples ## ####################### data(obk.long, package = "afex") # replicating ?Anova using aov_car: obk_anova <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, type = 2) # in contrast to aov you do not need the within-subject factors outside Error() str(obk_anova, 1, give.attr = FALSE) # List of 5 # $ anova_table:Classes 'anova' and 'data.frame': 15 obs. of 6 variables: # $ aov :List of 5 # $ Anova :List of 14 # $ lm :List of 13 # $ data :List of 3 obk_anova$Anova ## Type II Repeated Measures MANOVA Tests: Pillai test statistic ## Df test stat approx F num Df den Df Pr(>F) ## (Intercept) 1 0.970 318 1 10 0.0000000065 *** ## treatment 2 0.481 5 2 10 0.03769 * ## gender 1 0.204 3 1 10 0.14097 ## treatment:gender 2 0.364 3 2 10 0.10447 ## phase 1 0.851 26 2 9 0.00019 *** ## treatment:phase 2 0.685 3 4 20 0.06674 . ## gender:phase 1 0.043 0 2 9 0.82000 ## treatment:gender:phase 2 0.311 1 4 20 0.47215 ## hour 1 0.935 25 4 7 0.00030 *** ## treatment:hour 2 0.301 0 8 16 0.92952 ## gender:hour 1 0.293 1 4 7 0.60237 ## treatment:gender:hour 2 0.570 1 8 16 0.61319 ## phase:hour 1 0.550 0 8 3 0.83245 ## treatment:phase:hour 2 0.664 0 16 8 0.99144 ## gender:phase:hour 1 0.695 1 8 3 0.62021 ## treatment:gender:phase:hour 2 0.793 0 16 8 0.97237 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 } \references{ Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies. \emph{Psychonomic Bulletin & Review}, 1-8. doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} Maxwell, S. E., & Delaney, H. D. (2004). \emph{Designing Experiments and Analyzing Data: A Model-Comparisons Perspective}. Mahwah, N.J.: Lawrence Erlbaum Associates. Venables, W.N. (2000). \emph{Exegeses on linear models}. Paper presented to the S-Plus User's Conference, Washington DC, 8-9 October 1998, Washington, DC. Available from: \url{http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf} } \seealso{ Various methods for objects of class \code{afex_aov} are available: \code{\link{afex_aov-methods}} \code{\link{nice}} creates the nice ANOVA tables which is by default printed. See also there for a slightly longer discussion of the available effect sizes. \code{\link{mixed}} provides a (formula) interface for obtaining p-values for mixed-models via \pkg{lme4}. The functions presented here do not estimate mixed models. } \author{ Henrik Singmann The design of these functions was influenced by \code{\link[ez]{ezANOVA}} from package \pkg{ez}. } afex/man/round_ps.Rd0000644000176200001440000000107313351525342014074 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/round_ps.R \encoding{UTF-8} \name{round_ps} \alias{round_ps} \title{Helper function which rounds p-values} \usage{ round_ps(x) } \arguments{ \item{x}{a numeric vector} } \value{ A character vector with the same length of x. } \description{ p-values are rounded in a sane way: .99 - .01 to two digits, < .01 to three digits, < .001 to four digits. } \examples{ round_ps(runif(10)) round_ps(runif(10, 0, .01)) round_ps(runif(10, 0, .001)) round_ps(0.0000000099) } \author{ Henrik Singmann } afex/man/obk.long.Rd0000644000176200001440000000555413351525342013764 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/obk.long-data.R \docType{data} \encoding{UTF-8} \name{obk.long} \alias{obk.long} \title{O'Brien Kaiser's Repeated-Measures Dataset with Covariate} \format{A data frame with 240 rows and 7 variables.} \source{ O'Brien, R. G., & Kaiser, M. K. (1985). MANOVA method for analyzing repeated measures designs: An extensive primer. \emph{Psychological Bulletin}, 97, 316-333. doi:10.1037/0033-2909.97.2.316 } \usage{ obk.long } \description{ This is the long version of the \code{OBrienKaiser} dataset from the \pkg{car} pakage adding a random covariate \code{age}. Originally the dataset ist taken from O'Brien and Kaiser (1985). The description from \code{\link[carData]{OBrienKaiser}} says: "These contrived repeated-measures data are taken from O'Brien and Kaiser (1985). The data are from an imaginary study in which 16 female and male subjects, who are divided into three treatments, are measured at a pretest, postest, and a follow-up session; during each session, they are measured at five occasions at intervals of one hour. The design, therefore, has two between-subject and two within-subject factors." } \examples{ # The dataset is constructed as follows: data("OBrienKaiser", package = "carData") set.seed(1) OBrienKaiser2 <- within(OBrienKaiser, { id <- factor(1:nrow(OBrienKaiser)) age <- scale(sample(18:35, nrow(OBrienKaiser), replace = TRUE), scale = FALSE)}) attributes(OBrienKaiser2$age) <- NULL # needed or resahpe2::melt throws an error. OBrienKaiser2$age <- as.numeric(OBrienKaiser2$age) obk.long <- reshape2::melt(OBrienKaiser2, id.vars = c("id", "treatment", "gender", "age")) obk.long[,c("phase", "hour")] <- lapply(as.data.frame(do.call(rbind, strsplit(as.character(obk.long$variable), "\\\\."),)), factor) obk.long <- obk.long[,c("id", "treatment", "gender", "age", "phase", "hour", "value")] obk.long <- obk.long[order(obk.long$id),] rownames(obk.long) <- NULL str(obk.long) ## 'data.frame': 240 obs. of 7 variables: ## $ id : Factor w/ 16 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ... ## $ treatment: Factor w/ 3 levels "control","A",..: 1 1 1 1 1 1 1 1 1 1 ... ## $ gender : Factor w/ 2 levels "F","M": 2 2 2 2 2 2 2 2 2 2 ... ## $ age : num -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 ... ## $ phase : Factor w/ 3 levels "fup","post","pre": 3 3 3 3 3 2 2 2 2 2 ... ## $ hour : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ... ## $ value : num 1 2 4 2 1 3 2 5 3 2 ... head(obk.long) ## id treatment gender age phase hour value ## 1 1 control M -4.75 pre 1 1 ## 2 1 control M -4.75 pre 2 2 ## 3 1 control M -4.75 pre 3 4 ## 4 1 control M -4.75 pre 4 2 ## 5 1 control M -4.75 pre 5 1 ## 6 1 control M -4.75 post 1 3 } \keyword{dataset} afex/man/deprecated.Rd0000644000176200001440000000115513351525342014344 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/deprecated.R \name{aov.car} \alias{aov.car} \alias{afex-deprecated} \alias{ez.glm} \alias{aov4} \title{Deprecated functions} \usage{ aov.car(...) ez.glm(...) aov4(...) } \arguments{ \item{...}{arguments passed from the old functions of the style \code{foo.bar()} to the new functions \code{foo_bar()}} } \description{ These functions have been renamed and deprecated in \pkg{afex}: \code{aov.car()} (use \code{\link{aov_car}()}), \code{ez.glm()} (use \code{\link{aov_ez}()}), \code{aov4()} (use \code{\link{aov_4}()}). } \keyword{internal} afex/man/compare.2.vectors.Rd0000644000176200001440000001056613351525342015524 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compare.2.vectors.R \encoding{UTF-8} \name{compare.2.vectors} \alias{compare.2.vectors} \title{Compare two vectors using various tests.} \usage{ compare.2.vectors(x, y, paired = FALSE, na.rm = FALSE, tests = c("parametric", "nonparametric"), coin = TRUE, alternative = "two.sided", perm.distribution, wilcox.exact = NULL, wilcox.correct = TRUE) } \arguments{ \item{x}{a (non-empty) numeric vector of data values.} \item{y}{a (non-empty) numeric vector of data values.} \item{paired}{a logical whether the data is paired. Default is \code{FALSE}.} \item{na.rm}{logical. Should \code{NA} be removed? Default is \code{FALSE}.} \item{tests}{Which tests to report, parametric or nonparamteric? The default \code{c("parametric", "nonparametric")} reports both. See details. (Arguments may be abbreviated).} \item{coin}{logical or character. Should (permutation) tests from the \pkg{coin} package be reported? Default is \code{TRUE} corresponding to all implemented tests. \code{FALSE} calculates no tests from \pkg{coin}. A character vector may include any of the following (potentially abbreviated) implemented tests (see also Details): \code{c("permutation", "Wilcoxon", "median")}} \item{alternative}{a character, the alternative hypothesis must be one of \code{"two.sided"} (default), \code{"greater"} or \code{"less"}. You can specify just the initial letter, will be passed to all functions.} \item{perm.distribution}{\code{distribution} argument to \pkg{coin}, see \code{\link[coin]{NullDistribution}} or , \code{\link[coin]{IndependenceTest}}. If missing, defaults to \code{coin::approximate(100000)} indicating an approximation of the excat conditional distribution with 100.000 Monte Carlo samples. One can use \code{"exact"} for small samples and if \code{paired = FALSE}.} \item{wilcox.exact}{\code{exact} argument to \code{\link{wilcox.test}}.} \item{wilcox.correct}{\code{correct} argument to \code{\link{wilcox.test}}.} } \value{ a list with up to two elements (i.e., \code{paramteric} and/or \code{nonparamteric}) each containing a \code{data.frame} with the following columns: \code{test}, \code{test.statistic}, \code{test.value}, \code{test.df}, \code{p}. } \description{ Compares two vectors \code{x} and \code{y} using t-test, Welch-test (also known as Satterthwaite), Wilcoxon-test, and a permutation test implemented in \pkg{coin}. } \details{ The \code{parametric} tests (currently) only contain the \emph{t}-test and Welch/Statterwaithe/Smith/unequal variance \emph{t}-test implemented in \code{\link{t.test}}. The latter one is only displayed if \code{paired = FALSE}. The \code{nonparametric} tests (currently) contain the Wilcoxon test implemented in \code{\link{wilcox.test}} (\code{stats::Wilcoxon}) and (if \code{coin = TRUE}) the following tests implemented in \pkg{coin}: \itemize{ \item a \code{permutation} test \code{\link[coin]{oneway_test}} (the only test in this selction not using a rank transformation), \item the \code{Wilcoxon} test \code{\link[coin]{wilcox_test}} (\code{coin::Wilcoxon}), and \item the \code{median} test \code{\link[coin]{median_test}}. } Note that the two implementations of the Wilcoxon test probably differ. This is due to differences in the calculation of the Null distributions. } \examples{ with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2])) # gives: ## $parametric ## test test.statistic test.value test.df p ## 1 t t -1.861 18.00 0.07919 ## 2 Welch t -1.861 17.78 0.07939 ## ## $nonparametric ## test test.statistic test.value test.df p ## 1 stats::Wilcoxon W 25.500 NA 0.06933 ## 2 permutation Z -1.751 NA 0.08154 ## 3 coin::Wilcoxon Z -1.854 NA 0.06487 ## 4 median Z -1.744 NA 0.17867 # compare with: with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], alternative = "less")) with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], alternative = "greater")) # doesn't make much sense as the data is not paired, but whatever: with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], paired = TRUE)) # from ?t.test: compare.2.vectors(1:10,y=c(7:20, 200)) } afex/man/sk2011.1.Rd0000644000176200001440000000570613607673671013347 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/sk2011.1-data.R \docType{data} \encoding{UTF-8} \name{sk2011.1} \alias{sk2011.1} \title{Data from Singmann & Klauer (2011, Experiment 1)} \format{A data.frame with 640 rows and 9 variables.} \source{ Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. Thinking & Reasoning, 17(3), 247-281. doi:10.1080/13546783.2011.572718 } \usage{ sk2011.1 } \description{ Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and plausibility of the problem (inferences which were consisted with the background knowledge versus problems that were inconsistent with the background knowledge). The critical comparison across the two conditions was among problems which were valid and implausible with problems that were invalid and plausible. For example, the next problem was invalid and plausible: } \details{ If a person is wet, then the person fell into a swimming pool. \cr A person fell into a swimming pool. \cr How valid is the conclusion/How likely is it that the person is wet? For those problems we predicted that under deductive instructions responses should be lower (as the conclusion does not necessarily follow from the premises) as under probabilistic instructions. For the valid but implausible problem, an example is presented next, we predicted the opposite pattern: If a person is wet, then the person fell into a swimming pool. \cr A person is wet. \cr How valid is the conclusion/How likely is it that the person fell into a swimming pool? Our study also included valid and plausible and invalid and implausible problems. Note that the factor `plausibility` is not present in the original manuscript, there it is a results of a combination of other factors. } \examples{ data(sk2011.1) # Table 1 (p. 264): aov_ez("id", "response", sk2011.1[ sk2011.1$what == "affirmation",], within = c("inference", "type"), between = "instruction", anova_table=(es = "pes")) aov_ez("id", "response", sk2011.1[ sk2011.1$what == "denial",], within = c("inference", "type"), between = "instruction", anova_table=(es = "pes")) } \keyword{dataset} afex/DESCRIPTION0000644000176200001440000000631413607773463012727 0ustar liggesusersPackage: afex Type: Package Title: Analysis of Factorial Experiments Depends: R (>= 3.1.0), lme4 (>= 1.1-8) Suggests: emmeans (>= 1.4), coin, xtable, parallel, plyr, optimx, nloptr, knitr, rmarkdown, R.rsp, lattice, latticeExtra, multcomp, testthat, mlmRev, dplyr, tidyr, dfoptim, Matrix, psychTools, ggplot2, MEMSS, effects, carData, ggbeeswarm, nlme, cowplot, jtools, ggpubr, ggpol, MASS, glmmTMB, brms, rstanarm Imports: pbkrtest (>= 0.4-1), lmerTest (>= 3.0-0), car, reshape2, stats, methods, utils Description: Convenience functions for analyzing factorial experiments using ANOVA or mixed models. aov_ez(), aov_car(), and aov_4() allow specification of between, within (i.e., repeated-measures), or mixed (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), automatically aggregating multiple observations per individual and cell of the design. mixed() fits mixed models using lme4::lmer() and computes p-values for all fixed effects using either Kenward-Roger or Satterthwaite approximation for degrees of freedom (LMM only), parametric bootstrap (LMMs and GLMMs), or likelihood ratio tests (LMMs and GLMMs). afex_plot() provides a high-level interface for interaction or one-way plots using ggplot2, combining raw data and model estimates. afex uses type 3 sums of squares as default (imitating commercial statistical software). URL: http://afex.singmann.science/, https://github.com/singmann/afex BugReports: https://github.com/singmann/afex/issues License: GPL (>= 2) Encoding: UTF-8 VignetteBuilder: knitr, R.rsp Authors@R: c(person(given="Henrik", family="Singmann", role=c("aut", "cre"), email="singmann@gmail.com", comment=c(ORCID="0000-0002-4842-3657")), person(given="Ben", family="Bolker", role=c("aut")), person(given="Jake",family="Westfall", role=c("aut")), person(given="Frederik", family="Aust", role=c("aut"), comment = c(ORCID = "0000-0003-4900-788X")), person(given="Mattan S.",family="Ben-Shachar", role=c("aut")), person(given="Søren", family="Højsgaard", role=c("ctb")), person(given="John", family="Fox", role=c("ctb")), person(given="Michael A.", family="Lawrence", role=c("ctb")), person(given="Ulf", family="Mertens", role=c("ctb")), person(given="Jonathon", family="Love", role=c("ctb")), person(given="Russell", family="Lenth", role=c("ctb")), person(given="Rune", family="Haubo Bojesen Christensen", role=c("ctb"))) Version: 0.26-0 RoxygenNote: 7.0.2 LazyData: true NeedsCompilation: no Packaged: 2020-01-15 21:03:10 UTC; henrik Author: Henrik Singmann [aut, cre] (), Ben Bolker [aut], Jake Westfall [aut], Frederik Aust [aut] (), Mattan S. Ben-Shachar [aut], Søren Højsgaard [ctb], John Fox [ctb], Michael A. 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dI&dI&mɎ}ĚdL%;G[3ٺLv&ive2^x;32^xog匿Ⱦ¾¾±o'dT*}SEvoMl"Tɞk#>Vad"*23 w0 [u1lL ~eh84oPgaޱC|;\̨| z)Ya6~^xy[6wSq֕XaՕ;*vTеe1ea|x:q9p}u `I&dI&d}Kvt#$Lf*8֕md#H(YP\:1ɬcNfCv2Yǐ:1Jף|xY`Cס:PJ|{wݍS䊕>dQo%%a!g%}h%òiU+i+L^\bV2:A%3+=XrJ _Vtyi.Jw%t\Zs:+߷;@lӊ}{`[Sv={W}(6z^esBZͮ7nl5A5=u>r {}Sn޳|m}`:I:_30&w̬djYY ²,\;~({-.[s5k]ԌDe%cz{\mhF`lی7+mf%C=+n>d++S\V2zpz+j]ұdnڬv\0+&ʅ6ʅax\ cV.͙թ\hdI&dI&ܷ53$Jv5gue[-&Lx/evf^Y=/e2kJ!tBsυ]#1+YydVYyʣdVe'(; <+^)[y} f#bHfꃙ@>H.[.}vݢ.Sn'N$:}b_ѣǭjUYẺ212TJbV 3{Ta*Q=U~zrZUUkdWtloAZ)1eR;ϛ[t{cs7&-XI7=m?\i||؞.m=tĝwߦ\Jl#336ϱxI+t^/vƤx+93+=| B8xSM| =Oj,yƢft[*+W Έ]l9b7NEWkiP莎jP1֞>t򕊕3i"=7rz+j.?s҉tr =F <ɮ]RBv ̻Wz}5S|0rᚅU릗aH.:MJ:ZEh?wc1oV9m~#uS{TJuh<8 jg ]+4J\pg^,'IdBxH)xL6ChmTXc6!4yqt} 8Y?²1I cSI&qJ΅!N$&\&˝9{RDG //UcE.]!Yk׎1ZBٺo\T бjլEf"~[$Q6@"(\R_J(\M{#-RiM:@_iUZ"GϞY{qZdqy߷ vJmE&i&rRe :;_߸ƕ_tMBH%v~48_]RXSSV+#,FV+bOQF)"],2), equals(0.03)) }) test_that("mixed: Maxell & Delaney (2004), Table 16.6, p. 845", { data(md_16.4) skip_if_not_installed("Matrix") md_16.4b <- within(md_16.4, cond <- C(cond, contr.treatment, base = 2)) mixed2_orig <- mixed(induct ~ cond + (1|room:cond), md_16.4b, check_contrasts=FALSE, progress=FALSE) expect_equivalent(unname(round(fixef(mixed2_orig$full_model), 4)), c(35.6261, -8.1485)) expect_that(round(sqrt(Matrix::diag(vcov(mixed2_orig$full_model))), 3), equals(c(3.229, 4.548))) expect_that(round(mixed2_orig[[1]]$F, 1), equals(3.2)) }) test_that("mixed: Maxell & Delaney (2004), Table 16.7, p. 851 (uses simple F!)", { data(md_16.4) skip_if_not_installed("Matrix") md_16.4b <- within(md_16.4, cond <- C(cond, contr.treatment, base = 2)) ### replicate results from Table 16.7 (Maxwell & Delaney, 2004, p. 851) # F-values (almost) hold, p-values (especially for skill) are off # however, parameters are perfectly recovered when using the original contrasts: mixed3_orig <- mixed(induct ~ cond + skill + (1|room:cond), md_16.4b, check_contrasts=FALSE, progress=FALSE) expect_that(round(fixef(mixed3_orig$full_model), 2), is_equivalent_to(c(20.25, -7.57, 2.31))) expect_that(round(sqrt(Matrix::diag(vcov(mixed3_orig$full_model))), 2), equals(c(5.82, 2.72, 0.81))) expect_that(round(mixed3_orig[[1]]$F), equals(c(8, 8))) #mixed3_F_simple <- mixed(induct ~ cond + skill + (1|room:cond), md_16.4b, check_contrasts=FALSE, progress=FALSE, method = "F") #expect_that(round(fixef(mixed3_F_simple$full_model), 2), is_equivalent_to(c(20.25, -7.57, 2.31))) #expect_that(round(sqrt(diag(vcov(mixed3_F_simple$full_model))), 2), equals(c(5.82, 2.72, 0.81))) #expect_that(round(mixed3_F_simple[[1]]$F, 1), equals(c(7.8, 8.2))) }) test_that("mixed: Maxell & Delaney (2004), Table 16.10, p. 862 (does not replicate the table!)", { data(md_16.4) md_16.4b <- within(md_16.4, cond <- C(cond, contr.treatment, base = 2)) #note: the values in this test should not replicate the table... md_16.4b$cog <- scale(md_16.4b$cog, scale=FALSE) mixed4 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, progress=FALSE, check_contrasts=FALSE) expect_that(unname(round(fixef(mixed4$full_model), 2)), is_equivalent_to(c(36.1, -9.07, 0.64, 0.03))) }) afex/tests/testthat/test-aov_car-structural.R0000644000176200001440000001571313520615175021133 0ustar liggesusers context("ANOVAs: structural tests") test_that("dv is numeric", { data(obk.long) expect_that(aov_car(treatment ~ gender + Error(id/phase*hour), data = obk.long, observed = "gender"), throws_error("dv needs to be numeric.")) }) test_that("non Type 3 sums give warning", { data(obk.long) expect_that(aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long, observed = "gender", check.contrasts = FALSE), gives_warning("contrasts")) }) test_that("return='aov' works", { data(obk.long) data(md_12.1) # purely within expect_that(aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), return = "aov"), is_a(c( "aovlist", "listof" ))) expect_that(aov_car(value ~ Error(id/phase*hour), data = obk.long, return = "aov"), is_a(c( "aovlist", "listof" ))) #purely between expect_that(suppressWarnings(aov_car(value ~ treatment * gender + Error(id), data = obk.long, return = "aov")), is_a(c( "aov"))) expect_that(suppressWarnings(aov_car(value~treatment * gender + Error(id/phase*hour), data = obk.long, return = "aov")), is_a(c( "aovlist", "listof" ))) # terms within Error() are within parentheses: test <- summary(aov_car(value ~ Error(id/phase*hour), data = obk.long, return = "aov")) positive <- summary(aov(value ~ phase*hour+Error(id/(phase*hour)), data = obk.long)) negative <- summary(aov(value ~ phase*hour+Error(id/phase*hour), data = obk.long)) expect_equal(test, positive) expect_false(isTRUE(all.equal(test, negative, check.attributes = FALSE))) orig1 <- aov_car(value ~ Error(id/phase*hour), data = obk.long) obk.long$id <- as.numeric(obk.long$id) obk.long$phase <- as.numeric(obk.long$phase) obk.long$hour <- as.numeric(obk.long$hour) positive2 <- summary(aov_car(value ~ Error(id/phase*hour), data = obk.long, return = "aov")) expect_equal(test, positive2) positive3 <- aov_car(value ~ Error(id/phase*hour), data = obk.long) expect_equal(summary(orig1), summary(positive3)) expect_equal(summary(orig1$Anova, multivariate = FALSE), summary(positive3$Anova, multivariate = FALSE)) expect_equal(summary(orig1$aov), summary(positive3$aov)) }) test_that("anova_table attributes", { data(md_12.1) no_attr <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table = list(correction = "none")) expect_that(attr(no_attr$anova_table, "correction"), equals("none")) expect_that(attr(no_attr$anova_table, "p_adjust_method"), equals("none")) expect_output(print(attr(no_attr$anova_table, "observed")), "character\\(0\\)") all_attr <- suppressWarnings(aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), observed = "angle", anova_table=list(correction = "HF", p_adjust_method = "bonferroni"))) expect_that(attr(all_attr$anova_table, "correction"), equals("HF")) expect_that(attr(all_attr$anova_table, "p_adjust_method"), equals("bonferroni")) expect_that(attr(all_attr$anova_table, "observed"), equals("angle")) expect_output(print(all_attr), "bonferroni") expect_output(print(all_attr), "HF") expect_false(isTRUE(all.equal(nice(no_attr), suppressWarnings(nice(all_attr)), check.attributes = FALSE))) added_attr <- suppressWarnings(nice(no_attr, correction = "HF", p_adjust_method = "bonferroni", observed = "angle")) expect_that(suppressWarnings(nice(all_attr)), is_identical_to(added_attr)) expect_that(nice(all_attr$anova_table), is_identical_to(added_attr)) reset_attr <- nice(no_attr, correction = "none", p.adjust = "none", observed = NULL) expect_that(nice(no_attr), is_identical_to(reset_attr)) expect_that(nice(no_attr$anova_table), is_identical_to(reset_attr)) intercept_test <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table = list(intercept = TRUE)) expect_output(print(intercept_test), "(Intercept)") mse_test <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table = list(MSE = FALSE)) expect_null(mse_test$anova_table$MSE) expect_output(print(nice(mse_test, MSE = TRUE)), "MSE") symbol_test <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table = list(sig_symbols = c(" ", " a", " aa", " aaa")), return = "nice") expect_output(print(symbol_test), "aaa") symbol_test <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), anova_table = list(sig_symbols = c(" ", " a", " aa", " aaa"))) expect_output(print(symbol_test), "aaa") new_symbols <- c(" ", " b", " bb", " bbb") symbol_test <- anova(symbol_test, sig_symbols = c(" ", " b", " bb", " bbb")) expect_identical(attr(symbol_test, "sig_symbols"), new_symbols) expect_output(print(nice(symbol_test)), "bbb") # Test support for old afex objects old_afex_object <- default_options <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) attr(old_afex_object$anova_table, "observed") <- NULL attr(old_afex_object$anova_table, "correction") <- NULL attr(old_afex_object$anova_table, "p.adjust.method") <- NULL expect_that(nice(old_afex_object), is_identical_to(nice(default_options))) # Test if sphericity correction is set to "none" in the absence of within-subject factors or if within-subject factors have only two levels data(obk.long) between_anova <- suppressWarnings(aov_car(value ~ treatment * gender + Error(id), data = obk.long)) expect_that(attr(between_anova$anova_table, "correction"), equals("none")) obk.long <- droplevels(obk.long[obk.long$phase %in% c("post","pre"),]) two_level_anova <- suppressWarnings(aov_ez("id", "value", obk.long, between = c("treatment"), within = c("phase"))) expect_that(attr(two_level_anova$anova_table, "correction"), equals("none")) more_levels_anova <- aov_ez("id", "value", obk.long, between = c("treatment"), within = c("phase", "hour")) expect_that(attr(more_levels_anova$anova_table, "correction"), equals("GG")) obk.long <- droplevels(obk.long[obk.long$hour %in% c("1","2"),]) two_levels_anova <- aov_ez("id", "value", obk.long, between = c("treatment"), within = c("phase", "hour")) expect_that(attr(two_levels_anova$anova_table, "correction"), equals("none")) # Test incomplete observation attribute incomplete_cases <- suppressWarnings( aov_ez("id", "rt", md_12.1[-10, ], within = c("angle", "noise")) ) expect_equal(as.character(attr(incomplete_cases, "incomplete_cases")), "10") expect_equal(as.character(attr(incomplete_cases$anova_table, "incomplete_cases")), "10") expect_equal(as.character(attr(anova(incomplete_cases), "incomplete_cases")), "10") }) test_that("error messages for common problems", { data(md_12.1) md_12.2 <- md_12.1[!(md_12.1$noise == "present" & md_12.1$angle == "0"),] expect_error( aov_ez("id", "rt", md_12.2, within = c("angle", "noise")), "within-subjects design") data(obk.long) obk2 <- obk.long[ !(obk.long$treatment == "A" & obk.long$gender == "F"), ] expect_error( aov_car(value ~ treatment * gender + Error(id), data = obk2), "between-subjects design") expect_error( aov_car(value ~ treatment 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data(obk.long) expect_is(aov_car(value ~ treatment * gender*phase*hour + Error(id/phase*hour), data = obk.long), "afex_aov") }) test_that("another label bug (May 2014)", { data("sk2011.1") levels(sk2011.1$inference) <- c("A+:D-", "A+:D+", "A-:D+", "A- : D-") expect_is(aov_ez("id", "response", sk2011.1, between = "instruction", within = c("type", "inference"), return = "Anova", fun_aggregate = mean), "Anova.mlm") }) test_that("orig label bug", { data(obk.long) obk2 <- obk.long levels(obk2$phase) <- c("fup test", "post-hans", "pre tenetious") expect_is(aov_car(value ~ treatment * gender + age + Error(id/phase*hour), data = obk2, factorize=FALSE, return = "Anova"), "Anova.mlm") }) test_that("ANCOVA check bug (reported by Gang Chen), January 2013", { dat <- read.table(header=TRUE, text = "ID Group Gender ROI Value Propdd00 GAS0 MAD0 CPD0 2016 AE M 05_06 1.581 0.543 1.908 0.439999999999998 -0.5335 2016 AE M 07_08 1.521 0.543 1.908 0.439999999999998 -0.5335 2016 AE M 09_10 1.623 0.543 1.908 0.439999999999998 -0.5335 2016 AE M 03_04 1.569 0.543 1.908 0.439999999999998 -0.5335 2016 AE M 11_12 1.719 0.543 1.908 0.439999999999998 -0.5335 2016 AE M 01_02 1.509 0.543 1.908 0.439999999999998 -0.5335 2031 HC F 09_10 1.739 -0.014 0.0480000000000018 -2.347 1.9665 2031 HC F 01_02 1.763 -0.014 0.0480000000000018 -2.347 1.9665 2031 HC F 03_04 1.8 -0.014 0.0480000000000018 -2.347 1.9665 2031 HC F 11_12 1.793 -0.014 0.0480000000000018 -2.347 1.9665 2031 HC F 05_06 1.765 -0.014 0.0480000000000018 -2.347 1.9665 2031 HC F 07_08 1.654 -0.014 0.0480000000000018 -2.347 1.9665 2063 AE F 11_12 1.742 -0.027 2.348 -8.88 -0.0335000000000001 2063 AE F 01_02 1.634 -0.027 2.348 -8.88 -0.0335000000000001 2063 AE F 03_04 1.638 -0.027 2.348 -8.88 -0.0335000000000001 2063 AE F 07_08 1.604 -0.027 2.348 -8.88 -0.0335000000000001 2063 AE F 09_10 1.654 -0.027 2.348 -8.88 -0.0335000000000001 2063 AE F 05_06 1.625 -0.027 2.348 -8.88 -0.0335000000000001 2042 HC M 05_06 1.649 -0.014 2.058 -3.497 -0.8635 2042 HC M 07_08 1.565 -0.014 2.058 -3.497 -0.8635 2042 HC M 09_10 1.765 -0.014 2.058 -3.497 -0.8635 2042 HC M 03_04 1.677 -0.014 2.058 -3.497 -0.8635 2042 HC M 11_12 1.706 -0.014 2.058 -3.497 -0.8635 2042 HC M 01_02 1.618 -0.014 2.058 -3.497 -0.8635 2071 AE M 05_06 1.712 -0.317 -0.802 6.74 1.9665 2071 AE M 07_08 1.64 -0.317 -0.802 6.74 1.9665 2071 AE M 09_10 1.791 -0.317 -0.802 6.74 1.9665 2071 AE M 03_04 1.725 -0.317 -0.802 6.74 1.9665 2071 AE M 11_12 1.782 -0.317 -0.802 6.74 1.9665 2071 AE M 01_02 1.712 -0.317 -0.802 6.74 1.9665 2134 HC M 05_06 1.672 -0.014 0.347999999999999 -5.807 -2.5335 2134 HC M 07_08 1.657 -0.014 0.347999999999999 -5.807 -2.5335 2134 HC M 09_10 1.791 -0.014 0.347999999999999 -5.807 -2.5335 2134 HC M 03_04 1.633 -0.014 0.347999999999999 -5.807 -2.5335 2134 HC M 11_12 1.859 -0.014 0.347999999999999 -5.807 -2.5335 2134 HC M 01_02 1.653 -0.014 0.347999999999999 -5.807 -2.5335 2009 AE F 09_10 1.672 -0.027 1.058 3.36 11.1365 2009 AE F 03_04 1.723 -0.027 1.058 3.36 11.1365 2009 AE F 05_06 1.676 -0.027 1.058 3.36 11.1365 2009 AE F 07_08 1.622 -0.027 1.058 3.36 11.1365 2009 AE F 01_02 1.633 -0.027 1.058 3.36 11.1365 2009 AE F 11_12 1.853 -0.027 1.058 3.36 11.1365 2132 HC M 05_06 1.758 -0.014 -1.082 -2.857 -0.0335000000000001 2132 HC M 07_08 1.623 -0.014 -1.082 -2.857 -0.0335000000000001 2132 HC M 09_10 1.843 -0.014 -1.082 -2.857 -0.0335000000000001 2132 HC M 03_04 1.773 -0.014 -1.082 -2.857 -0.0335000000000001 2132 HC M 11_12 1.806 -0.014 -1.082 -2.857 -0.0335000000000001 2132 HC M 01_02 1.708 -0.014 -1.082 -2.857 -0.0335000000000001 2127 HC F 11_12 1.824 -0.014 0.628 6.223 -0.5335 2127 HC F 09_10 1.871 -0.014 0.628 6.223 -0.5335 2127 HC F 01_02 1.687 -0.014 0.628 6.223 -0.5335 2127 HC F 03_04 1.699 -0.014 0.628 6.223 -0.5335 2127 HC F 07_08 1.646 -0.014 0.628 6.223 -0.5335 2127 HC F 05_06 1.738 -0.014 0.628 6.223 -0.5335 2081 AE M 09_10 1.807 -0.027 -2.082 2.43 -1.5335 2081 AE M 11_12 1.917 -0.027 -2.082 2.43 -1.5335 2081 AE M 03_04 1.767 -0.027 -2.082 2.43 -1.5335 2081 AE M 05_06 1.776 -0.027 -2.082 2.43 -1.5335 2081 AE M 07_08 1.733 -0.027 -2.082 2.43 -1.5335 2081 AE M 01_02 1.775 -0.027 -2.082 2.43 -1.5335 2086 AE F 11_12 1.768 -0.457 -1.082 -1.76 6.9665 2086 AE F 09_10 1.769 -0.457 -1.082 -1.76 6.9665 2086 AE F 01_02 1.752 -0.457 -1.082 -1.76 6.9665 2086 AE F 03_04 1.769 -0.457 -1.082 -1.76 6.9665 2086 AE F 05_06 1.751 -0.457 -1.082 -1.76 6.9665 2086 AE F 07_08 1.728 -0.457 -1.082 -1.76 6.9665 2033 HC M 05_06 1.804 0.126 2.768 7.083 -2.2035 2033 HC M 07_08 1.784 0.126 2.768 7.083 -2.2035 2033 HC M 09_10 1.948 0.126 2.768 7.083 -2.2035 2033 HC M 03_04 1.821 0.126 2.768 7.083 -2.2035 2033 HC M 11_12 2.143 0.126 2.768 7.083 -2.2035 2033 HC M 01_02 1.824 0.126 2.768 7.083 -2.2035 2007 AE M 07_08 1.554 -0.027 0.488 -6.05 -0.5335 2007 AE M 05_06 1.643 -0.027 0.488 -6.05 -0.5335 2007 AE M 09_10 1.674 -0.027 0.488 -6.05 -0.5335 2007 AE M 03_04 1.593 -0.027 0.488 -6.05 -0.5335 2007 AE M 11_12 1.726 -0.027 0.488 -6.05 -0.5335 2007 AE M 01_02 1.517 -0.027 0.488 -6.05 -0.5335 6062 HC M 05_06 1.911 -0.014 -3.802 4.093 -3.5335 6062 HC M 07_08 1.887 -0.014 -3.802 4.093 -3.5335 6062 HC M 09_10 1.951 -0.014 -3.802 4.093 -3.5335 6062 HC M 03_04 1.798 -0.014 -3.802 4.093 -3.5335 6062 HC M 11_12 1.953 -0.014 -3.802 4.093 -3.5335 6062 HC M 01_02 1.772 -0.014 -3.802 4.093 -3.5335 2072 AE M 05_06 1.667 0.253 1.908 0.289999999999999 -1.0335 2072 AE M 07_08 1.587 0.253 1.908 0.289999999999999 -1.0335 2072 AE M 09_10 1.739 0.253 1.908 0.289999999999999 -1.0335 2072 AE M 03_04 1.638 0.253 1.908 0.289999999999999 -1.0335 2072 AE M 11_12 1.784 0.253 1.908 0.289999999999999 -1.0335 2072 AE M 01_02 1.662 0.253 1.908 0.289999999999999 -1.0335 2008 HC F 05_06 1.623 -0.014 -1.372 -2.317 2.1365 2008 HC F 07_08 1.6 -0.014 -1.372 -2.317 2.1365 2008 HC F 09_10 1.688 -0.014 -1.372 -2.317 2.1365 2008 HC F 03_04 1.624 -0.014 -1.372 -2.317 2.1365 2008 HC F 11_12 1.772 -0.014 -1.372 -2.317 2.1365 2008 HC F 01_02 1.656 -0.014 -1.372 -2.317 2.1365 2070 AE F 05_06 1.657 0.113 -1.372 -0.140000000000001 -5.5335 2070 AE F 07_08 1.579 0.113 -1.372 -0.140000000000001 -5.5335 2070 AE F 09_10 1.75 0.113 -1.372 -0.140000000000001 -5.5335 2070 AE F 03_04 1.808 0.113 -1.372 -0.140000000000001 -5.5335 2070 AE F 11_12 1.777 0.113 -1.372 -0.140000000000001 -5.5335 2070 AE F 01_02 1.702 0.113 -1.372 -0.140000000000001 -5.5335 2064 AE F 11_12 1.781 -0.027 -5.512 3.57 -3.5335 2064 AE F 09_10 1.724 -0.027 -5.512 3.57 -3.5335 2064 AE F 01_02 1.631 -0.027 -5.512 3.57 -3.5335 2064 AE F 03_04 1.607 -0.027 -5.512 3.57 -3.5335 2064 AE F 05_06 1.577 -0.027 -5.512 3.57 -3.5335 2064 AE F 07_08 1.546 -0.027 -5.512 3.57 -3.5335 2039 HC M 09_10 1.879 -0.014 2.628 -1.867 -5.5335 2039 HC M 11_12 1.918 -0.014 2.628 -1.867 -5.5335 2039 HC M 03_04 1.794 -0.014 2.628 -1.867 -5.5335 2039 HC M 05_06 1.787 -0.014 2.628 -1.867 -5.5335 2039 HC M 07_08 1.687 -0.014 2.628 -1.867 -5.5335 2039 HC M 01_02 1.774 -0.014 2.628 -1.867 -5.5335 2117 HC F 09_10 1.712 -0.014 0.917999999999999 1.293 3.7965 2117 HC F 11_12 1.75 -0.014 0.917999999999999 1.293 3.7965 2117 HC F 03_04 1.717 -0.014 0.917999999999999 1.293 3.7965 2117 HC F 07_08 1.587 -0.014 0.917999999999999 1.293 3.7965 2117 HC F 05_06 1.667 -0.014 0.917999999999999 1.293 3.7965 2117 HC F 01_02 1.663 -0.014 0.917999999999999 1.293 3.7965 ") dat$ID <- as.factor(dat$ID) fm <- aov_car(Value ~ Propdd00 + Group + Gender + GAS0 + MAD0 + CPD0 + Error(ID/ROI), data=dat, factorize=FALSE, return = "Anova") fm0 <- aov_car(Value ~ MAD0 + CPD0 + Error(ID/ROI), data=dat, factorize=FALSE, return='afex_aov') expect_is(fm, "Anova.mlm") expect_is(fm0, "afex_aov") }) test_that("ANOVA: ids in multiple between.subjects conditions", { species<- c("a","b","c","c","b","c","b","b","a","b","c","c","a","a","b","b","a","a","b","c") habitat<- c("x","x","x","y","y","y","x","x","y","z","y","y","z","z","x","x","y","y","z","z") mvt.rate<-c(6,5,7,8,9,4,3,5,6,9,3,6,6,7,8,9,5,6,7,8) ind<-as.factor(c(1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4)) data1<-data.frame(species, habitat, mvt.rate, ind) # should give an error expect_error(aov_ez("ind", "mvt.rate", data1, within = "habitat", between = "species"), "Following ids are in more than one between subjects condition:") }) test_that("empty factors are not causing aov.cat to choke", { data(sleepstudy) #Example data in lme4 sleepstudy$Days<-factor(sleepstudy$Days) #Works with all factors expect_is(aov_ez("Subject","Reaction",sleepstudy, within="Days", return = "Anova"), "Anova.mlm") #If you remove a factor it fails... expect_is(aov_ez("Subject","Reaction",sleepstudy[sleepstudy$Days!=9,], within="Days", return = "Anova"), "Anova.mlm") }) test_that("factors have more than one level", { data(obk.long) expect_error(aov_car(value ~ treatment+ Error(id/phase), data = obk.long[ obk.long$treatment == "control",]), "one level only.") expect_error(aov_car(value ~ treatment+ Error(id/phase), data = obk.long[ obk.long$phase == "pre",]), "one level only.") }) test_that("variable names longer", { data(obk.long) obk.long$gender2 <- obk.long$treatment orig <- aov_car(value ~ treatment * gender + age + Error(id/phase*hour), data = obk.long, factorize=FALSE, observed = "gender") v1 <- aov_car(value ~ gender2 * gender + age + Error(id/phase*hour), data = obk.long, factorize=FALSE, observed = "gender") v2 <- aov_car(value ~ gender2 * gender + age + Error(id/phase*hour), data = obk.long, factorize=FALSE, observed = "gender2") expect_equivalent(orig$anova_table, v1$anova_table) expect_identical(nice(orig)[,-1], nice(v1)[,-1]) expect_identical(nice(orig)[,c("df", "MSE", "F", "p.value")], nice(v2)[,c("df", "MSE", "F", "p.value")]) expect_equivalent(orig$anova_table[,c("num Df", "den Df", "MSE", "F", "Pr(>F)")], v2$anova_table[c("num Df", "den Df", "MSE", "F", "Pr(>F)")]) }) test_that("works with dplyr data.frames (see https://github.com/singmann/afex/issues/6):", { if (getRversion() >= "3.1.2") { require(dplyr) data(md_12.1) md2 <- tbl_df(md_12.1) expect_is(aov_ez("id", "rt", md2, within = c("angle", "noise"), anova_table=list(correction = "none", es = "none")), "afex_aov") } }) test_that("return='nice' works", { data(md_12.1) expect_is(aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), return = "nice"), "data.frame") }) test_that("aov_car works with column names containing spaces: https://github.com/singmann/afex/issues/22", { data <- list("dependent" = rnorm(100), "RM Factor 1" = factor(rep(c("Level 1", "Level 2"), 50)), "subject" = factor(rep(1:50, each = 2))) attr(data, 'row.names') <- seq_len(length(data[[1]])) attr(data, 'class') <- 'data.frame' expect_is(aov_car(dependent ~ `RM Factor 1` + Error(subject/(`RM Factor 1`)), data), "afex_aov") expect_is(aov_4(dependent ~ `RM Factor 1` + (`RM Factor 1`|subject), data), "afex_aov") expect_is(aov_ez("subject", "dependent", data, within = "RM Factor 1"), "afex_aov") }) test_that("aov_car works with column names containing spaces for between factors", { data <- list("dependent" = rnorm(100), "RM Factor 1" = factor(rep(c("Level 1", "Level 2"), 50)), "subject" = factor(rep(1:100))) attr(data, 'row.names') <- seq_len(length(data[[1]])) attr(data, 'class') <- 'data.frame' expect_is(aov_car(dependent ~ `RM Factor 1` + Error(subject), data), "afex_aov") expect_is(aov_4(dependent ~ `RM Factor 1` + (1|subject), data), "afex_aov") expect_is(aov_ez("subject", "dependent", data, between = "RM Factor 1"), "afex_aov") }) test_that("aov_ez works with multiple covariates", { skip_if_not_installed("psychTools") require(psychTools) data(msq) msq2 <- msq[!is.na(msq$Extraversion),] msq2 <- droplevels(msq2[msq2$ID != "18",]) msq2$TOD <- msq2$TOD-mean(msq2$TOD) msq2$MSQ_Time <- msq2$MSQ_Time-mean(msq2$MSQ_Time) msq2$condition <- msq2$condition-mean(msq2$condition) # that is somewhat stupid expect_is(aov_ez(data=msq2, dv="Extraversion", id = "ID", between = "condition", covariate=c("TOD", "MSQ_Time"), factorize=FALSE, fun_aggregate = mean), "afex_aov") }) test_that("aov_car works with p.val adjustment == NA for HF as well as GG", { # see: https://github.com/singmann/afex/issues/36 load("anova_hf_error.rda") expect_is(nice(aov_ez("Snum", "RT", demo, within=c("DistF", "WidthF", "AngleF"))), "nice_table") expect_is(nice(aov_ez("Snum", "RT", demo, within=c("DistF", "WidthF", "AngleF"), anova_table = list(correction = "GG"))), "nice_table") expect_is(nice(aov_ez("Snum", "RT", demo, within=c("DistF", "WidthF", "AngleF"), anova_table = list(correction = "HF"))), "nice_table") }) test_that("aov_car: character variables and factorize = FALSE", { data(obk.long) obk2 <- obk.long obk2$treatment <- as.character(obk2$treatment) a1 <- aov_car(value ~ treatment * gender + Error(id), data = obk.long, fun_aggregate = mean) a2 <- aov_car(value ~ treatment * gender + Error(id), data = obk2, fun_aggregate = mean) a3 <- aov_car(value ~ treatment * gender + Error(id), data = obk2, fun_aggregate = mean, factorize = FALSE) expect_equal(a1$anova_table, a2$anova_table) expect_equal(a1$anova_table, a3$anova_table) }) afex/tests/testthat/test-aov_car-basic.R0000644000176200001440000002025013351525342017772 0ustar liggesusers context("ANOVAs: replicating published results") test_that("purely within ANOVA, return='univ': Maxell & Delaney (2004), Table 12.5 and 12.6, p. 578", { ### replicate results from Table 12.6 data(md_12.1) # valus from table: f <- c(40.72, 33.77, 45.31) ss_num <- c(289920, 285660, 105120) ss_error <- c(64080, 76140, 20880) num_df <- c(2, 1, 2) den_df <- c(18, 9, 18) md_ez_r <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) md_car_r <- aov_car(rt ~ 1 + Error(id/angle*noise), md_12.1) md_aov_4_r <- aov_4(rt ~ 1 + (angle*noise|id), md_12.1) expect_that(md_ez_r, is_equivalent_to(md_car_r)) expect_that(md_ez_r, is_equivalent_to(md_aov_4_r)) expect_that(round(md_ez_r$anova_table[,"F"], 2), is_equivalent_to(f)) tmp_univ <- suppressWarnings(summary(md_ez_r$Anova)$univariate.tests) if ("Sum Sq" %in% colnames(tmp_univ)) { # to allow both car 3.0 and earlier versions ss_test <- tmp_univ[,"Sum Sq"][-1] } else { ss_test <- tmp_univ[,"SS"][-1] } expect_that(ss_test, is_equivalent_to(ss_num)) expect_that(tmp_univ[,"Error SS"][-1], is_equivalent_to(ss_error)) expect_that(anova(md_ez_r, correction = "none")[,"num Df"], is_equivalent_to(num_df)) expect_that(anova(md_ez_r, correction = "none")[,"den Df"], is_equivalent_to(den_df)) }) test_that("Analysis of Singmann & Klauer (2011, Exp. 1)", { data(sk2011.1, package = "afex") out1 <- aov_ez("id", "response", sk2011.1[ sk2011.1$what == "affirmation",], within = c("inference", "type"), between = "instruction", anova_table=(es = "pes"), fun_aggregate = mean, return = "afex_aov") df_num <- rep(1, 7) df_den <- rep(38, 7) MSE <- c(1072.42, 1007.21, 1007.21, 187.9, 187.9, 498.48, 498.48) F <- c(0.13, 13.01, 12.44, 0.06, 3.09, 29.62, 10.73) pes <- c(0, 0.26, 0.25, 0, 0.08, 0.44, 0.22) p <- c(0.72, 0.0009, 0.001, 0.81, 0.09, 0.001, 0.002) expect_that(out1$anova_table[["num Df"]], is_equivalent_to(df_num)) expect_that(out1$anova_table[["den Df"]], is_equivalent_to(df_den)) expect_that(out1$anova_table[["MSE"]], equals(MSE, tolerance = 0.001)) expect_that(out1$anova_table[["F"]], equals(F, tolerance = 0.001)) expect_that(out1$anova_table[["pes"]], equals(pes, tolerance = 0.02)) expect_that(out1$anova_table[["Pr(>F)"]], equals(p, tolerance = 0.01)) }) test_that("Data from O'Brien & Kaiser replicates their paper (p. 328, Table 8, column 'average'", { data(obk.long, package = "afex") out1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", return = "afex_aov", anova_table = list(correction = "none")) expect_that(unname(unlist(out1[["anova_table"]]["treatment", c("num Df", "den Df", "F")])), equals(c(2, 10, 3.94), tolerance = 0.001)) expect_that(unname(unlist(out1[["anova_table"]]["gender", c("num Df", "den Df", "F")])), equals(c(1, 10, 3.66), tolerance = 0.001)) expect_that(round(unname(unlist(out1[["anova_table"]]["treatment:gender", c("num Df", "den Df", "F")])), 2), equals(c(2, 10, 2.86), tolerance = 0.001)) ## check against own results: anova_tab <- structure(list(`num Df` = c(2, 1, 2, 2, 4, 2, 4, 4, 8, 4, 8, 8, 16, 8, 16), `den Df` = c(10, 10, 10, 20, 20, 20, 20, 40, 40, 40, 40, 80, 80, 80, 80), MSE = c(22.8055555555555, 22.8055555555555, 22.8055555555555, 4.01388888888889, 4.01388888888889, 4.01388888888889, 4.01388888888889, 1.5625, 1.5625, 1.5625, 1.5625, 1.20208333333333, 1.20208333333333, 1.20208333333333, 1.20208333333333), F = c(3.940494501098, 3.65912050065102, 2.85547267441343, 16.1329196993199, 4.85098375975551, 0.282782484190432, 0.636602429722426, 16.6856704980843, 0.0933333333333336, 0.450268199233716, 0.620437956204379, 1.17990398215104, 0.345292160558641, 0.931293452060798, 0.735935938468544), ges = c(0.198248507309966, 0.114806410630587, 0.179183259116394, 0.151232705544895, 0.0967823866181358, 0.00312317714869712, 0.0140618480455475, 0.12547183572154, 0.00160250371109459, 0.0038716854273722, 0.010669821220833, 0.0153706689696344, 0.00905399063368842, 0.012321395080303, 0.0194734697889242), `Pr(>F)` = c(0.0547069269265198, 0.0848002538616402, 0.104469234023772, 6.73163655770545e-05, 0.00672273209545241, 0.756647338927411, 0.642369488905348, 4.02664339633774e-08, 0.999244623719389, 0.771559070589063, 0.755484449904079, 0.32158661418337, 0.990124565656718, 0.495611922963992, 0.749561639456282)), .Names = c("num Df", "den Df", "MSE", "F", "ges", "Pr(>F)"), heading = c("Anova Table (Type 3 tests)\n", "Response: value"), row.names = c("treatment", "gender", "treatment:gender", "phase", "treatment:phase", "gender:phase", "treatment:gender:phase", "hour", "treatment:hour", "gender:hour", "treatment:gender:hour", "phase:hour", "treatment:phase:hour", "gender:phase:hour", "treatment:gender:phase:hour" ), class = c("data.frame")) expect_equal(out1[["anova_table"]], anova_tab, check.attributes = FALSE) }) test_that("Data from O'Brien & Kaiser adjusted for familywise error rate (p. 328, Table 8, column 'average'", { data(obk.long, package = "afex") out1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", return = "afex_aov", anova_table = list(correction = "none", p_adjust_method = "bonferroni")) expect_that(unname(unlist(out1[["anova_table"]]["treatment", c("num Df", "den Df", "F")])), equals(c(2, 10, 3.94), tolerance = 0.001)) expect_that(unname(unlist(out1[["anova_table"]]["gender", c("num Df", "den Df", "F")])), equals(c(1, 10, 3.66), tolerance = 0.001)) expect_that(round(unname(unlist(out1[["anova_table"]]["treatment:gender", c("num Df", "den Df", "F")])), 2), equals(c(2, 10, 2.86), tolerance = 0.001)) ## check against own results: anova_tab <- structure(list(`num Df` = c(2, 1, 2, 2, 4, 2, 4, 4, 8, 4, 8, 8, 16, 8, 16), `den Df` = c(10, 10, 10, 20, 20, 20, 20, 40, 40, 40, 40, 80, 80, 80, 80), MSE = c(22.8055555555555, 22.8055555555555, 22.8055555555555, 4.01388888888889, 4.01388888888889, 4.01388888888889, 4.01388888888889, 1.5625, 1.5625, 1.5625, 1.5625, 1.20208333333333, 1.20208333333333, 1.20208333333333, 1.20208333333333), F = c(3.940494501098, 3.65912050065102, 2.85547267441343, 16.1329196993199, 4.85098375975551, 0.282782484190432, 0.636602429722426, 16.6856704980843, 0.0933333333333336, 0.450268199233716, 0.620437956204379, 1.17990398215104, 0.345292160558641, 0.931293452060798, 0.735935938468544), ges = c(0.198248507309966, 0.114806410630587, 0.179183259116394, 0.151232705544895, 0.0967823866181358, 0.00312317714869712, 0.0140618480455475, 0.12547183572154, 0.00160250371109459, 0.0038716854273722, 0.010669821220833, 0.0153706689696344, 0.00905399063368842, 0.012321395080303, 0.0194734697889242), `Pr(>F)` = c(0.0547069269265198, 0.0848002538616402, 0.104469234023772, 6.73163655770545e-05, 0.00672273209545241, 0.756647338927411, 0.642369488905348, 4.02664339633774e-08, 0.999244623719389, 0.771559070589063, 0.755484449904079, 0.32158661418337, 0.990124565656718, 0.495611922963992, 0.749561639456282)), .Names = c("num Df", "den Df", "MSE", "F", "ges", "Pr(>F)"), heading = c("Anova Table (Type 3 tests)\n", "Response: value"), row.names = c("treatment", "gender", "treatment:gender", "phase", "treatment:phase", "gender:phase", "treatment:gender:phase", "hour", "treatment:hour", "gender:hour", "treatment:gender:hour", "phase:hour", "treatment:phase:hour", "gender:phase:hour", "treatment:gender:phase:hour" ), class = c("data.frame")) anova_tab$`Pr(>F)` <- p.adjust(anova_tab$`Pr(>F)`, method = "bonferroni") expect_equal(out1[["anova_table"]], anova_tab, check.attributes = FALSE) }) test_that("afex_aov printing", { data(sk2011.1, package = "afex") out_new <- aov_ez("id", "response", sk2011.1[ sk2011.1$what == "affirmation",], within = c("inference", "type"), between = "instruction", anova_table=(es = "pes"), fun_aggregate = mean, return = "afex_aov") expect_output(print(out_new), "Signif. codes") expect_output(print(anova(out_new)), "Signif. codes") expect_output(print(nice(out_new)), "Anova") load("afex_aov_16_1.rda") expect_output(print(out1), "Anova") expect_output(print(anova(out1)), "Signif. codes") expect_output(print(nice(out1)), "Anova") }) afex/tests/testthat/lmm_old_object.rda0000644000176200001440000066111213351525342017652 0ustar liggesusers]EټKZ$ :( llBeL$bY&iMg> xg3+Y13S̙BwW KUWWտUիוzތb A PPE% пZ WT(O$M$TV\R/SoA#J\r{J~K;iϾni;}Aa^)rw}&%0_u?|x*zۧ$[7i;sS|Cm7PW<WKYs@:@uF8iQ=J۫IT%?QE^jJCX |e qxȳ"Oc >, wE+IvI . */@1mT=YXi_,ΐxCR8(Z(=M?iyBEDLw4lb@z" E)]Э.Gl.x$FH渄*gi|i,Cs#R5G(tZlf* YscD4]jԿtɹJ UQNN'[[:;[**oJd8_(d$E#K-ۤDk4W PYV-JF,53|KB8TjjLVM{n*%:)ScgVj3#ֶ$ DeuI c8Y6OVOK1.`RcHU0J4TUUP /7xD)&E[M՝KAw w5W=䆲8!$5W& p?s'#>8"D xA_i h;'@a⁡*eq;B᰻I ɠpx< (Wh.qݑ(Dÿ=Nj^n{{xYU*j r@APL $@`$pG$ @Hv' WrZ0ȝ;)FqみiBXH/&UU%gZRWqK_Hd&!ר֣Ӷ%&GTJR e"ZK)9.2|ˣMǃ-,$]G B⳥\*{!"6C3EEZ3:u 3ePK*Id,WU@9$1 FR@,쯍_v eyL{rBިfmV>T}н)99LVXn 3  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@\<ݹuZjKu{_eIq൦wSgܢ~"=aP٩cq2pްƼ:yd.졏8W`~mmU͢U (zw^RKͲ0'!~/\yO~RΊĎ 2A(^JABf1ipȅYΰ`asߗ$1IĖT?Kn>!"?V.1@4{?MfzpJKcv_]"ߗѩ'U]2[!Y12P`*U8)#/+4qpQEaxtpA[>V}Y3'pílsRɎR==eC̑Gi{Cf k/L\gЗC_Js]ҳ_1a[5)_+B/D\eK_sDͽ_qZv|IV/b`^ ZBA飮_)}aW-pTK4?/d⥏quO5l.U4BqU9&K.! />~qpq8䣴bW}rch2neJ7_!9"3z"!> xJ:U/Xެ{Q$VD~%z`?(#P) R.RQ+cg\4 |@^u]1ЎFrO7-FS" t4kίUOU7_,>YF!rc ]5 Ppӎc_\fYœlɈ [w2ۡgGדdoWktdXxC˔"7ˆ#f{C#/$SȖj*3#7ϱņ8}q~BiAM^GXϪ^].8(w6HRW7'E3c ވf=s_>Uw4|Iה}\/Hei'νihj2krDӏ c2/D20_ UUߊ<-]} 33ީ>ݕ}ܣS8y]rQz7rhٕ'4ٹ2LuTZv tk˶~Ժyig%ԉ0m wIKL){ q+ţq6/>u SOzڃx1KpfYoqcDdχ21>٭:j̲#]˶AS7+3Mw;=ynjoC<:R|X 1YYM'ndCw~4{{M86cs2,+qzfUQ/ i:& dHywd͓emJwFn?Sveoއ|A=oI4EE8 -ţ !N틞y5MvfۉN 낽Wۻ0z1R)-B¿0[Symx2)bG~voxt? 4ٗ;:~+|0PoFwws'{r8yzf+6kTJ"~[>[9^v4 kޏ]}ӽ`lŮ~q; ~9㚃A9M6^o  .f%HڶW/W< X~c+7Ӽj*a;}ZpƷ%Mxێ8(LDh/4 ^4 w5Ss7_Ofmgo*+ d|Ltc1Gg1U2+@UeAتȵo}1j/Ec1Nz0x$~[n$ZQA/0ssnxxi,}ܫ M5)!%l) CrոnxaoxSCFؿ<6־A_Q.Hfr/"cow|_ZC8_XnED7Wv t{5>Z_U t=31OHe~wdrF\n.ܖ@ aש#afex/tests/testthat/test-compare_2_vectors.R0000644000176200001440000000043513351525342020720 0ustar liggesusers context("compare.2.vectors: known bugs") test_that("exactly equal mean does not fail", { x <- c(0.309, 0.222, 0.293, 0.238, 0.33, 0.215) y <- c(0.313, 0.213, 0.306, 0.253, 0.294, 0.228) out <- suppressWarnings(compare.2.vectors(x, y, paired = TRUE)) expect_is(out,"list") }) afex/tests/testthat/test-mixed-structure.R0000644000176200001440000004577413432553127020471 0ustar liggesusers context("Mixed: structural tests") # note: all calls with type 2 are wrapped in suppressWarnings()! test_that("mixed: Maxell & Delaney (2004), Table 16.4, p. 842: Type 2", { data(md_16.4) md_16.4b <- md_16.4 md_16.4b$cog <- scale(md_16.4b$cog, scale=FALSE) contrasts(md_16.4b$cond) <- "contr.sum" mixed4_2 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, type = 2, progress=FALSE, method = "nested-KR") lmer4_full <- lmer(induct ~ cond*cog + (cog|room:cond), md_16.4b) lmer4_small <- lmer(induct ~ cond+cog + (cog|room:cond), md_16.4b) expect_that(fixef(mixed4_2$full_model[[2]]), equals(fixef(lmer4_full))) expect_that(fixef(mixed4_2$full_model[[1]]), is_equivalent_to(fixef(lmer4_small))) }) test_that("mixed: Maxell & Delaney (2004), Table 16.4, p. 842: Type 3", { data(md_16.4) md_16.4b <- md_16.4 md_16.4b$cog <- scale(md_16.4b$cog, scale=FALSE) contrasts(md_16.4b$cond) <- "contr.sum" mixed4_2 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, type = 3, progress=FALSE, method = "nested-KR") lmer4_full <- lmer(induct ~ cond*cog + (cog|room:cond), md_16.4b) lmer4_small <- lmer(induct ~ cond+cog + (cog|room:cond), md_16.4b) expect_that(fixef(mixed4_2$full_model), equals(fixef(lmer4_full))) expect_that(mixed4_2$full_model, is_equivalent_to(lmer4_full)) expect_that(fixef(mixed4_2$restricted_models$`cond:cog`), is_equivalent_to(fixef(lmer4_small))) }) test_that("mixed, obk.long: type 2 and LRTs", { data(obk.long, package = "afex") contrasts(obk.long$treatment) <- "contr.sum" contrasts(obk.long$phase) <- "contr.sum" t2 <- mixed(value ~ treatment*phase +(1|id), data = obk.long, method = "LRT", type = 2, progress=FALSE) expect_output(print(t2), "treatment") a2.f <- lmer(value ~ treatment*phase +(1|id), data = obk.long, REML=FALSE) a2.h <- lmer(value ~ treatment+phase +(1|id), data = obk.long, REML=FALSE) a2.t <- lmer(value ~ treatment +(1|id), data = obk.long, REML=FALSE) a2.p <- lmer(value ~ phase +(1|id), data = obk.long, REML=FALSE) extract_anova <- function(anova) unlist(anova)[c("Df1", "Chisq2", "Chi Df2", "Pr(>Chisq)2" )] expect_that( unlist(t2$anova_table[3,]) , is_equivalent_to( extract_anova(anova(a2.h, a2.f)) )) expect_that( unlist(t2$anova_table[2,]) , is_equivalent_to( extract_anova(anova(a2.t, a2.h)) )) expect_that( unlist(t2$anova_table[1,]) , is_equivalent_to( extract_anova(anova(a2.p, a2.h)) )) }) test_that("mixed, mlmRev: type 3 and 2 LRTs for GLMMs", { skip_if_not_installed("mlmRev") if (require("mlmRev")) { suppressWarnings(gm1 <- mixed(use ~ age*urban + (1 | district), family = binomial, data = Contraception, method = "LRT", progress=FALSE)) suppressWarnings(gm2 <- mixed(use ~ age*urban + (1 | district), family = binomial, data = Contraception, method = "LRT", type = 2, progress=FALSE)) expect_that(gm1, is_a("mixed")) expect_that(gm1, is_a("mixed")) } }) test_that("mixed, obk.long: LMM with method = PB", { expect_that(mixed(value ~ treatment+phase*hour +(1|id), data = obk.long, method = "PB", args_test = list(nsim = 10), progress=FALSE), is_a("mixed")) }) test_that("mixed, obk.long: multicore loads lme4 and produces the same results", { #if (packageVersion("testthat") >= "0.9") { if (FALSE) { # that never seems to run... testthat::skip_on_cran() testthat::skip_on_travis() data(obk.long, package = "afex") require(parallel) cl <- makeCluster(rep("localhost", 2)) # make cluster # 1. Obtain fits with multicore: m_mc1 <- mixed(value ~ treatment +(phase|id), data = obk.long, method = "LRT", cl = cl, control = lmerControl(optCtrl=list(maxfun = 100000)), progress=FALSE) cl_search <- clusterEvalQ(cl, search()) stopCluster(cl) m_mc2 <- mixed(value ~ treatment +(phase|id), data = obk.long, method = "LRT", control = lmerControl(optCtrl=list(maxfun = 100000)), progress=FALSE) expect_that(all(vapply(cl_search, function(x) any(grepl("^package:lme4$", x)), NA)), is_true()) expect_that(m_mc1, equals(m_mc2, check.attributes = FALSE)) } }) test_that("print(mixed) works: only 1 or 2 fixed effects with all methods", { data(obk.long, package = "afex") expect_that(print(mixed(value ~ treatment+(1|id), data = obk.long, progress=FALSE)), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+phase+(1|id), data = obk.long, progress=FALSE)), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+(1|id), data = obk.long, method = "LRT", progress=FALSE)), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+phase+(1|id), data = obk.long, method = "LRT", progress=FALSE)), is_a("data.frame")) skip_if_not_installed("mlmRev") require("mlmRev") # for the data, see ?Contraception expect_that(print(mixed(use ~ urban + (1 | district), method = "PB", family = binomial, data = Contraception, args_test=list(nsim=2), progress=FALSE)), is_a("data.frame")) expect_that(print(mixed(use ~ urban + livch + (1 | district), method = "PB", family = binomial, data = Contraception, args_test=list(nsim=2), progress=FALSE)), is_a("data.frame")) }) # test_that("mixed, Maxell & Delaney (2004), Table 16.4, p. 842: bobyqa not fitting well", { # data(md_16.4) # # F-values and p-values are relatively off: # expect_that(mixed(induct ~ cond*cog + (cog|room:cond), md_16.4, control=lmerControl(optimizer="bobyqa")), gives_warning("better fit")) # expect_that(mixed(induct ~ cond*cog + (cog|room:cond), md_16.4, type=2, control=lmerControl(optimizer="bobyqa")), gives_warning("better fit")) # }) test_that("mixed: set.data.arg", { data(obk.long, package = "afex") suppressWarnings(m1 <- mixed(value ~ treatment*phase +(1|id), obk.long, method = "LRT", progress=FALSE, set_data_arg = TRUE)) suppressWarnings(m2 <- mixed(value ~ treatment*phase +(1|id), obk.long, method = "LRT", progress=FALSE, set_data_arg = FALSE)) expect_that(m1$full_model@call[["data"]], is_identical_to(as.name("obk.long"))) expect_that(m2$full_model@call[["data"]], is_identical_to(as.name("data"))) }) test_that("mixed: anova with multiple mixed objexts", { data("sk2011.2") data("ks2013.3") sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk_m1 <- mixed(response ~ instruction+(1|id), sk2_aff, method = "LRT", progress = FALSE, set_data_arg = TRUE) sk_m2 <- mixed(response ~ instruction+(1|id)+(1|content), sk2_aff, method = "LRT", progress = FALSE, set_data_arg = TRUE) sk_m3 <- lmer(response ~ instruction+(1|id)+(validity|content), sk2_aff, REML = FALSE) sk_m4 <- lmer(response ~ instruction+(1|id)+(validity|content), sk2_aff, REML = TRUE) t <- anova(sk_m1, sk_m2, sk_m3) xx <- anova(sk_m1$full_model, sk_m2$full_model, sk_m3, model.names = c("sk_m1", "sk_m2", "sk_m3")) expect_identical(rownames(xx), rownames(t)) expect_identical(rownames(xx), c("sk_m1", "sk_m2", "sk_m3")) expect_is(t, c("anova", "data.frame")) expect_is(anova(sk_m1, object = sk_m2, sk_m3), c("anova", "data.frame")) expect_is(anova(sk_m1, object = sk_m2, sk_m3, ks2013.3), c("anova", "data.frame")) expect_warning(anova(sk_m1, object = sk_m2, sk_m3, sk_m4), "some models fit with REML = TRUE, some not") }) context("Mixed: Expand random effects") test_that("mixed: expand_re argument, return = 'merMod'", { data("ks2013.3") set_default_contrasts() m2 <- mixed(response ~ validity + (believability||id), ks2013.3, expand_re = TRUE, method = "LRT", progress=FALSE) m3 <- mixed(response ~ validity + (believability|id), ks2013.3, method = "LRT", progress=FALSE) expect_identical(length(unlist(summary(m2)$varcor)), nrow(summary(m3)$varcor$id)) expect_true(all.equal(unlist(summary(m2)$varcor), diag(summary(m3)$varcor$id), tolerance = 0.03, check.attributes = FALSE)) l2 <- mixed(response ~ validity + (believability||id), ks2013.3, expand_re = TRUE, return = "merMod", progress=FALSE) expect_is(l2, "merMod") expect_equivalent(m2$full_model, l2) l3 <- lmer_alt(response ~ validity + (believability||id), ks2013.3) l4 <- lmer_alt(response ~ validity + (believability||id), ks2013.3, control = lmerControl(optimizer = "Nelder_Mead")) expect_equivalent(l2, l3) expect_equal(l3, l4, check.attributes = FALSE) l5 <- lmer_alt(response ~ validity + (believability||id), ks2013.3, control = lmerControl(optimizer = "Nelder_Mead"), check_contrasts = TRUE) expect_equal(l2, l5, check.attributes = FALSE ) # parameter names need to be identical (same contrasts): expect_identical(names(coef(l2)$id), names(coef(l5)$id)) # parameter names need to be different (different contrasts): expect_false(all(names(coef(l2)$id) == names(coef(l3)$id))) l7 <- lmer_alt(response ~ validity + (1|id) + (0+validity*condition||content), ks2013.3, control = lmerControl(optCtrl = list(maxfun=1e6))) expect_is(l7, "merMod") expect_error(lmer_alt(response ~ validity + (0|id) + (0+validity*condition||content), ks2013.3), "Invalid random effects term") expect_is(lmer_alt(response ~ validity + (validity||id) + (validity|content), ks2013.3), "merMod") }) test_that("mixed: expand_re argument (longer)", { if (packageVersion("testthat") >= "0.9") { testthat::skip_on_cran() testthat::skip_on_travis() data("ks2013.3") m4 <- mixed(response ~ validity + (believability*validity||id) + (validity*condition|content), ks2013.3, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE) m5 <- suppressWarnings(mixed(response ~ validity + (believability*validity|id) + (validity*condition||content), ks2013.3, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), expand_re = TRUE, progress=FALSE)) expect_identical(length(unlist(summary(m4)$varcor[-7])), nrow(summary(m5)$varcor$id)) expect_identical(length(unlist(summary(m5)$varcor[-1])), nrow(summary(m4)$varcor$content)) expect_equal(attr(summary(m5)$varcor, "sc"), attr(summary(m4)$varcor, "sc"), tolerance = 0.02) } }) test_that("mixed: return=data, expand_re argument, and allFit", { #if (packageVersion("testthat") >= "0.9") { #testthat::skip_on_travis() testthat::skip_if_not_installed("optimx") testthat::skip_on_cran() require(optimx) data("ks2013.3") ks2013.3_tmp <- ks2013.3 m6 <- mixed(response ~ validity + (believability*validity||id), ks2013.3_tmp, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE, return = "merMod") m6_all_1 <- all_fit(m6, verbose = FALSE, data = ks2013.3_tmp) expect_output(print(m6_all_1$`bobyqa.`), "object 're1.believability1' not found") ks2013.3_tmp <- mixed(response ~ validity + (believability*validity||id), ks2013.3_tmp, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE, return = "data") m6_all_2 <- suppressWarnings(all_fit(m6, verbose = FALSE, data = ks2013.3_tmp)) expect_is(m6_all_2$`bobyqa.`, "merMod") expect_is(m6_all_2$`Nelder_Mead.`, "merMod") expect_is(m6_all_2$`nmkbw.`, "merMod") expect_is(m6_all_2$optimx.nlminb, "merMod") expect_is(m6_all_2$`optimx.L-BFGS-B`, "merMod") expect_is(m6_all_2$nloptwrap.NLOPT_LN_NELDERMEAD, "merMod") }) test_that("mixed with all_fit = TRUE", { testthat::skip_if_not_installed("optimx") testthat::skip_if_not_installed("MEMSS") testthat::skip_if_not_installed("dfoptim") testthat::skip_on_cran() require(optimx) data("Machines", package = "MEMSS") aop <- afex_options() afex_options(lmer_function = "lmerTest") m1 <- mixed(score ~ Machine + (Machine||Worker), data=Machines, expand_re = TRUE, all_fit = TRUE, progress = FALSE) afex_options(lmer_function = "lme4") m2 <- mixed(score ~ Machine + (Machine||Worker), data=Machines, expand_re = TRUE, all_fit = TRUE, method = "LRT", progress = FALSE) afex_options(aop) all_loglik1 <- attr(m1, "all_fit_logLik") all_loglik2 <- attr(m2, "all_fit_logLik") expect_false(any(is.na(all_loglik1[,1]))) expect_false(any(is.na(all_loglik2[,1]))) expect_equivalent(rep(all_loglik1[1,1], nrow(all_loglik1)), all_loglik1[,1]) expect_equivalent(rep(all_loglik2[1,1], nrow(all_loglik2)), all_loglik2[,1]) }) test_that("mixed: return=data works", { data("ks2013.3") ks2013.3_tmp <- ks2013.3 ks2013.3_tmp <- mixed(response ~ validity + (believability*validity||id), ks2013.3_tmp, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE, return = "data") expect_is(ks2013.3_tmp, "data.frame") if (packageVersion("testthat") >= "0.11.0.9000") expect_gt(ncol(ks2013.3_tmp), ncol(ks2013.3)) expect_output(print(colnames(ks2013.3_tmp)), "re1.believability1_by_validity1") }) test_that("mixed with all available methods", { data("sk2011.2") # see example("mixed") testthat::skip_on_travis() testthat::skip_on_cran() sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) for (i in c(2, 3)) { sk2_aff_kr <- mixed(response ~ instruction*type+(inference||id), sk2_aff, expand_re = TRUE, all_fit = FALSE, method = "KR", progress=FALSE, type = i) sk2_aff_s <- mixed(response ~ instruction*type+(inference||id), sk2_aff, expand_re = TRUE, all_fit = FALSE, method = "S", progress=FALSE, type = i) sk2_aff_nkr <- mixed(response ~ instruction*type+(inference||id), sk2_aff, progress = FALSE, type = i, expand_re = TRUE, all_fit = FALSE, method = "nested-KR") sk2_aff_lrt <- mixed(response ~ instruction*type+(inference||id), sk2_aff, progress = FALSE, type = i, expand_re = TRUE, all_fit = FALSE, method = "LRT") sk2_aff_pb <- mixed(response ~ instruction*type+(inference||id), sk2_aff, progress = FALSE, type = i, args_test = list(nsim = 10), expand_re = TRUE, all_fit = FALSE, method = "PB") expect_is(sk2_aff_kr, "mixed") expect_is(sk2_aff_s, "mixed") expect_is(sk2_aff_nkr, "mixed") expect_is(sk2_aff_lrt, "mixed") expect_is(sk2_aff_pb, "mixed") expect_is(anova(sk2_aff_kr), "anova") expect_is(anova(sk2_aff_s), "anova") expect_is(anova(sk2_aff_nkr), "anova") expect_is(anova(sk2_aff_lrt), "anova") expect_is(anova(sk2_aff_pb), "anova") expect_output(print(sk2_aff_kr), "Effect") expect_output(print(sk2_aff_kr), "F") expect_output(print(sk2_aff_s), "Effect") expect_output(print(sk2_aff_s), "F") expect_output(print(sk2_aff_nkr), "Effect") expect_output(print(sk2_aff_nkr), "F") expect_output(print(sk2_aff_lrt), "Effect") expect_output(print(sk2_aff_lrt), "Chisq") expect_output(print(sk2_aff_pb), "Effect") expect_output(print(sk2_aff_pb), "Chisq") } }) test_that("mixed all_fit = TRUE works with old methods", { data("sk2011.2") # see example("mixed") testthat::skip_on_cran() sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk2_aff_b <- mixed(response ~ instruction+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE, method = "nested-KR", progress = FALSE) sk2_aff_b2 <- mixed(response ~ instruction*type+(inference||id), sk2_aff, type = 2, expand_re = TRUE, all_fit = TRUE, method = "nested-KR", progress = FALSE) expect_is(sk2_aff_b, "mixed") expect_length(attr(sk2_aff_b, "all_fit_selected"), 2) expect_length(attr(sk2_aff_b, "all_fit_logLik"), 2) expect_is(sk2_aff_b2, "mixed") expect_length(attr(sk2_aff_b2, "all_fit_selected"), 5) expect_length(attr(sk2_aff_b2, "all_fit_logLik"), 5) }) test_that("mixed all_fit = TRUE works with new (KR) methods", { data("sk2011.2") # see example("mixed") testthat::skip_on_cran() sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk2_aff_b <- mixed(response ~ instruction+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE, method = "KR", progress = FALSE) sk2_aff_b2 <- mixed(response ~ instruction*type+(inference||id), sk2_aff, type = 2, expand_re = TRUE, all_fit = TRUE, method = "KR", progress = FALSE) expect_is(sk2_aff_b, "mixed") expect_named(attr(sk2_aff_b, "all_fit_selected"), "full_model") expect_false(is.null(attr(sk2_aff_b, "all_fit_logLik"))) expect_is(sk2_aff_b2, "mixed") expect_named(attr(sk2_aff_b2, "all_fit_selected"), "full_model") expect_false(is.null(attr(sk2_aff_b2, "all_fit_logLik"))) }) test_that("anova_table attributes", { data(obk.long) symbol_test <- mixed(value ~ treatment * phase + (1|id), obk.long, sig_symbols = c("", "a", "aa", "aaa"), progress = FALSE, return = "nice") expect_output(print(symbol_test), "aaa") symbol_test <- mixed(value ~ treatment * phase + (1|id), obk.long, sig_symbols = c("", "a", "aa", "aaa"), progress = FALSE) expect_output(print(symbol_test), "aaa") expect_output(print(nice(symbol_test, sig_symbols = c("", "b", "bb", "bbb"))), "bbb") new_symbols <- c(" ", " b", " bb", " bbb") symbol_test <- anova(symbol_test, sig_symbols = c(" ", " b", " bb", " bbb")) expect_identical(attr(symbol_test, "sig_symbols"), new_symbols) expect_output(print(nice(symbol_test)), "bbb") # Test support for old afex objects old_afex_object <- default_options <- mixed(value ~ treatment * phase + (1|id), obk.long, progress = FALSE) attr(old_afex_object$anova_table, "sig_symbols") <- NULL expect_that(nice(old_afex_object), is_identical_to(nice(default_options))) }) afex/tests/testthat/test-afex_plot-default-support.R0000644000176200001440000000503313432553127022422 0ustar liggesuserscontext("afex_plot: default method supported models") test_that("lm works", { warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks) p1 <- afex_plot(warp.lm, "tension") d1 <- afex_plot(warp.lm, "tension", return = "data") p2 <- afex_plot(warp.lm, "tension", "wool") d2 <- afex_plot(warp.lm, "tension", "wool", return = "data") expect_is(p1, "ggplot") expect_is(p2, "ggplot") expect_equal(nrow(d2$data), nrow(warpbreaks)) expect_equal(nrow(d1$data), nrow(warpbreaks)) }) test_that("poisson glm works", { ins <- data.frame( n = c(500, 1200, 100, 400, 500, 300), size = factor(rep(1:3,2), labels = c("S","M","L")), age = factor(rep(1:2, each = 3)), claims = c(42, 37, 1, 101, 73, 14)) ins.glm <- glm(claims ~ size + age + offset(log(n)), data = ins, family = "poisson") p1 <- afex_plot(ins.glm, "size") p2 <- afex_plot(ins.glm, "size", "age") expect_is(p1, "ggplot") expect_is(p2, "ggplot") }) test_that("binomial glm works", { ldose <- factor(rep(0:5, 2)) numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16) sex <- factor(rep(c("M", "F"), c(6, 6))) SF <- numdead/20 ## dv should be a vector, no matrix budworm.lg <- glm(SF ~ sex*ldose, family = binomial, weights = rep(20, length(numdead))) p1 <- afex_plot(budworm.lg, "ldose") p2 <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! expect_is(p1, "ggplot") expect_is(p2, "ggplot") }) test_that("nlme works", { skip_if_not_installed("nlme") data(Oats, package = "nlme") Oats$nitro <- factor(Oats$nitro) oats.1 <- nlme::lme(yield ~ nitro * Variety, random = ~ 1 | Block / Variety, data = Oats) p1 <- afex_plot(oats.1, "nitro", "Variety", data = Oats) p2 <- afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block") p3 <- afex_plot(oats.1, "nitro", data = Oats) p4 <- afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")) p5 <- afex_plot(oats.1, "nitro", data = Oats, id = "Block") expect_is(p1, "ggplot") expect_is(p2, "ggplot") expect_is(p3, "ggplot") expect_is(p4, "ggplot") expect_is(p5, "ggplot") d3 <- afex_plot(oats.1, "nitro", data = Oats, return = "data") d4 <- afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety"), return = "data") d5 <- afex_plot(oats.1, "nitro", data = Oats, id = "Block", return = "data") expect_equal(nrow(d3$data), nrow(Oats)) expect_equal(nrow(d4$data), nrow(Oats)) expect_true(nrow(d5$data) < nrow(Oats)) })afex/tests/testthat/anova_hf_error.rda0000644000176200001440000001016413351525342017666 0ustar liggesusers7zXZi"6!X-5])TW"nRʟx8OgWF7,ا$ͺ]{¡u?n~ .\G$U"|y;ᑘ; F%~$"(n 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treatment + Error(id), data = obk.long, fun_aggregate = mean) between_2 <- aov_car(value ~ treatment*gender + Error(id), data = obk.long, fun_aggregate = mean) mixed <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long) within <- aov_car(value ~ 1 + Error(id/(phase*hour)), data = obk.long) test_that("Levene Test works", { l1 <- test_levene(between_1) l2 <- test_levene(between_2) l3 <- test_levene(mixed) expect_is(l1, "anova") expect_is(l1, "data.frame") expect_is(l2, "anova") expect_is(l2, "data.frame") expect_is(l3, "anova") expect_is(l3, "data.frame") expect_error(test_levene(within), "between-subjects") }) test_that("Sphericity Test works", { expect_error(test_sphericity(between_1), "within-subjects") expect_error(test_sphericity(between_2), "within-subjects") s1 <- test_sphericity(mixed) expect_is(s1, "anova") s2 <- test_sphericity(within) expect_is(s2, "anova") }) afex/tests/testthat/test-afex_plot-vignette.R0000644000176200001440000001030513531236423021104 0ustar liggesuserscontext("afex_plot vignette: saved objects replicate") test_that("glmmTMB object", { skip_on_cran() skip_if_not_installed("glmmTMB") library("glmmTMB") set_sum_contrasts() tmb2 <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) load(system.file("extdata/", "tmb_example_fit.rda", package = "afex")) expect_equivalent(tmb, tmb2, tolerance = 0.001) skip_if_not_installed("cowplot") skip_if_not_installed("ggplot2") library("ggplot2") po <- cowplot::plot_grid( afex_plot(tmb, "spp"), afex_plot(tmb, "spp", data_geom = geom_violin), afex_plot(tmb, "spp", id = "site", data = Salamanders), labels = "AUTO", nrow = 1 ) pn <- cowplot::plot_grid( afex_plot(tmb2, "spp"), afex_plot(tmb2, "spp", data_geom = geom_violin), afex_plot(tmb2, "spp", id = "site", data = Salamanders), labels = "AUTO", nrow = 1 ) expect_equivalent(po$data, pn$data) }) test_that("rstanarm plots", { skip_on_cran() skip_if_not_installed("rstanarm") library("rstanarm") ## requires resetting the ggplot2 theme skip_if_not_installed("ggplot2") library("ggplot2") set_sum_contrasts() cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) capture_output({ example_model <- rstanarm::stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) }) b1n <- afex_plot(example_model, "period") b2n <- afex_plot(example_model, "period", data_geom = geom_violin) expect_is(b1n, "ggplot") expect_is(b2n, "ggplot") ## make cbpp long cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$herd[i], period = cbpp$period[i], incidence = rep(0, cbpp$size[i]) ) cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 } cbpp_l <- do.call("rbind", cbpp_l) cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) capture_output({ example_model2 <- rstanarm::stan_glmer(incidence ~ period + (1|herd), data = cbpp_l, family = binomial, chains = 2, cores = 1, seed = 12345, iter = 500) }) b3n <- afex_plot(example_model2, "period") b4n <- afex_plot(example_model2, "period", id = "herd") # b3n <- afex_plot(example_model2, "period", id = "herd", data = cbpp_l) expect_is(b3n, "ggplot") expect_is(b4n, "ggplot") skip_if_not_installed("MEMSS") data("Machines", package = "MEMSS") suppressWarnings(capture_output({ mm <- rstanarm::stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) })) b5n <- afex_plot(mm, "Machine") b6n <- afex_plot(mm, "Machine", id = "Worker") load(system.file("extdata/", "plots_rstanarm.rda", package = "afex")) expect_equivalent(b1$data, b1n$data, tolerance = 0.1) expect_equivalent(b2$data, b2n$data, tolerance = 0.1) expect_equivalent(b3$data, b3n$data, tolerance = 0.1) expect_equivalent(b4$data, b4n$data, tolerance = 0.1) expect_equivalent(b5$data, b5n$data, tolerance = 0.1) expect_equivalent(b6$data, b6n$data, tolerance = 0.1) }) test_that("brms plots", { skip_on_cran() skip_on_travis() skip_if_not_installed("brms") library("brms") ## requires resetting the ggplot2 theme skip_if_not_installed("ggplot2") skip_if_not_installed("MEMSS") library("ggplot2") set_sum_contrasts() data("Machines", package = "MEMSS") suppressWarnings(capture_output({ mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) })) bb1n <- afex_plot(mm2, "Machine", data = Machines, dv = "score") bb2n <- afex_plot(mm2, "Machine", id = "Worker", data = Machines, dv = "score") load(system.file("extdata/", "plots_brms.rda", package = "afex")) expect_equivalent(bb1$data, bb1n$data, tolerance = 0.1) expect_equivalent(bb2$data, bb2n$data, tolerance = 0.1) }) afex/tests/testthat/test-lmerTest-support.R0000644000176200001440000000250113351525342020611 0ustar liggesusers context("interplay with lmerTest") test_that("mixed allows both lme4 and lmerText calls and exports lmerTest::lmer", { aop <- afex_options() data(sk2011.1) m1 <- mixed(response ~ instruction*inference*plausibility +(1|id), sk2011.1, progress = FALSE, return = "merMod") m1b <- lmer(response ~ instruction*inference*plausibility +(1|id), sk2011.1) expect_true(inherits(m1, "merModLmerTest") || inherits(m1, "lmerModLmerTest")) expect_is(m1, "merMod") expect_true(inherits(m1b, "merModLmerTest") || inherits(m1b, "lmerModLmerTest")) afex_options(lmer_function = "lme4") m2 <- mixed(response ~ instruction*inference*plausibility +(1|id), sk2011.1, progress = FALSE, return = "merMod") expect_false(inherits(m2, "merModLmerTest") && inherits(m2, "lmerModLmerTest")) expect_is(m2, "merMod") afex_options(aop) expect_true("Pr(>F)" %in% colnames(lmerTest_anova(m1))) expect_true("Pr(>F)" %in% colnames(lmerTest_anova(m1b))) expect_false("Pr(>F)" %in% colnames(anova(m2))) expect_true("Pr(>F)" %in% colnames(lmerTest_anova(m2))) ## following tests only work with new lmerTest (March 2018) pkg_version <- "2.0-37.9005" skip_if(packageVersion(pkg = "lmerTest") < pkg_version) expect_true("Pr(>F)" %in% colnames(anova(m1))) expect_true("Pr(>F)" %in% colnames(anova(m1b))) }) afex/tests/testthat/test-mixed-bugs.R0000644000176200001440000001022513506224623017346 0ustar liggesusers context("mixed: known bugs") test_that("character variables are treated as factors", { data("sk2011.2") # use only affirmation problems (S&K also splitted the data like this) sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk_m1 <- mixed(response ~ instruction*inference+(1|id), sk2_aff, method = "LRT", progress = FALSE) sk2_aff$instruction <- as.character(sk2_aff$instruction) sk2_aff$inference <- as.character(sk2_aff$inference) sk_m2 <- mixed(response ~ instruction*inference+(1|id), sk2_aff, method = "LRT", progress = FALSE) expect_equivalent(anova(sk_m1), anova(sk_m2)) }) test_that("mixed works with long formulas", { data(obk.long) obk2 <- obk.long colnames(obk2) <- sapply(colnames(obk2), function(x) paste0(x, x, x, x, x, x)) expect_is(mixed(valuevaluevaluevaluevaluevalue ~ treatmenttreatmenttreatmenttreatmenttreatmenttreatment * phasephasephasephasephasephase * hourhourhourhourhourhour + (1|idididididid), obk2, method = "LRT", progress = FALSE), "mixed") }) test_that("nice.mixed and print.mixed can handle old objects", { # created via: # require(devtools) # dev_mode() # install_url("https://cran.rstudio.com/src/contrib/Archive/afex/afex_0.13-145.tar.gz") # require(afex) # data(obk.long) # m1 <- mixed(value ~ treatment * phase + (1|id), obk.long) # m2 <- mixed(value ~ treatment * phase + (1|id), obk.long, method = "LRT") # m3 <- mixed(value ~ treatment * phase + (1|id), obk.long, method = "PB") # save(m1, m2, m3, file = "lmm_old_object.rda") # dev_mode() load("lmm_old_object.rda") # # load("tests/testthat/lmm_old_object.rda") expect_is(suppressWarnings(nice(m1)), "data.frame") expect_is(suppressWarnings(nice(m2)), "data.frame") expect_is(suppressWarnings(nice(m3)), "data.frame") expect_output(suppressWarnings(print(m1)), "treatment") expect_output(suppressWarnings(print(m2)), "treatment") expect_output(suppressWarnings(print(m3)), "treatment") }) test_that("nice.mixed, print.mixed, and anova.mixed can handle objects with full.models", { load("mixed_with_dot.rda") # #load("tests/testthat/mixed_with_dot.rda") expect_is(suppressWarnings(nice(sk_m1)), "data.frame") expect_is(suppressWarnings(nice(sk_m2)), "data.frame") expect_is(suppressWarnings(nice(t2)), "data.frame") expect_output(suppressWarnings(print(sk_m1)), "instruction") expect_output(suppressWarnings(print(sk_m2)), "instruction") expect_output(suppressWarnings(print(t2)), "treatment") expect_is(anova(sk_m1), "data.frame") expect_is(anova(sk_m2), "data.frame") expect_is(anova(t2), "data.frame") }) test_that("lmer_alt works with GLMMs", { skip_if_not_installed("mlmRev") if (require("mlmRev")) { expect_that(lmer_alt(use ~ age*urban + (1 | district), family = binomial, data = Contraception, progress=FALSE), is_a("glmerMod")) } }) test_that("lmer_alt works with NA in independent variables", { data(sk2011.2) # use only affirmation problems (S&K also splitted the data like this) sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk2_aff$instruction[5] <- NA assign("sk2_aff", sk2_aff, envir = .GlobalEnv) # set up model with maximal by-participant random slopes sk_m1 <- suppressWarnings(lmer_alt(response ~ instruction*inference*type+(inference*type||id), sk2_aff, expand_re = TRUE)) expect_true(inherits(sk_m1, "merModLmerTest") || inherits(sk_m1, "lmerModLmerTest")) }) test_that("lmer_alt works with custom contrasts", { ## see: https://afex.singmann.science/forums/topic/trouble-with-ordered-contrasts-and-lmer_alt Subj <- rep(1:10, each = 10) Item <- rep(1:10, times = 10) IV1 <- rep(1:5, times = 20) DV <- rnorm(100) data <- as.data.frame(cbind(Subj, Item, IV1, DV)) data$Subj <- as.factor(data$Subj) data$Item <- as.factor(data$Item) data$IV1 <- as.factor(data$IV1) contrasts(data$IV1) <- MASS::contr.sdif(5) mafex <- lmer_alt(DV ~ IV1 + (1 + IV1||Subj) + (1|Item), data = data) expect_is(mafex, "merMod") expect_identical(colnames(ranef(mafex)$Subj), c("(Intercept)", "re1.IV12.1", "re1.IV13.2", "re1.IV14.3", "re1.IV15.4")) }) afex/tests/testthat/test-afex_aov.R0000644000176200001440000001135113506224623017073 0ustar liggesusers context("ANOVAs: check that afex_aov return value works") test_that("split-plot produces an afex_aov object without error", { data(obk.long, package = "afex") split_plot1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", return = "afex_aov") split_plot2 <- aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long, observed = "gender", return = "afex_aov") split_plot3 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), observed = "gender", return = "afex_aov") expect_that(split_plot1, is_equivalent_to(split_plot2)) expect_that(split_plot1, is_equivalent_to(split_plot3)) expect_that(split_plot1, is_a("afex_aov")) ## is same with numeric factor: obk.long$hour <- as.numeric(as.character(obk.long$hour)) split_plot4 <- aov_car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long,observed = c("gender"), return = "afex_aov") expect_that(split_plot1, is_equivalent_to(split_plot4)) }) test_that("purely-between produces afex_aov objects without error", { data(obk.long, package = "afex") out1 <- aov_car(value ~ treatment * gender + Error(id), data = obk.long, observed = "gender", return = "afex_aov", fun_aggregate = mean) out2 <- aov_4(value ~ treatment * gender + (1|id), data = obk.long, observed = "gender", return = "afex_aov", fun_aggregate = mean) out3 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), observed = "gender", return = "afex_aov", fun_aggregate = mean) expect_that(out1, is_equivalent_to(out2)) expect_that(out1, is_equivalent_to(out3)) expect_that(out1, is_a("afex_aov")) }) test_that("purely-within produces afex_aov objects without error", { data(obk.long, package = "afex") out1 <- aov_car(value ~ Error(id/(phase*hour)), data = obk.long, return = "afex_aov") out2 <- aov_4(value ~ 1 + (phase*hour|id), data = obk.long, return = "afex_aov") out3 <- aov_ez("id", "value", obk.long, within = c("phase", "hour"), return = "afex_aov") expect_that(out1, is_equivalent_to(out2)) expect_that(out1, is_equivalent_to(out3)) expect_that(out1, is_a("afex_aov")) }) test_that("within plus covariate produces afex_aov objects without error", { data(obk.long, package = "afex") out1 <- aov_car(value ~ gender + Error(id/(phase*hour)), data = obk.long, return = "afex_aov") out2 <- aov_4(value ~ gender + (phase*hour|id), data = obk.long, return = "afex_aov") out3 <- aov_ez("id", "value", obk.long, within = c("phase", "hour"), covariate = "gender", return = "afex_aov") expect_that(out1, is_equivalent_to(out2)) expect_that(out1, is_equivalent_to(out3)) expect_that(out1, is_a("afex_aov")) }) test_that("afex_aov object contains the right things", { data(obk.long, package = "afex") out1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", return = "afex_aov") expect_that(out1[["anova_table"]], is_a(c("anova", "data.frame"))) expect_that(out1[["aov"]], is_a(c("aovlist", "listof"))) expect_that(out1[["Anova"]], is_a(c("Anova.mlm"))) expect_that(out1[["lm"]], is_a(c("mlm", "lm"))) expect_that(out1[["data"]], is_a(c("list"))) expect_that(attr(out1, "dv"), is_a(c("character"))) }) test_that("afex_aov objects works without aov object", { data(obk.long, package = "afex") a1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", include_aov = FALSE) a2 <- aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long, observed = "gender", include_aov = FALSE) a3 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), observed = "gender", include_aov = FALSE) expect_equal(a1, a2) expect_equal(a1, a3) expect_null(a1$aov) skip_if_not_installed("emmeans") expect_message(em1 <- emmeans::emmeans(a1, "treatment"), "multivariate") expect_message(em2 <- emmeans::emmeans(a1, c("phase", "hour")), "multivariate") expect_identical(as.data.frame(summary(em1))$df[1], as.data.frame(summary(em2))$df[2]) op <- afex_options() ad <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") afex_options(include_aov = FALSE) an <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") expect_null(an$aov) expect_is(ad$aov, "aovlist") em3 <- emmeans::emmeans(ad, c("phase", "hour")) expect_message(em4 <- emmeans::emmeans(a1, c("phase", "hour")), "multivariate") expect_false(any(as.data.frame(summary(em3))$df == as.data.frame(summary(em4))$df)) afex_options(op) })afex/tests/testthat/test-mixed-effects.R0000644000176200001440000000142713351525342020031 0ustar liggesuserscontext("mixed interplay with effects") test_that("mixed works with effects", { data("Machines", package = "MEMSS") # simple model with random-slopes for repeated-measures factor # requires: set_data_arg = TRUE m1 <- mixed(score ~ Machine + (Machine|Worker), data=Machines, set_data_arg = TRUE, progress = FALSE) testthat::skip_if_not_installed("effects") testthat::skip_if_not_installed("emmeans") library("effects") set_default_contrasts() em1 <- emmeans::emmeans(m1, "Machine") ef1 <- Effect("Machine", m1$full_model) # expect_false(any( as.data.frame(ef1)$fit == as.data.frame(em1)$emmean )) set_sum_contrasts() ef2 <- Effect("Machine", m1$full_model) expect_equal(as.data.frame(ef2)$fit, as.data.frame(em1)$emmean) }) afex/tests/testthat/test-afex_plot-basics.R0000644000176200001440000003056013607671457020546 0ustar liggesuserscontext("afex_plot: basic functionality") test_that("all input type works and warnings are correct", { data(obk.long, package = "afex") # estimate mixed ANOVA on the full design: a1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") expect_warning( em1 <- afex_plot(a1, ~phase*hour, ~treatment+gender, return = "data"), "mixed within-between-design" ) expect_warning( em2 <- afex_plot(a1, c("phase", "hour"), ~treatment+gender, return = "data"), "mixed within-between-design" ) expect_warning( em3 <- afex_plot(a1, ~phase*hour, c("treatment", "gender"), return = "data"), "mixed within-between-design" ) expect_warning( em4 <- afex_plot(a1, c("phase", "hour"), c("treatment", "gender"), return = "data"), "mixed within-between-design" ) expect_equal(em1, em2) expect_equal(em1, em3) expect_equal(em1, em4) expect_warning( em5 <- afex_plot(a1, c("phase", "hour"), return = "data"), "show within-subjects factors, but not within-subjects error bars" ) expect_warning( em6 <- afex_plot(a1, ~phase*hour, return = "data"), "show within-subjects factors, but not within-subjects error bars" ) expect_equal(em5, em6) expect_warning( em7 <- afex_plot(a1, c("treatment", "gender"), panel = "phase", return = "data", error = "within"), "between-subjects factors, but within-subjects error bars" ) expect_warning( em8 <- afex_plot(a1, ~treatment*gender, panel = "phase", return = "data", error = "within"), "between-subjects factors, but within-subjects error bars" ) expect_equal(em7, em8) }) test_that("ANOVA plots are produced", { data(obk.long, package = "afex") a1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") expect_is(afex_plot(a1, "hour", error = "within"), "ggplot") expect_is(afex_plot(a1, c("phase", "hour"), trace = "treatment", error = "none"), "ggplot") expect_is(afex_plot(a1, "phase", trace = "hour", panel = "treatment", error = "within"), "ggplot") }) test_that("mixed plots are produced", { data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### reduced data.frame length # fhch <- fhch[unlist(lapply(which(as.numeric(fhch$id) != # c(NA, fhch$id[-length(fhch$id)])), # function(x) 0:29 + x)),] mrt <- mixed(log_rt ~ task*stimulus*frequency + (1|id), fhch, method = "S", progress = FALSE) p1 <- afex_plot(mrt, "task", id = "id") expect_is(p1, "ggplot") expect_equal(p1$labels$y, "log_rt") p2 <- afex_plot(mrt, x = "stimulus", panel = "task", id = "id") expect_is(p2, "ggplot") expect_equal(p2$labels$y, "log_rt") p3 <- afex_plot(mrt, x = "stimulus", trace = "task", id = "id") expect_is(p3, "ggplot") expect_equal(p3$labels$y, "log_rt") p4 <- afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id") expect_is(p4, "ggplot") expect_equal(p4$labels$y, "log_rt") }) test_that("lme4::merMod plots are produced", { Oats <- nlme::Oats Oats$VarBlock <- Oats$Variety:Oats$Block Oats.lmer <- lmer(yield ~ Variety * factor(nitro) + (1|VarBlock) + (1|Block), data = Oats) p1 <- afex_plot(Oats.lmer, "nitro", id = "VarBlock") expect_is(p1, "ggplot") expect_equal(p1$labels$y, "yield") expect_is(afex_plot(Oats.lmer, "nitro", "Variety", id = "VarBlock"), "ggplot") expect_is(afex_plot(Oats.lmer, "nitro", panel = "Variety", id = "VarBlock"), "ggplot") ## check that id argument works: d1 <- afex_plot(Oats.lmer, "nitro", id = "VarBlock", return = "data") d2 <- afex_plot(Oats.lmer, "nitro", id = "Block", return = "data") d3 <- afex_plot(Oats.lmer, "nitro", id = c("Block", "VarBlock"), return = "data") expect_lt(nrow(d2$data), nrow(d1$data)) expect_lt(nrow(d2$data), nrow(d3$data)) expect_identical(nrow(d1$data), nrow(d3$data)) }) test_that("afex_plot works with various geoms (from examples)", { testthat::skip_if_not_installed("ggplot2") testthat::skip_if_not_installed("ggpol") testthat::skip_if_not_installed("ggbeeswarm") data(md_12.1) aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 5, dodge.width = 0.3 ## needs to be same as dodge ), color = "darkgrey")) expect_is(p1, "ggplot") # 2. using ggbeeswarm::geom_beeswarm p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8, color = "darkgrey")) expect_is(p2, "ggplot") # 3. do not display points, but use a violinplot: ggplot2::geom_violin p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) expect_is(p3, "ggplot") # 4. violinplots with color: ggplot2::geom_violin p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("linetype", "shape", "fill"), data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) expect_is(p4, "ggplot") # 5. do not display points, but use a boxplot: ggplot2::geom_boxplot p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3)) expect_is(p5, "ggplot") # 6. combine points with boxplot: ggpol::geom_boxjitter p6 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggpol::geom_boxjitter, data_arg = list(width = 0.3)) ## hides error bars! expect_is(p6, "ggplot") # 7. nicer variant of ggpol::geom_boxjitter p7 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.3, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0)) expect_is(p7, "ggplot") # 8. nicer variant of ggpol::geom_boxjitter without lines p8 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), line_arg = list(linetype = 0), error_arg = list(size = 1.5, width = 0)) expect_is(p8, "ggplot") }) test_that("relabeling of factors and legend works", { data(md_12.1) aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")) ## relabel factor levels via new_levels p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", factor_levels = list(angle = c("0", "4", "8"), noise = c("Absent", "Present"))) expect_equal(levels(p1$data$noise), c("Absent", "Present")) expect_equal(levels(p1$data$angle), c("0", "4", "8")) p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", factor_levels = list( angle = c(X8 = "8", X4 = "4", X0 = "0"), noise = c(present = "Present"))) expect_equal(levels(p2$data$angle), rev(c("0", "4", "8"))) expect_equal(levels(p2$data$noise), c("absent", "Present")) p1d <- afex_plot(aw, x = "noise", trace = "angle", error = "within", factor_levels = list(angle = c("0", "4", "8"), noise = c("Absent", "Present")), return = "data") p2d <- afex_plot(aw, x = "noise", trace = "angle", error = "within", factor_levels = list( angle = c(X8 = "8", X4 = "4", X0 = "0"), noise = c(present = "Present")), return = "data") expect_equal(p1d$means$lower, p2d$means$lower) expect_warning(p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "mean", factor_levels = list( angle = c(X8 = "8", X4 = "4", X0 = "0"), noise = c(present = "Present"))), "show within-subjects factors, but not within-subjects error bars") expect_equal(levels(p3$data$angle), rev(c("0", "4", "8"))) expect_warning(p3d <- afex_plot(aw, x = "noise", trace = "angle", error = "mean", factor_levels = list( angle = c(X8 = "8", X4 = "4", X0 = "0"), noise = c(present = "Present")), return = "data"), "show within-subjects factors, but not within-subjects error bars") expect_warning(p3nd <- afex_plot(aw, x = "noise", trace = "angle", error = "mean", factor_levels = list(angle = c("0", "4", "8"), noise = c("Absent", "Present")), return = "data"), "show within-subjects factors, but not within-subjects error bars") expect_equal(p3d$means$lower, p3nd$means$lower) expect_warning(p4d <- afex_plot(aw, x = "noise", trace = "angle", error = "between", factor_levels = list( angle = c(X8 = "8", X4 = "4", X0 = "0"), noise = c(present = "Present")), return = "data"), "show within-subjects factors, but not within-subjects error bars") expect_warning(p4nd <- afex_plot(aw, x = "noise", trace = "angle", error = "between", factor_levels = list(angle = c("0", "4", "8"), noise = c("Absent", "Present")), return = "data"), "show within-subjects factors, but not within-subjects error bars") expect_equal(p4d$means$lower, p4nd$means$lower) expect_error( afex_plot(aw, x = "noise", trace = "angle", error = "within", factor_levels = list(angle = c("0", "4"), noise = c("Absent", "Present"))), "length of new factor_levels for 'angle' != length of factor levels" ) p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", legend_title = "Noise Condition") expect_equal(p2$guides$shape$title, "Noise Condition") expect_equal(p2$guides$linetype$title, "Noise Condition") }) test_that("labels are correct in case variables are of lenth > 1", { data(obk.long, package = "afex") # estimate mixed ANOVA on the full design: a1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender") p1 <- afex_plot(a1, c("phase", "hour"), c("treatment", "gender"), error = "none") p2 <- afex_plot(a1, c("phase", "hour"), error = "none") expect_match(p1$labels$x, "phase") expect_match(p1$labels$x, "hour") expect_match(p1$guides$shape$title, "treatment") expect_match(p1$guides$shape$title, "gender") expect_match(p2$labels$x, "phase") expect_match(p2$labels$x, "hour") }) afex/tests/testthat/afex_aov_16_1.rda0000644000176200001440000043576513351525342017234 0ustar 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%)<ퟁ@\iGx9zc}Τ\/M9rfϏӉ4s&맣>gg_c?rĆXyD@+J'1uCPkY}kwrT*h5uXE^c1|}xW}:5}h,TQ֪ӿCA_yk"XU?VU$c/Q$c\dLKcz\gK7߽ w7VFYd?5ҫ}!Ӱ?isTƁž|h,6VD<@vnn6փXػ ,\k T`\X_Se¶$e,뺐.v璓zYǯb隻} =b#Vl̊؄X)+6c؂[<+b֬؆۲b;Vlϊ ؁;b'VTdά؅b7VTb؃{b/V͊}X/+*G33>v~QdOwy_-ozI},W;{wҨ4+8Lw7`cM3@G`{IiiQ+]PQ~8OGc 4?{gOovq)+?>?F__y\;st/~id~|qzt~?{_7hsj;d+]?Ҿn?i||}c?'y?g?&b_,:7@O }[% zdmd^B6%k;씊 NdHv2dm'J1ck;bO;:KE'd񘻩Eվ,,9K]qǵ2Lu+kakl^U"}Zz@i>Eqe98 afex/tests/testthat/test-emmeans-interface.R0000644000176200001440000002240113351525342020664 0ustar liggesusers context("interplay with emmeans") test_that("ANOVA functions work with emmeans, univariate & multivariate", { skip_if_not_installed("emmeans") data(sk2011.1) a1 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("inference", "plausibility"), fun_aggregate = mean) em1 <- emmeans::emmeans(a1, ~ inference, model = "univariate") em2 <- emmeans::emmeans(a1, ~ inference, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) em1 <- emmeans::emmeans(a1, ~ inference*plausibility, model = "univariate") em2 <- emmeans::emmeans(a1, ~ inference*plausibility, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) em1 <- emmeans::emmeans(a1, ~ plausibility*inference, model = "univariate") em2 <- emmeans::emmeans(a1, ~ plausibility*inference, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) a1b <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("plausibility", "inference"), fun_aggregate = mean) em1 <- emmeans::emmeans(a1b, ~ inference, model = "univariate") em2 <- emmeans::emmeans(a1b, ~ inference, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("inference"), fun_aggregate = mean) em1 <- emmeans::emmeans(a2, ~ inference, model = "univariate") em2 <- emmeans::emmeans(a2, ~ inference, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) a3 <- aov_ez("id", "response", sk2011.1, within = c("inference"), fun_aggregate = mean) em1 <- emmeans::emmeans(a3, ~ inference, model = "univariate") em2 <- emmeans::emmeans(a3, ~ inference, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) a4 <- aov_ez("id", "response", sk2011.1, between = "instruction", fun_aggregate = mean) em1 <- emmeans::emmeans(a4, ~ instruction, model = "univariate") em2 <- emmeans::emmeans(a4, ~ instruction, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean) expect_true(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) #### data("sk2011.2") ab1 <- aov_ez("id", "response", sk2011.2, between = "instruction", within = c("what", "validity", "type"), fun_aggregate = mean) em1 <- emmeans::emmeans(ab1, ~ what*validity*type, model = "univariate") em2 <- emmeans::emmeans(ab1, ~ what*validity*type, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean, tolerance = 0.1) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) em1 <- emmeans::emmeans(ab1, ~ validity*what*type, model = "univariate") em2 <- emmeans::emmeans(ab1, ~ validity*what*type, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean, tolerance = 0.1) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) em1 <- emmeans::emmeans(ab1, ~ type, model = "univariate") em2 <- emmeans::emmeans(ab1, ~ type, model = "multivariate") expect_is(em1, "emmGrid") expect_is(em2, "emmGrid") expect_equal(as.data.frame(summary(em2))$emmean, as.data.frame(summary(em1))$emmean, tolerance = 0.1) expect_false(isTRUE(all.equal( as.data.frame(summary(em2))$SE, as.data.frame(summary(em1))$SE))) }) test_that("ANCOVA with emmeans is correct for univariate & multivariate", { skip_if_not_installed("emmeans") data(sk2011.1) # a1 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), # within = c("phase", "hour"), covariate = "age", # observed = c("gender", "age"), factorize = FALSE) # emmeans(a1, ~ phase, model = "multivariate") # emmeans(a1, ~ phase, model = "univariate") # # emmeans(a1, ~ treatment, model = "multivariate") # emmeans(a1, ~ treatment, model = "univariate") # deactivated, see: https://github.com/rvlenth/emmeans/issues/32 a2 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), covariate = "age", fun_aggregate = mean, observed = c("gender", "age"), factorize = FALSE) em1 <- emmeans::emmeans(a2, ~ treatment, model = "univariate") em2 <- emmeans::emmeans(a2, ~ treatment, model = "multivariate") expect_equal(summary(em1)$emmean, summary(em2)$emmean) }) test_that("mixed works with emmeans", { skip_if_not_installed("emmeans") data(sk2011.1) m1 <- mixed(response ~ instruction*inference*plausibility +(1|id), sk2011.1, progress = FALSE) expect_is(emmeans::emmeans(m1, ~ inference), "emmGrid") m2 <- mixed(response ~ inference +(inference|id), sk2011.1, progress = FALSE) expect_is(emmeans::emmeans(m2, ~ inference), "emmGrid") m3 <- mixed(response ~ instruction +(inference|id), sk2011.1, progress = FALSE) expect_is(emmeans::emmeans(m3, ~ instruction), "emmGrid") }) test_that("mixed works with type=2 and all methods", { skip_if_not_installed("emmeans") emmeans::emm_options(lmer.df = "asymptotic") ## in all tests, data needs to be passed because of nested evaluation. data("sk2011.2") sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) mixed_kr <- mixed(response ~ inference*type+(1|id), sk2_aff, type=2, method="KR", progress = FALSE) expect_is(emmeans::emmeans(mixed_kr, specs = c("type"), data = sk2_aff), "emmGrid") mixed_s <- mixed(response ~ inference*type+(1|id), sk2_aff, type=2, method="S", progress = FALSE) expect_is(emmeans::emmeans(mixed_s, specs = c("type"), data = sk2_aff), "emmGrid") mixed_lrt <- mixed(response ~ inference*type+(1|id), sk2_aff, type=2, method="LRT", progress = FALSE) expect_is(emmeans::emmeans(mixed_lrt, specs = c("type"), data = sk2_aff), "emmGrid") mixed_pb <- suppressWarnings(mixed(response ~ inference*type+(1|id), sk2_aff, type=2, method="PB", progress = FALSE, args_test = list(nsim = 10))) expect_is(emmeans::emmeans(mixed_pb, specs = c("type"), data = sk2_aff), "emmGrid") mixed_oldkr <- mixed(response ~ inference*type+(1|id), sk2_aff, type=2, method="nested-KR", progress = FALSE) expect_is(emmeans::emmeans(mixed_oldkr, specs = c("type"), data = sk2_aff), "emmGrid") }) test_that("emmeans works with mixed and expand_er = TRUE", { skip_if_not_installed("emmeans") data("Machines", package = "MEMSS") m2 <- mixed(score ~ Machine + (Machine||Worker), data=Machines, expand_re = TRUE, progress = FALSE) t1 <- emmeans::emmeans(m2, "Machine", lmer.df = "asymptotic") t2 <- emmeans::emmeans(m2, "Machine", lmer.df = "Satterthwaite") t3 <- emmeans::emmeans(m2, "Machine", lmer.df = "kenward-roger") expect_is(t1, "emmGrid") expect_is(t2, "emmGrid") expect_is(t3, "emmGrid") expect_is(summary(t1), "data.frame") expect_is(summary(t2), "data.frame") expect_is(summary(t3), "data.frame") }) test_that("emmeans with mixed & expand_re = TRUE with pre 3.0 lmerTest objects", { skip_if_not_installed("emmeans") load("m_machines_lmerTest-pre3.0.rda") # load("tests/testthat/m_machines_lmerTest-pre3.0.rda") t1 <- emmeans::emmeans(m_machines, "Machine", lmer.df = "asymptotic") t2 <- emmeans::emmeans(m_machines, "Machine", lmer.df = "Satterthwaite") t3 <- emmeans::emmeans(m_machines, "Machine", lmer.df = "kenward-roger") expect_is(t1, "emmGrid") expect_is(t2, "emmGrid") expect_is(t3, "emmGrid") expect_is(summary(t1), "data.frame") expect_is(summary(t2), "data.frame") expect_is(summary(t3), "data.frame") }) afex/tests/testthat.R0000644000176200001440000000006413351525342014325 0ustar liggesuserslibrary(testthat) library(afex) test_check("afex") afex/vignettes/0000755000176200001440000000000013607677016013222 5ustar liggesusersafex/vignettes/introduction-mixed-models.pdf.asis0000644000176200001440000000027713351525342021755 0ustar liggesusers%\VignetteIndexEntry{An Introduction to Mixed Models for Experimental Psychology} %\VignetteEngine{R.rsp::asis} %\VignetteKeyword{PDF} %\VignetteKeyword{vignette} %\VignetteKeyword{package} afex/vignettes/afex_plot_introduction.Rmd0000644000176200001440000006345713607676143020467 0ustar liggesusers--- title: "afex_plot: Publication Ready Plots for Experimental Designs" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{afex_plot: Publication Ready Plots for Experimental Designs} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` `afex_plot()` visualizes results from factorial experiments combining estimated marginal means and uncertainties associated with the estimated means in the foreground with a depiction of the raw data in the background. Currently, `afex_plots()` supports the following models: - ANOVAs estimated with `aov_car()`, `aov_ez()`, or `aov_4()` (i.e., objects of class `"afex_aov"`) - Linear mixed models estimated with `mixed()` (i.e., objects of class `"mixed"`) - Linear mixed models estimated with `lme4::lmer` (i.e., objects of class `"merMod"`) This document provides an overview of the plots possible with `afex_plot()`. It does so mostly using the `afex_plot()` examples, see `?afex_plot`. We begin by loading `afex` and [`ggplot2`](https://ggplot2.tidyverse.org/) which is the package `afex_plot()` uses for plotting. Loading `ggplot2` explicitly is not strictly necessary, but makes the following code nicer. Otherwise, we would need to prepend each call to a function from `ggplot2` needed for customization with `ggplot2::` (as is done in the examples in `?afex_plot`). We also load the [`cowplot`](https://cran.r-project.org/package=cowplot) package ([introduction](https://cran.r-project.org/package=cowplot/vignettes/introduction.html)) which makes combining plots (with functions `plot_grid()` and `legend()`) very easy. However, loading `cowplot` sets a different theme for `ggplot2` plots than the default grey one. Although I am not a big fan of the default theme with its grey background, we reset the theme globally using `theme_set(theme_grey())` to start with the default behavior if `cowplot` it not attached. Note that `cowplot` also has the cool `draw_plot()` function which allows embedding plots within other plots. We furthermore will need the following packages, however, we will not attach them directly, but only call a few selected functions using the `package::function` notation. - [`jtools`](https://cran.r-project.org/package=jtools) for `theme_apa()` - [`ggpubr`](https://cran.r-project.org/package=jtools) for `theme_pubr()` - [`ggbeeswarm`](https://cran.r-project.org/package=ggbeeswarm) for producing bee swarm plots with `geom_beeswarm` - [`ggpol`](https://cran.r-project.org/package=ggpol) for producing combined box plots and jitter plots using `geom_boxjitter()` ```{r message=FALSE, warning=FALSE} library("afex") library("ggplot2") library("cowplot") theme_set(theme_grey()) ``` # Two-Way Within-Subjects ANOVA We begin with a two-way within-subjects ANOVA using synthetic data from Maxwell and Delaney (2004, p. 547). The data are hypothetical reaction times from a 2 x 3 Perceptual Experiment with factors `angle` with 3 levels and factor `noise` with 2 levels (see `?md_12.1` for a longer description). We first load the data and then fit the corresponding ANOVA. ```{r} data(md_12.1) (aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"))) ``` The ANOVA shows that both, the two main effect as well as the interaction, are significant. We therefore inspect the pattern underlying the interaction. There exist two different ways of plotting a 2-way interaction. Either of the two variables can be depicted on the x-axis. And before having looked at both cases, it is often not clear which visualization of the interaction is more instructive. Consequently, we plot both next to each other. For this we simply need to exchange which variable is the `x` factor and which is the `trace` factor. We then use `plot_grid()` to plot them next to each other. ## Basic Plot ```{r fig.width=9, fig.height=4} p_an <- afex_plot(aw, x = "angle", trace = "noise") p_na <- afex_plot(aw, x = "noise", trace = "angle") plot_grid(p_an, p_na) ## try adding: labels = "AUTO" ``` Before we can even take a look at the plot, we notice that creating the plots has produced two warnings. These warnings complain that the plots depict within-subject factors, but do not use within-subject error bars. However, the warnings also tell us the solution (i.e., adding `error = "within"`), which we will do in the following. The help page `?afex_plot` contains more information on which type of error bars are appropriate in which situation and how to interpret different type of error bars. For ANOVAs, `afex_plot()` will emit warnings if it thinks the error bars are not appropriate for the chosen factors. Comparing both plots, my impression is that the plot with `angle` on the `x`-axis tells the clearer story. We can see that when `noise` is `absent` there is hardly any effect of the increase of `angle`. However, if `noise` is `present` an increasing `angle` clearly leads to increased RTs. We therefore use this plot in the following. ## Exploring Graphical Options and Themes We now produce a new variant of the left plot using more appropriate error bars and change several other graphical details which make the plot publication ready. We use the `factor_levels` argument to `afex_plot()` for renaming the factor levels (for technical reasons the ANOVA functions in `afex` transform all factor levels to proper `R` variable names using `make.names()` which changed the labels from e.g., `4` to `X4`) and the `legend_title` argument for changing the title of the legend. We also change the labels on the `x` and `y` axis. ```{r} p_an <- afex_plot(aw, x = "angle", trace = "noise", error = "within", factor_levels = list(angle = c("0°", "4°", "8°"), noise = c("Absent", "Present")), legend_title = "Noise") + labs(y = "RTs (in ms)", x = "Angle (in degrees)") ``` As the additional output shows, changing the factor levels via `factor_levels` emits a `message` detailing old and new factor levels in the form `old -> new`. This message can be suppressed by wrapping the `afex_plot()` call into a `suppressMessages()` call or via `RMarkdown` settings. Note that we could have also used the `factor_levels` argument for changing the order of the factor levels by passing a named character vector (e.g., `factor_levels = list(angle = c(X8 = "8°", X4 = "4°", X0 = "0°"))`). This would change the order either on the x-axis or in the legend. As said above, I am not a big fan of the default grey theme of `ggplot2` plots. Consequently, we compare a number of different themes for this plot in the following. For all but `ggpubr::theme_pubr()`, we also move the legend to the bottom as this better allows the plot to cover only a single column in a two-column layout. `ggpubr::theme_pubr()` automatically plots the legend on top. ```{r fig.width=8.5, fig.height=6, dpi = 150} plot_grid( p_an + theme_bw() + theme(legend.position="bottom"), p_an + theme_light() + theme(legend.position="bottom"), p_an + theme_minimal() + theme(legend.position="bottom"), p_an + jtools::theme_apa() + theme(legend.position="bottom"), p_an + ggpubr::theme_pubr(), p_an + theme_cowplot() + theme(legend.position="bottom"), labels = "AUTO" ) ``` The first row, panels A to C, shows themes coming with `ggplot2` and the second row, panels D to F, shows themes from additional packages. In my opinion all of these plots are an improvement above the default grey theme. For the themes coming with `ggplot2`, I really like that those shown here have a reference grid in the background. This often makes it easier to judge the actual values the shown data points have. I know that many people find this distracting, so many of the contributed themes do not have this grid. One thing I really like about the last two themes is that they per default use larger font sizes for the axes labels. One way to achieve something similar for most themes is to change `base_size`. One general criticism I have with the current plots is that they show too many values on the y-axis. In the following I plot one more variant of this plot in which we change this to three values on the y-axis. We also increase the axes labels and remove the vertical grid lines. ```{r fig.width=3.5, fig.height=3, dpi = 150, out.width='50%'} p_an + scale_y_continuous(breaks=seq(400, 900, length.out = 3)) + theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank()) ``` We can also set this theme for the reminder of the `R` session with `theme_set()`. ```{r} theme_set(theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank())) ``` ## Saving Plots and Plot Sizes To get our plot into a publication, we need to export it as a graphics file. I would generally advise against exporting plots via the `RStudio` interface as this is not reproducible. Instead I would use some of the following functions which save the document in the current working directory. Note that following [Elsevier guidelines](https://www.elsevier.com/authors/author-schemas/artwork-and-media-instructions/artwork-sizing), a single column figure should have a width of 9 cm (~ 3 inch) and a two column figure should have a width of 19 cm (~ 7.5 inch). For Word or similar documents I would export the plot as a `png` (never `jpg`): ```{r, eval=FALSE} ggsave("my_plot.png", device = "png", width = 9, height = 8, units = "cm", dpi = 600) ## the higher the dpi, the better the resolution ``` For `LaTeX` I would export as `pdf`: ```{r, eval=FALSE} ggsave("my_plot.pdf", device = "pdf", width = 9, height = 8, units = "cm") ``` ## Data in the Background `afex_plot()` per default plots the raw data in the background. It does so using an [alpha blending](https://en.wikipedia.org/wiki/Alpha_compositing#Alpha_blending) of `0.5`. Thus, overlapping points appear darker. Examples of this can be seen in the previous graphs where some data points in the background appear clearly darker than others. The darker points indicate values for which several data points lie exactly on top of each other. `afex_plot()` provides the possibility to change or alter the graphical primitive, called `geom` in `ggplot2` parlance, used for plotting the points in the background. This offers a vast array of options for handling overlapping points or, more generally, how to display the raw data in the background. I show some of these examples in the following. The first two variants display only points, whereas the remaining ones use different visualizations of the raw data. Note that depending on the specific variant we change a few further plot options to obtain a visually pleasing result. For example, the `dodge` argument controls the spread of points belonging to different levels of the `trace` factor at each x-axis position. 1. Add jitter on the y-axis to points which avoids perfect overlap. 2. Display points using a bee swarm plot, which displaces overlapping points on the x-axis: `ggbeeswarm::geom_beeswarm` 3. Size of points show number of data points at a given y-axis position: `geom_count`. For this geom, adding a call to `scale_size_area()` can sometimes be beneficial. 3. Violin plot: `geom_violin` 4. Box plot: `geom_boxplot`. Note that for this plot we have added `linetype = 1` to `data_arg`, which avoids that the outline of the box plots is affected by the linetype mapping (this is in contrast with the violin plot). 5. Combine box plot with jittered points: `ggpol::geom_boxjitter` ```{r fig.width=8.5, fig.height=12, dpi = 150} p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 10, dodge.width = 0.3 ## needs to be same as dodge ), color = "darkgrey")) p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8, color = "darkgrey")) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = geom_count) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3, linetype = 1)) p6 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0)) plot_grid(p1, p2, p3, p4, p5, p6, ncol = 2, labels = 1:6) ``` ## Adding Color to Plots So far, all plots were shown in black and white only. However, it is easy to include color. We do so for plots 2 to 5 from above. To achieve this, we have to change the value of the `mapping` argument. ```{r fig.width=8.5, fig.height=8, dpi = 150} p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, mapping = c("shape", "color"), data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8)) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("linetype", "shape", "fill"), data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("shape", "fill"), data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), line_arg = list(linetype = 0), error_arg = list(size = 1.5, width = 0)) plot_grid(p2, p3, p4, p5, ncol = 2, labels = 2:5) ``` ## Plotting Order and Error Bars For graphical element in the foreground, `afex_plot` first plots all graphical elements belonging to the same factor level before plotting graphical elements belonging to different factor levels. This provides a consistent graphical impression for each factor level that is particularly relevant in case color is mapped. In case we have overlapping lines and error bars or use thick lines, we sometimes do not want that the error bars also receives different line types. In this case, we can simply pass `linetype = 1` to `error_arg` to overwrite the corresponding mapping. This is shown in the right plot. ```{r fig.width=8.5, fig.height=4, dpi = 150} p1 <- afex_plot(aw, x = "noise", trace = "angle", mapping = "color", error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2)) p2 <- afex_plot(aw, x = "noise", trace = "angle", mapping = c("color", "shape", "linetype"), error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2, width = 0, linetype = 1)) plot_grid(p1, p2, ncol = 2) ``` ## One-way Plots Without Trace Factor If `afex_plot` is called without a trace factor, a one-way plot is created. We can customize this plot in very much the same way. Per default a one-way plot contains a legend if `mapping` is not empty (i.e., `""`). We show this legend for the left plot, but suppress it for the right one. ```{r fig.width=7, fig.height=3.5, message=FALSE} po1 <- afex_plot(aw, x = "angle", mapping = "color", error = "within", data_arg = list(), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) po2 <- afex_plot(aw, x = "angle", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") plot_grid(po1, po2) ``` One-way plots can also be split across different panels by specifying a `panel` factor: ```{r fig.width=7, fig.height=3.5, message=FALSE} afex_plot(aw, x = "angle", panel = "noise", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") ``` Sometimes we still want to add a line connecting the estimated marginal means. As `afex_plot` returns a `ggplot2` object, we can do this easily by adding a `geom_line()` object to the call. As we want to add a line through all of the shown points in the foreground, we need to add the corresponding groups aesthetics to this call: `geom_line(aes(group = 1))`. We can add further arguments to this call, as shown in the left panel below. ```{r fig.width=7, fig.height=3.5, message=FALSE} plot_grid( po1 + geom_line(aes(group = 1), color = "darkgrey", size = 1.5), po2 + geom_line(aes(group = 1)) ) ``` # 3-Way Mixed Model ## Data and Model ```{r, eval=FALSE, echo=FALSE, results='hide'} data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### following model should take less than a minute to fit: mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ (task||item), fhch, method = "S", expand_re = TRUE) save(mrt, file = "../inst/extdata/freeman_reduced_model.rda", compress = "xz") ``` To exemplify the support for linear mixed models, we will use the data from Freeman and colleagues also discussed in the [mixed model vignette](https://cran.r-project.org/package=afex/vignettes/afex_mixed_example.html). These data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The dependent variable we are interested in is `log` RTs. Here, we are only looking at a reduced design with factors `task` (between participants, but within items), `stimulus`, and `frequency` (within participants, but between items), for a total of almost 13,000 observations. We fit the model with crossed-random effects for participants (`id`) and `item`s with maximal random-slopes. To reduce computation time we suppress the correlations among random-effects parameters. ```{r, eval=FALSE} data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### following model should take less than a minute to fit: mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ (task||item), fhch, method = "S", expand_re = TRUE) ``` Instead of fitting the model, you can also load the fitted model. We also disable calculation of degrees of freedom for `emmeans` as this speeds up computation and/or avoids messages we are currently not interested in. ```{r} load(system.file("extdata/", "freeman_reduced_model.rda", package = "afex")) emmeans::emm_options(lmer.df = "asymptotic") ``` The ANOVA table of the mixed model indicates that the three-way interaction is significant on which we focus in the following. ```{r} mrt ``` ## Which Data to Plot in the Background For mixed models, one important decision is the random-effects grouping factor(s) based on which the raw data plotted in the background is aggregated. This decision is necessary, because without such a factor, there would only be one observation for each cell of the design (unless the full design is considered). In the default setting, with `id` missing, the combination of all random-effects grouping factor is used. ```{r fig.width=7, fig.height=3.5} afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task") ``` In the present case, a message informs us that the data is aggregated over both random-effects grouping factors. However, this leads to way too many data points in the background. Let us compare this plot with plots in which we use each of the two random-effects grouping factors in turn. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item"), labels = c("ID", "Item") ) ``` The by-id plot looks usable. However, the by-item plot has still way too many data-points to be informative. Some other ways of displaying the raw data, such as violin plots or box plots, seems preferable for it. ## Ways of Plotting Data in the Background We compare violin plots or box plots for the by-item data in the next plot. For the box plot, we increase the width of the error bars and use a consistent line type to distinguish them more easily from the graphical elements of the box plot. We could probably further improve these plots by, for example, adding colors or using some of the other customizations discussed above for the ANOVA example. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_violin, data_arg = list(width = 0.5)), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_boxplot, data_arg = list(width = 0.5), error_arg = list(size = 1.5, width = 0, linetype = 1)) ) ``` ## Error Bars for Mixed Models The default error bars for `afex_plot()` are based on the statistical model (i.e., the mixed model in the present case). These error bars can only be used to judge whether or not two means differ from each other, if the corresponding factor (or factors) are independent samples factors (i.e., not repeated-measures factors for any of the random-effects grouping factors). Of course, in addition to this the requirement of approximately equal sample size and variance also needs to hold. In the present case, all of the factors are repeated-measures factors with respect to one of the random-effects grouping factors. Consequently, the default error bars cannot be used for "inference by eye" for any of the factors. This is also easy to see when looking at all pairwise comparisons between means for each of the panels/tasks. This shows that for the `naming` task all comparisons are significant. In visual contrast with that, the two error bars for the `low` versus `high` `word`s are overlapping very strongly. ```{r} pairs(emmeans::emmeans(mrt, c("stimulus", "frequency"), by = "task")) ``` An alternative in the present situation would be using within-subjects error bars and aggregating the data by-id (i.e., `error = "within"`), as done in the left panel below. This is somewhat appropriate here as the factors within each panel are all within-subject factors. In contrast, using by-item within-subjects error bars, as done in the right panel below, seems not appropriate as the only within-item factor, `task`, is spread across panels. Unfortunately, it is not immediately clear if these error bars allow one to correctly detect, which means do not differ from each other. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id", error = "within"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, error = "within", data_geom = geom_violin, data_arg = list(width = 0.5)) ) ``` In sum, using error bars for performing "inference by eye" - that is, using overlap or non-overlap of error bars to judge which means differ or do not differ from each other - is highly problematic for mixed models, due to the potentially complex dependency structures between the means. It would be best to avoid comparisons between means altogether. Instead, it is perhaps a good idea to plot the model-based error bars (which is the default) and use them for their intended purpose; judging which values of the estimated means are likely given what we have learned from the model (however, note that one cannot interpret a 95% confidence interval as having a 95% probability of containing the population mean). The help page `?afex_plot` contains further information and references on how to interpret confidence intervals and other error bars. # References * Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. _Journal of Memory and Language_, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004 * Maxwell, S. E., & Delaney, H. D. (2004). _Designing Experiments and Analyzing Data: A Model-Comparisons Perspective._ Mahwah, N.J.: Lawrence Erlbaum Associates. afex/vignettes/afex_plot_supported_models.Rmd0000644000176200001440000004274713531256341021323 0ustar liggesusers--- title: "afex_plot: Supported Models" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{afex_plot: Supported Models} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) knitr::knit_hooks$set(document = function(x){ gsub("```\n*```r*\n*", "", x) }) ``` # Introduction `afex_plot()` visualizes results from factorial experiments and, more generally, data set with interactions of categorical/factor variables. It does so by combining estimated marginal means and uncertainties associated with these means in the foreground with a depiction of the raw data in the background. If models include continuous covariates, other approaches are recommended (e.g., such as implemented in package [`effects`](https://cran.r-project.org/package=effects) or by using the possibility of `afex_plot` [to return the data and build the plot on ones own](https://github.com/singmann/afex/issues/65)). This document provides an overview of the different models supported by `afex_plot()` in addition to the `afex` objects (i.e., `afex_aov` and `mixed`). In general, these are models which are supported by the [`emmeans`](https://cran.r-project.org/package=emmeans) package as the `afex_plot.default()` method uses `emmeans` to get the estimated marginal means. `afex_plot.default()` then guesses whether there are repeated measures or all samples are independent. Based on this guess (which can be changed via the `id` argument) data in the background is plotted. Calculation of error bars can also be based on this guess (but the default is to plot the model based error bars obtained from `emmeans`). For a generally introduction to the functionality of `afex_plot` see: [`afex_plot`: Publication Ready Plots for Experimental Designs](afex_plot_introduction.html) Throughout the document, we will need `afex` as well as `ggplot2`. In addition, we load [`cowplot`](https://cran.r-project.org/package=cowplot) for function `plot_grid()` (which allows to easily combine multiple `ggplot2` plots). In addition, we will set a somewhat nicer `ggplot2` theme. ```{r message=FALSE, warning=FALSE} library("afex") library("ggplot2") library("cowplot") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) ``` Importantly, we also set the contrasts for the current `R` session to sum-to-zero contrasts. For models that include interactions with categorical variables this generally produces estimates that are easier to interpret. ```{r} set_sum_contrasts() ``` Please note, the best way to export a figure is via `ggsave()` or a similar function call. For Word and similar document formats, `png` is a good file type, for `LaTeX` and similar document formats, `pdf` is a good file type. # Base R stats models: lm, glm `afex_plot()` generally supports models implemeneted via the `stats` package. Here I show the main model functions that work with independent samples. These models can be passed to `afex_plot` without specifying additional arguments. Most importantly, `lm` models work directly. For those we use the `warpbreaks` data. ```{r} warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks) ``` Note that `afex_plot` produces several messages that are shown here as comments below the corresponding calls. Important is maybe that `afex_plot` assumes all observations (i.e., rows) are independent. This is of course the case here. In addition, for the first plot we are informed that the presence of an interaction may lead to a misleading impression if only a lower-order effect (here a main effect) is shown. This message is produced by `emmeans` and passed through. ```{r fig.width=7, fig.height=3} p1 <- afex_plot(warp.lm, "tension") p2 <- afex_plot(warp.lm, "tension", "wool") plot_grid(p1, p2) ``` `glm` models also work without further setting. Here we first use a poisson GLM for which we need to generate the data. ```{r} ins <- data.frame( n = c(500, 1200, 100, 400, 500, 300), size = factor(rep(1:3,2), labels = c("S","M","L")), age = factor(rep(1:2, each = 3)), claims = c(42, 37, 1, 101, 73, 14)) ``` We can then fit the data and pass the model object as is. ```{r fig.width=3, fig.height=3} ins.glm <- glm(claims ~ size + age + offset(log(n)), data = ins, family = "poisson") afex_plot(ins.glm, "size", "age") ``` `afex_plot` also works with binomial GLMs for which we also first need to generate some data which we will then fit. ```{r} ## binomial glm adapted from ?predict.glm ldose <- factor(rep(0:5, 2)) numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16) sex <- factor(rep(c("M", "F"), c(6, 6))) SF <- numdead/20 ## dv should be a vector, no matrix budworm.lg <- glm(SF ~ sex*ldose, family = binomial, weights = rep(20, length(numdead))) ``` For this model, we will produce three plots we can then compare. The first only shows the main effect of one variable (`ldose`). The other show the interaction of the two variables. Because for binomial GLMs we then only have one data point (with several observations), the individual data points and mean cannot be distinguished. This is made clear in the ther two (panels B and C). ```{r fig.width=8, fig.height=3} a <- afex_plot(budworm.lg, "ldose") b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! c <- afex_plot(budworm.lg, "ldose", "sex", data_arg = list(size = 4, color = "red")) plot_grid(a, b, c, labels = "AUTO", nrow = 1) ``` # nlme mixed model Hot to use `afex_plot` for mixed models fitted with `afex::mixed` (or [`lme4`](https://cran.r-project.org/package=lme4) directly) is shown in the [other vignette](afex_plot_introduction.html). However, we can also use `afex_plot` for mixed models fitted with the older `nlme` package. For this, however we need to pass the data used for fitting via the `data` argument. We can change on which of the two nested factors the individual data points in the background are based via the `id` argument. This is shown below. ```{r fig.width=8, fig.height=6} ## nlme mixed model data(Oats, package = "nlme") Oats$nitro <- factor(Oats$nitro) oats.1 <- nlme::lme(yield ~ nitro * Variety, random = ~ 1 | Block / Variety, data = Oats) plot_grid( afex_plot(oats.1, "nitro", "Variety", data = Oats), # A afex_plot(oats.1, "nitro", "Variety", data = Oats), # B afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block"), # C afex_plot(oats.1, "nitro", data = Oats), # D afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")), # E afex_plot(oats.1, "nitro", data = Oats, id = "Block"), # F labels = "AUTO" ) ``` # glmmTMB Support for [`glmmTMB`](https://cran.r-project.org/package=glmmTMB) is also provided. Here we use an example data set for which we model zero-inflation as well as overdispersion. The latter is achieved with a variant of the negative binomial distribution. ```{r, eval=FALSE} library("glmmTMB") tmb <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) ``` ```{r, eval=FALSE, include=FALSE} library("glmmTMB") set_sum_contrasts() tmb <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) save(tmb, file = "inst/extdata/tmb_example_fit.rda", compress = "xz") ``` ```{r, echo=FALSE, include=FALSE} library("glmmTMB") data(Salamanders, package = "glmmTMB") load(system.file("extdata/", "tmb_example_fit.rda", package = "afex")) ``` `afex_plot` does not automatically detect the random-effect for `site`. This means that per default all `r nrow(Salamanders)` data points are shown. When plotting only one variable, in which the default `data_geom` is `ggbeeswarm::geom_beeswarm`, this can lead to rather ugly plots due to the zero inflation. This is shon in panel A below. In panel B, we address this by changing the geom to a violin plot. In panel C, we address this by aggregating the data within site, but still use the beeswarm plot. Note that for panel C it is necessary to pass the data via the `data` argument as otherwise `site` cannot be found for aggregation. ```{r fig.width=8, fig.height=3} plot_grid( afex_plot(tmb, "spp"), afex_plot(tmb, "spp", data_geom = geom_violin), afex_plot(tmb, "spp", id = "site", data = Salamanders), labels = "AUTO", nrow = 1 ) ``` When plotting both variables, the problem is somewhat hidden, because instead of beeswarm plots, semi-transparency (i.e., `alpha` < 1) is used to show overlapping points. In panel B we again make this clearer but this time by adding jitter (on both the y- and x-axis) and increasing the degree of semi-transparancy (i.e., decreasing alpha). ```{r fig.width=8.5, fig.height=3.5} a <- afex_plot(tmb, "spp", "mined") b <- afex_plot(tmb, "spp", "mined", data_alpha = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0.2, jitter.height = 0.5, dodge.width = 0.5 ## needs to be same as dodge ), color = "darkgrey")) plot_grid(a, b, labels = "AUTO") ``` For the final plot we also plot the interaction, but this time aggregate the individual-data within site. This allows us again to use a beeswarm plot (after decreasing the width of the "bees") and produces a relatively clear result. ```{r fig.width=5.5, fig.height=3.5} afex_plot(tmb, "spp", "mined", id = "site", data = Salamanders, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list(dodge.width = 0.5, cex = 0.4, color = "darkgrey") ) ``` # rstanarm `afex_plot()` also supports Bayesian models that are also supported via `emmeans`. For example, we can easily fit a binomial model with [`rstanarm`](https://cran.r-project.org/package=rstanarm). ```{r, eval=FALSE} library("rstanarm") ## requires resetting the ggplot2 theme theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) example_model <- stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) ``` We can directly pass this model to `afex_plot`. However, we also see quite some zeros leading to a not super nice plot. It looks a bit better using a violin plot for the raw data. ```{r, eval=FALSE} b1 <- afex_plot(example_model, "period") ## dv column detected: prob ## No id column passed. Assuming all rows are independent samples. b2 <- afex_plot(example_model, "period", data_geom = geom_violin) ## dv column detected: prob ## No id column passed. Assuming all rows are independent samples. plot_grid(b1, b2, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} load(system.file("extdata/", "plots_rstanarm.rda", package = "afex")) plot_grid(b1, b2, labels = "AUTO") ``` We can also produce a plot based on the individual Bernoulli observations in the data. For this, we first need to expand the data such that we have one row per observation. With this, we can then fit the essentially same model as above. ```{r, eval=FALSE} cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$herd[i], period = cbpp$period[i], incidence = rep(0, cbpp$size[i]) ) cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 } cbpp_l <- do.call("rbind", cbpp_l) cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) example_model2 <- stan_glmer(incidence ~ period + (1|herd), data = cbpp_l, family = binomial, chains = 2, cores = 1, seed = 12345, iter = 500) ``` Again, this model can be directly passed to `afex_plot`. However, here we see even more 0 as the data is not yet aggregated. Consequently, we need to pass `id = "herd"` to aggregate the individual observations within each herd. ```{r, eval=FALSE} b3 <- afex_plot(example_model2, "period") ## dv column detected: incidence ## No id column passed. Assuming all rows are independent samples. b4 <- afex_plot(example_model2, "period", id = "herd") ## dv column detected: incidence plot_grid(b3, b4, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} plot_grid(b3, b4, labels = "AUTO") ``` We can of course also fit a model assuming a normal distribution using `rstanarm`. For example using the `Machines` data. ```{r, eval=FALSE} data("Machines", package = "MEMSS") mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) ``` As before, we can pass this model directly to `afex_plot` (see panel A). However, the data is again not aggregated within the grouping variable `Worker`. If we want to aggregate the individual data points for the grouping factor, we need to pass both the name of the grouping variable (`Worker`) and the data used for fitting. ```{r, eval=FALSE} b5 <- afex_plot(mm, "Machine") ## dv column detected: score ## No id column passed. Assuming all rows are independent samples. b6 <- afex_plot(mm, "Machine", id = "Worker") ## dv column detected: score plot_grid(b5, b6, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} plot_grid(b5, b6, labels = "AUTO") ``` ```{r, eval=FALSE, include=FALSE} library("rstanarm") ## requires resetting the ggplot2 theme library("ggplot2") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) set_sum_contrasts() cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) example_model <- stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) b1 <- afex_plot(example_model, "period") b2 <- afex_plot(example_model, "period", data_geom = geom_violin) cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$herd[i], period = cbpp$period[i], incidence = rep(0, cbpp$size[i]) ) cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 } cbpp_l <- do.call("rbind", cbpp_l) cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) example_model2 <- stan_glmer(incidence ~ period + (1|herd), data = cbpp_l, family = binomial, chains = 2, cores = 1, seed = 12345, iter = 500) b3 <- afex_plot(example_model2, "period") b4 <- afex_plot(example_model2, "period", id = "herd") data("Machines", package = "MEMSS") mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) b5 <- afex_plot(mm, "Machine") b6 <- afex_plot(mm, "Machine", id = "Worker", data = Machines) save(b1, b2, b3, b4, b5, b6, file = "../inst/extdata/plots_rstanarm.rda", compress = "xz", version = 2) ``` # brms We can also fit the `Machines` data using [`brms`](https://cran.r-project.org/package=brms). ```{r, eval=FALSE} library("brms") data("Machines", package = "MEMSS") mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) ``` However, to pass a `brms` object to `afex_plot` we need to pass both, the `data` used for fitting as well as the name of the dependent variable (here `score`) via the `dv` argument. We again build the plot such that the left panel shows the raw data without aggregation and the right panel shows the data aggregated within the grouping factor `Worker`. ```{r, eval=FALSE} bb1 <- afex_plot(mrt, "Machine", data = Machines, dv = "score") ## No id column passed. Assuming all rows are independent samples. bb2 <- afex_plot(mm, "Machine", id = "Worker", data = Machines, dv = "score") plot_grid(bb1, bb2) ``` ```{r fig.width=7, fig.height=3, echo=FALSE} load(system.file("extdata/", "plots_brms.rda", package = "afex")) plot_grid(bb1, bb2) ``` ```{r, eval=FALSE, include=FALSE} library("brms") data("Machines", package = "MEMSS") mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) bb1 <- afex_plot(mm2, "Machine", data = Machines, dv = "score") bb2 <- afex_plot(mm2, "Machine", id = "Worker", data = Machines, dv = "score") save(bb1, bb2, file = "../inst/extdata/plots_brms.rda", version = 2) ``` # Not Yet Supported: GLMMadaptive Some models are unfortunately not yet supported. For example, models fit with the new and pretty cool looking [`GLMMadaptive`](https://cran.r-project.org/package=GLMMadaptive) package using some of the special families do not seem to produce reasonable results. The following unfortunately does not produce a reasonable plot. ```{r fig.width=4, fig.height=3, eval = FALSE} library("GLMMadaptive") data(Salamanders, package = "glmmTMB") gm1 <- mixed_model(count~spp * mined, random = ~ 1 | site, data = Salamanders, family = zi.poisson(), zi_fixed = ~ mined) afex_plot(gm1, "spp", data = Salamanders) ``` afex/vignettes/afex_anova_example.Rmd0000644000176200001440000004161713531256332017507 0ustar liggesusers--- title: "ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` # Overview This documents reanalysis a dataset from an Experiment performed by Singmann and Klauer (2011) using the ANOVA functionality of __afex__ followed by post-hoc tests using package [__emmeans__](https://cran.r-project.org/package=emmeans) (Lenth, 2017). After a brief description of the dataset and research question, the code and results are presented. # Description of Experiment and Data Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and plausibility of the problem (inferences which were consisted with the background knowledge versus problems that were inconsistent with the background knowledge). The critical comparison across the two conditions was among problems which were valid and implausible with problems that were invalid and plausible. For example, the next problem was invalid and plausible: > If a person is wet, then the person fell into a swimming pool. > A person fell into a swimming pool. > How valid is the conclusion/How likely is it that the person is wet? For those problems we predicted that under deductive instructions responses should be lower (as the conclusion does not necessarily follow from the premises) as under probabilistic instructions. For the valid but implausible problem, an example is presented next, we predicted the opposite pattern: > If a person is wet, then the person fell into a swimming pool. > A person is wet. > How valid is the conclusion/How likely is it that the person fell into a swimming pool? Our study also included valid and plausible and invalid and implausible problems. In contrast to the analysis reported in the manuscript, we initially do not separate the analysis into affirmation and denial problems, but first report an analysis on the full set of inferences, MP, MT, AC, and DA, where MP and MT are valid and AC and DA invalid. We report a reanalysis of our Experiment 1 only. Note that the factor `plausibility` is not present in the original manuscript, there it is a results of a combination of other factors. # Data and R Preperation We begin by loading the packages we will be using throughout. ```{r message=FALSE, warning=FALSE} library("afex") # needed for ANOVA functions. library("emmeans") # emmeans must now be loaded explicitly for follow-up tests. library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("ggplot2") # for customizing plots. afex_options(emmeans_model = "multivariate") # use multivariate model for all follow-up tests. ``` Note that for ANOVAs involving repeated-measures factors, follow-up tests based on the multivariate model are generally preferrably to univariate follow-up tests. Consequently, we set this option globally. Future versions of `afex` will likely use the multivariate model as the default. ```{r} data(sk2011.1) str(sk2011.1) ``` An important feature in the data is that each participant provided two responses for each cell of the design (the content is different for each of those, each participant saw all four contents). These two data points will be aggregated automatically by `afex`. ```{r} with(sk2011.1, table(inference, id, plausibility)) ``` # ANOVA To get the full ANOVA table for the model, we simply pass it to `aov_ez` using the design as described above. We save the returned object for further analysis. ```{r} a1 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("inference", "plausibility")) a1 # the default print method prints a data.frame produced by nice ``` The equivalent calls (i.e., producing exactly the same output) of the other two ANOVA functions `aov_car` or `aov4` is shown below. ```{r, eval=FALSE} aov_car(response ~ instruction + Error(id/inference*plausibility), sk2011.1) aov_4(response ~ instruction + (inference*plausibility|id), sk2011.1) ``` As mentioned before, the two responses per cell of the design and participants are aggregated for the analysis as indicated by the warning message. Furthermore, the degrees of freedom are Greenhouse-Geisser corrected per default for all effects involving `inference`, as `inference` is a within-subject factor with more than two levels (i.e., MP, MT, AC, & DA). In line with our expectations, the three-way interaction is significant. The object printed per default for `afex_aov` objects (produced by `nice`) can also be printed nicely using `knitr`: ```{r, results='asis', } knitr::kable(nice(a1)) ``` Alternatively, the `anova` method for `afex_aov` objects returns a `data.frame` of class `anova` that can be passed to, for example, `xtable` for nice formatting: ```{r, results='asis'} print(xtable::xtable(anova(a1), digits = c(rep(2, 5), 3, 4)), type = "html") ``` # Post-Hoc Contrasts and Plotting To further analyze the data we need to pass it to package `emmeans`, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on `emmeans` can be obtained in [its vignettes](https://cran.r-project.org/package=emmeans) and [faq](https://CRAN.R-project.org/package=emmeans/vignettes/FAQs.html). `emmeans` can work with `afex_aov` objects directly as __afex__ comes with the necessary methods for the generic functions defined in `emmeans`. When using the `multivariate` options as described above, `emmeans` uses the ANOVA model estimated via base R's `lm` method (which in the case of a multivariate response is an object of class `c("mlm", "lm")`). In the default setting (i.e., `emmeans_model = "univariate"`), `emmeans` uses the object created by base R's `aov` function, which for now is also part of an `afex_aov` object. ## Some First Contrasts ### Main Effects Only This object can now be passed to `emmeans`, for example to obtain the marginal means of the four inferences: ```{r} m1 <- emmeans(a1, ~ inference) m1 ``` This object can now also be used to compare whether or not there are differences between the levels of the factor: ```{r} pairs(m1) ``` To obtain more powerful p-value adjustments, we can furthermore pass it to `multcomp` (Bretz, Hothorn, & Westfall, 2011): ```{r} summary(as.glht(pairs(m1)), test=adjusted("free")) ``` ### A Simple interaction We could now also be interested in the marginal means of the inferences across the two instruction types. `emmeans` offers two ways to do so. The first splits the contrasts across levels of the factor using the `by` argument. ```{r} m2 <- emmeans(a1, "inference", by = "instruction") ## equal: emmeans(a1, ~ inference|instruction) m2 ``` Consequently, tests are also only performed within each level of the `by` factor: ```{r} pairs(m2) ``` The second version considers all factor levels together. Consequently, the number of pairwise comparisons is a lot larger: ```{r} m3 <- emmeans(a1, c("inference", "instruction")) ## equal: emmeans(a1, ~inference*instruction) m3 pairs(m3) ``` ### Running Custom Contrasts Objects returned from `emmeans` can also be used to test specific contrasts. For this, we can simply create a list, where each element corresponds to one contrasts. A contrast is defined as a vector of constants on the reference grid (i.e., the object returned from `emmeans`, here `m3`). For example, we might be interested in whether there is a difference between the valid and invalid inferences in each of the two conditions. ```{r} c1 <- list( v_i.ded = c(0.5, 0.5, -0.5, -0.5, 0, 0, 0, 0), v_i.prob = c(0, 0, 0, 0, 0.5, 0.5, -0.5, -0.5) ) contrast(m3, c1, adjust = "holm") summary(as.glht(contrast(m3, c1)), test = adjusted("free")) ``` The results can be interpreted as in line with expectations. Responses are larger for valid than invalid problems in the deductive, but not the probabilistic condition. ## Plotting Since version `0.22`, `afex` comes with its own plotting function based on `ggplot2`, `afex_plot`, which works directly with `afex_aov` objects. As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. As we saw above, this interaction was significant. Consequently, we are interested in plotting this interaction. ### Basic Plots For `afex_plot`, we need to specify the `x`-factor(s), which determine which factor-levels or combinations of factor-levels are plotted on the x-axis. We can also define `trace` factor(s), which determine which factor levels are connected by lines. Finally, we can also define `panel` factor(s), which determine if the plot is split into subplots. `afex_plot` then plots the estimated marginal means obtained from `emmeans`, confidence intervals, and the raw data in the background. Note that the raw data in the background is per default drawn using an alpha blending of .5 (i.e., 50% semi-transparency). Thus, in case of several points lying directly on top of each other, this point appears noticeably darker. ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility") ``` In the default settings, the error bars show 95%-confidence intervals based on the standard error of the underlying model (i.e., the `lm` model in the present case). In the present case, in which each subplot (defined by `x`- and `trace`-factor) shows a combination of a within-subjects factor (i.e., `inference`) and a between-subjects (i.e., `instruction`) factor, this is not optimal. The error bars only allow to assess differences regarding the between-subjects factor (i.e., across the lines), but not inferences regarding the within-subjects factor (i.e., within one line). This is also indicated by a warning. An alternative would be within-subject confidence intervals: ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "within") ``` However, those only allow inferences regarding the within-subject factors and not regarding the between-subjecta factor. So the same warning is emitted again. A further alternative is to suppress the error bars altogether. This is the approach used in our original paper and probably a good idea in general when figures show both between- and within-subjects factors within the same panel. The presence of the raw data in the background still provides a visual depiction of the variability of the data. ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none") ``` ### Customizing Plots `afex_plot` allows to customize the plot in a number of different ways. For example, we can easily change the aesthetic mapping associated with the `trace` factor. So instead of using lineytpe and shape of the symbols, we can use color. Furthermore, we can change the graphical element used for plotting the data points in the background. For example, instead of plotting the raw data, we can replace this with a boxplot. Finally, we can also make both the points showing the means and the lines connecting the means larger. ```{r fig.width=7.5, fig.height=4} p1 <- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none", mapping = c("color", "fill"), data_geom = geom_boxplot, data_arg = list(width = 0.4), point_arg = list(size = 1.5), line_arg = list(size = 1)) p1 ``` Note that `afex_plot` returns a `ggplot2` plot object which can be used for further customization. For example, one can easily change the `theme` to something that does not have a grey background: ```{r fig.width=7.5, fig.height=4} p1 + theme_light() ``` We can also set the theme globally for the remainder of the `R` session. ```{r} theme_set(theme_light()) ``` The full set of customizations provided by `afex_plot` is beyond the scope of this vignette. The examples on the help page at `?afex_plot` provide a good overview. # Replicate Analysis from Singmann and Klauer (2011) However, the plots shown so far are not particularly helpful with respect to the research question. Next, we fit a new ANOVA model in which we separate the data in affirmation and denial inferences. This was also done in the original manuscript. We then lot the data a second time. ```{r} a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("validity", "plausibility", "what")) a2 ``` Then we plot the data from this ANOVA. Because each panel would again show a mixed-design, we suppress the error bars. ```{r fig.width=7.5, fig.height=4} afex_plot(a2, x = c("plausibility", "validity"), trace = "instruction", panel = "what", error = "none") ``` We see the critical and predicted cross-over interaction in the left of those two graphs. For implausible but valid problems deductive responses are larger than probabilistic responses. The opposite is true for plausible but invalid problems. We now tests these differences at each of the four x-axis ticks in each plot using custom contrasts (`diff_1` to `diff_4`). Furthermore, we test for a validity effect and plausibility effect in both conditions. ```{r} (m4 <- emmeans(a2, ~instruction+plausibility+validity|what)) c2 <- list( diff_1 = c(1, -1, 0, 0, 0, 0, 0, 0), diff_2 = c(0, 0, 1, -1, 0, 0, 0, 0), diff_3 = c(0, 0, 0, 0, 1, -1, 0, 0), diff_4 = c(0, 0, 0, 0, 0, 0, 1, -1), val_ded = c(0.5, 0, 0.5, 0, -0.5, 0, -0.5, 0), val_prob = c(0, 0.5, 0, 0.5, 0, -0.5, 0, -0.5), plau_ded = c(0.5, 0, -0.5, 0, -0.5, 0, 0.5, 0), plau_prob = c(0, 0.5, 0, -0.5, 0, 0.5, 0, -0.5) ) contrast(m4, c2, adjust = "holm") ``` We can also pass these tests to `multcomp` which gives us more powerful Type 1 error corrections. ```{r} summary(as.glht(contrast(m4, c2)), test = adjusted("free")) ``` Unfortunately, in the present case this function throws several warnings. Nevertheless, the p-values from both methods are very similar and agree on whether or not they are below or above .05. Because of the warnings it seems advisable to use the one provided by `emmeans` directly and not use the ones from `multcomp`. The pattern for the affirmation problems is in line with the expectations: We find the predicted differences between the instruction types for valid and implausible (`diff_2`) and invalid and plausible (`diff_3`) and the predicted non-differences for the other two problems (`diff_1` and `diff_4`). Furthermore, we find a validity effect in the deductive but not in the probabilistic condition. Likewise, we find a plausibility effect in the probabilistic but not in the deductive condition. # Some Cautionary Notes * Choosing the right correction for multiple testing can be difficult. In fact `multcomp` comes with an accompanying book (Bretz et al., 2011). If the degrees-of-freedom of all contrasts are identical using `multcomp`'s method `free` is more powerful than simply using the Bonferroni-Holm method. `free` is a generalization of the Bonferroni-Holm method that takes the correlations among the model parameters into account and uniformly more powerful. * For data sets with many within-subject factors, creating the `aov` object can take some time (i.e., compared to producing the ANOVA table which is usually very fast). Those objects are also comparatively large, often multiple MB. If speed is important and one is not interested in employing `emmeans` one can set `return = "nice"` in the call to the ANOVA function to only receive the ANOVA table (this can also be done globally: `afex_options(return_aov = "nice")`). # References * Bretz, F., Hothorn, T., & Westfall, P. H. (2011). _Multiple comparisons using R_. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp * Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. _Thinking & Reasoning_, 17(3), 247-281. doi: 10.1080/13546783.2011.572718 * Lenth, R. (2017). _emmeans: Estimated Marginal Means, aka Least-Squares Means_. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans afex/vignettes/afex_mixed_example.Rmd0000644000176200001440000007024413531256325017511 0ustar liggesusers--- title: "Mixed Model Reanalysis of RT data" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Mixed Model Example Analysis: Reanalysis of Freeman et al. (2010)} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` ## Overview This documents reanalysis response time data from an Experiment performed by Freeman, Heathcote, Chalmers, and Hockley (2010) using the mixed model functionality of __afex__ implemented in function `mixed` followed by post-hoc tests using package __emmeans__ (Lenth, 2017). After a brief description of the data set and research question, the code and results are presented. ## Description of Experiment and Data The data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The 300 items in each `stimulus` condition were selected to form a balanced $2 \times 2$ design with factors neighborhood `density` (low versus high) and `frequency` (low versus high). The `task` was a between subjects factor: 25 participants worked on the lexical decision task and 20 participants on the naming task. After excluding erroneous responses each participants responded to between 135 and 150 words and between 124 and 150 nonwords. We analyzed log RTs which showed an approximately normal picture. ## Data and R Preperation We start with loading some packages we will need throughout this example. For data manipulation we will be using the `dplyr` and `tidyr` packages from the [`tidyverse`](http://tidyverse.org/). A thorough introduction to these packages is beyond this example, but well worth it, and can be found in ['R for Data Science'](http://r4ds.had.co.nz/) by Wickham and Grolemund. For plotting we will be diverging from the `tidyverse` and use `lattice` instead. At some later point in time I will change this to `ggplot2` plots. After loading the packages, we will load the data (which comes with `afex`), remove the errors, and take a look at the variables in the data. ```{r message=FALSE, warning=FALSE} library("afex") # needed for mixed() and attaches lme4 automatically. library("emmeans") # emmeans is needed for follow-up tests (and not anymore loaded automatically). library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("dplyr") # for working with data frames library("tidyr") # for transforming data frames from wide to long and the other way round. library("lattice") # for plots library("latticeExtra") # for combining lattice plots, etc. lattice.options(default.theme = standard.theme(color = FALSE)) # black and white lattice.options(default.args = list(as.table = TRUE)) # better ordering data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors str(fhch2010) # structure of the data ``` To make sure our expectations about the data match the data we use some `dplyr` magic to confirm the number of participants per condition and items per participant. ```{r} ## are all participants in only one task? fhch2010 %>% group_by(id) %>% summarise(task = n_distinct(task)) %>% as.data.frame() %>% {.$task == 1} %>% all() ## participants per condition: fhch2010 %>% group_by(id) %>% summarise(task = first(task)) %>% ungroup() %>% group_by(task) %>% summarise(n = n()) ## number of different items per participant: fhch2010 %>% group_by(id, stimulus) %>% summarise(items = n_distinct(item)) %>% ungroup() %>% group_by(stimulus) %>% summarise(min = min(items), max = max(items), mean = mean(items)) ``` Before running the analysis we should make sure that our dependent variable looks roughly normal. To compare `rt` with `log_rt` within the same graph using `lattice` we first need to transform the data from the wide format (where both rt types occupy one column each) into the long format (in which the two rt types are combined into a single column with an additional indicator column). To do so we use `tidyr::gather`. Then we simply call the `histogram` function on the new `data.frame` and make a few adjustments to the defaults to obtain a nice looking output. The plot shows that `log_rt` looks clearly more normal than `rt`, although not perfectly so. An interesting exercise could be to rerun the analysis below using a transformation that provides an even better 'normalization'. ```{r, fig.width=7, fig.height=4} fhch_long <- fhch %>% gather("rt_type", "rt", rt, log_rt) histogram(~rt|rt_type, fhch_long, breaks = "Scott", type = "density", scale = list(x = list(relation = "free"))) ``` ## Descriptive Analysis The main factors in the experiment were the between-subjects factor `task` (`naming` vs. `lexdec`), and the within-subjects factors `stimulus` (`word` vs. `nonword`), `density` (`low` vs. `high`), and `frequency` (`low` vs. `high`). Before running an analysis it is a good idea to visually inspect the data to gather some expectations regarding the results. Should the statistical results dramatically disagree with the expectations this suggests some type of error along the way (e.g., model misspecification) or at least encourages a thorough check to make sure everything is correct. We first begin by plotting the data aggregated by-participant. In each plot we plot the raw data in the background. To make the individual data points visible we add some `jitter` on the x-axis and choose `pch` and `alpha` values such that we see where more data points are (i.e., where plot overlaps it is darker). Then we add the mean as a x in a circle. Both of this is done in the same call to `xyplot` using a custom panel function. Finally, we combine this plot with a simple boxplot using `bwplot`. ```{r, fig.width=7, fig.height=6} agg_p <- fhch %>% group_by(id, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_p, jitter.x = TRUE, pch = 20, alpha = 0.5, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_p, pch="|", do.out = FALSE) ``` Now we plot the same data but aggregated across items: ```{r, fig.width=7, fig.height=6} agg_i <- fhch %>% group_by(item, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_i, jitter.x = TRUE, pch = 20, alpha = 0.2, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_i, pch="|", do.out = FALSE) ``` These two plots show a very similar pattern and suggest several things: * Responses to `nonwords` appear slower than responses to `words`, at least for the `naming` task. * `lexdec` responses appear to be slower than `naming` responses, particularly in the `word` condition. * In the `nonword` and `naming` condition we see a clear effect of `frequency` with slower responses to `high` than `low` `frequency` words. * In the `word` conditions the `frequency` pattern appears to be in the opposite direction to the pattern described in the previous point: faster responses to `low` `frequency` than to `high` `frequency` words. * `density` appears to have no effect, perhaps with the exception of the `nonword` `lexdec` condition. ## Model Setup To set up a mixed model it is important to identify which factors vary within which grouping factor generating random variability (i.e., grouping factors are sources of stochastic variability). The two grouping factors are participants (`id`) and items (`item`). The within-participant factors are `stimulus`, `density`, and `frequency`. The within-item factor is `task`. The 'maximal model' (Barr, Levy, Scheepers, and Tily, 2013) therefore is the model with by-participant random slopes for `stimulus`, `density`, and `frequency` and their interactions and by-item random slopes for `task`. Occasionally, the maximal model does not converge successfully. In this case a good first approach for dealing with this problem is to remove the corelations among the random terms. In our example, there are two sets of correlations, one for each random effect grouping variable. Consequently, we can build four model that have the maximal structure in terms of random-slopes and only differ in which correlations among random terms are calculated: 1. With all correlations. 2. No correlation among by-item random effects (i.e., no correlation between random intercept and `task` random slope). 3. No correlation among by-participant random effect terms (i.e., no correlation among random slopes themselves and between the random slopes and the random intercept). 4. No correlation among either random grouping factor. The next decision to be made is which method to use for obtaining $p$-values. The default method is `KR` (=Kenward-Roger) which provides the best control against anti-conservative results. However, `KR` needs quite a lot of RAM, especially with complicated random effect structures and large data sets. As in this case we have both, relatively large data (i.e., many levels on each random effect, especially the item random effect) and a complicated random effect structure, it seems a reasonable decision to choose another method. The second 'best' method (in terms of controlling for Type I errors) is the 'Satterthwaite' approximation, `method='S'`. It provides a similar control of Type I errors as the Kenward-Roger approximation and needs less RAM, however one downside is that it simply fails in some cases. ## Results ### Satterthwaite Results The following code fits the four models using the Satterthwaite method. To suppress random effects we use the `||` notation. Note that it is necessary to set `expand_re=TRUE` when suppressing random effects among variables that are entered as factors and not as numerical variables (as done here). Also note that `mixed` automatically uses appropriate contrast codings if factors are included in interactions (`contr.sum`) in contrast to the `R` default (which is `contr.treatment`). To make sure the estimation does not end prematurely we set the allowed number of function evaluations to a very high value (using `lmerControl`). ```{r, eval = FALSE} m1s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task|item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6))) m2s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task||item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m3s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task|item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m4s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task||item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ``` As the estimation of these model may take some time, `afex` inlcudes the estimated models which can be loaded with the following code. Note that when using the `print` or `anova` method for `mixed` objects, the `warnings` emitted during estimation of the model by `lmer` will be printed again. So there is no downside of loading the already estimated models. We then inspect the four results. ```{r} load(system.file("extdata/", "freeman_models.rda", package = "afex")) m1s m2s m3s m4s ``` Before looking at the results we can see that for models 1 and 2, `lmer` emmited a warning that the model failed to converge. These warnings do not necessarily mean that the results cannot be used. As we will see below, model 2 (`m2s`) produces essentially the same results as models 3 and 4 suggesting that this warning is indeed a false positive. However, the results also show that estimating the Satterthwaite approximation failed for `m1s`, we have no denominator degrees of freedom and no $p$-values. If this happens, we can only try another method or a reduced model. Models 2 to 4 produce results and the results are extremely similar across models. A total of 9 or 10 effects reached significance. We found main effects for `task` and `stimulus`, two-way interactions of `task:stimulus`, `task:density`, `task:frequency`, and `stimulus:frequency`, three-way interactions of `task:stimulus:density`, `task:stimulus:frequency`, and `task:density:frequency`, a marginal three-way interaction (for two of three models) of `stimulus:density:frequency`, and the four-way interaction of `task:stimulus:density:frequency`. Additionally, all $F$ and $p$ values are very similar to each other across the three models. The only difference in terms of significant versus non-significant effects between the three models is the three-way interaction of `stimulus:density:frequency` which is only significant for model 3 with $F(1, 88.40) = 4.16$, $p = .04$, and only reaches marginal significance for the other two models with $p > .05$ and a very similar $F$-value. ### LRT Results It is instructive to compare those results with results obtained using the comparatively 'worst' method for obtaining $p$-value simplmeneted in `afex`, likelihood ratio tests. Likelihood ratio-tests should in principle deliver reasonable results for large data sets such as the current one, so we should expect not too many deviations. We again fit all four models, this time using `method='LRT'`. ```{r, eval = FALSE} m1lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task|item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6))) m2lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task||item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m3lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task|item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m4lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task||item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ``` Because the resulting `mixed` objects are of considerable size, we do not include the full objects, but only the resulting ANOVA tables and `data.frames` (`nice_lrt` is a list containing the result from calling `nice` on the objects, `anova_lrt` contains the result from calling `anova`). Before considering the results, we again first consider the warnings emitted when fitting the models. Because methods `'LRT'` and `'PB'` fit one `full_model` and one `restricted_model` for each effect (i.e., term), there can be more warnings than for methods `'KR'` and `'S'` which only fit one model (the `full_model`). And this is exactly what happens. For `m1lrt` there are 11 convergence warnings, almost one per fitted model. However, none of those immediately invalidates the results. This is different for models 2 and 3 for both of which warnings indicate that `nested model(s) provide better fit than full model`. What this warning means is that the `full_model` does not provide a better fit than at least one of the `restricted_model`, which is mathematically impossible as the `restricted_models` are nested within the full model (i.e., they result from setting one or several parameters equal to 0, so the `full_model` can always provide an at least as good account as the `restricted_models`). Model 4 finally shows no warnings. The following code produces a single output comparing models 1 and 4 next to each other. The results show basically the same pattern as obtained with the Satterthwaite approximation. Even the $p$-values are extremely similar to the $p$-values of the Satterthwaite models. The only 'difference' is that the `stimulus:density:frequency` three-way interaction is significant in each case now, although only barely so. ```{r} res_lrt <- cbind(nice_lrt[[1]], " " = " ", nice_lrt[[4]][,-(1:2)]) colnames(res_lrt)[c(3,4,6,7)] <- paste0( rep(c("m1_", "m4_"), each =2), colnames(res_lrt)[c(3,4)]) res_lrt ``` We can also compare this with the results from model 3. Although the `full_model` cannot be the maximum-likelihood estimate (as it provides a worse than the `density:frequency` model), the difference seems to be minimal as it also shows exactly the same pattern as the other models. ```{r} nice_lrt[[2]] ``` ### Summary of Results Fortunately, the results from all models that actually produced results and converged without a critical warning (e.g., one critical warning is that a `restricted_model` provides a better fit than the `full_model`) agreed very strongly providing a high degree of confidence in the results. This might not be too surprising given the comparatively large number of total data points and the fact that each random effect grouping factor has a considerable number of levels (way above 20 for both participants and items). This also suggests that the convergence warnings are likely false positives; the models seem to have converged successfully to the maximum likelihood estimate, or at least to a value very near the maximum likelihood estimate. How further reducing the random effects structure (e.g., removing the random slopes for the highest interaction) affects the results is left as an exercise for the reader. In terms of the significant findings, there are many that seem to be in line with the descriptive results described above. For example, the highly significant effect of `task:stimulus:frequency` with $F(1, 190.61) = 109.33$, $p < .0001$ (values from `m2s`), appears to be in line with the observation that the frequency effect appears to change its sign depending on the `task:stimulus` cell (with `nonword` and `naming` showing the opposite patterns than the other three conditions). Consequently, we start by investigating this interaction further below. ## Follow-Up Analyses Before investigating the significant interaction in detail it is a good idea to remind oneself what a significant interaction represents on a conceptual level; that one or multiple of the variables in the interaction moderate (i.e., affect) the effect of the other variable or variables. Consequently, there are several ways to investigate a significant interaction. Each of the involved variables can be seen as the moderating variables and each of the variables can be seen as the effect of interest. Which one of those possible interpretations is of interest in a given situation highly depends on the actual data and research question and multiple views can be 'correct' in a given situation. In addition to this conceptual issue, there are also multiple technical ways to investigate a significant interaction. One approach not followed here is to split the data according to the moderating variables and compute the statistical model again for the splitted data sets with the effect variable(s) as remaining fixed effect. This approach, also called _simple effects_ analysis, is, for example, recommended by Maxwell and Delaney (2004) as it does not assume variance homogeneity and is faithful to the data at each level. The approach taken here is to simply perform the test on the fitted full model. This approach assumes variance homogeneity (i.e., that the variances in all groups are homogeneous) and has the added benefit that it is computationally relatively simple. In addition, it can all be achieved using the framework provided by [`emmeans`](https://cran.r-project.org/package=emmeans) (Lenth, 2017). ### task:stimulus:frequency Interaction Our interest in the beginning is on the effect of `frequency` by `task:stimulus` combination. So let us first look at the estimated marginal means os this effect. In `emmeans` parlance these estimated means are called 'least-square means' because of historical reasons, but because of the lack of least-square estimation in mixed models we prefer the term estimated marginal means, or EMMs for short. Those can be obtained in the following way. To prevent `emmeans` from calculating the *df* for the EMMs (which can be quite costly), we use asymptotic *df*s (i.e., $z$ values and tests). `emmeans` requires to first specify the variable(s) one wants to treat as the effect variable(s) (here `frequency`) and then allows to specify condition variables. ```{r} emm_options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- emmeans(m2s, "frequency", by = c("stimulus", "task")) emm_i1 ``` The returned values are in line with our observation that the `nonword` and `naming` condition diverges from the other three. But is there actual evidence that the effect flips? We can test this using additional `emmeans` functionality. Specifically, we first use the `pairs` function which provides us with a pairwise test of the effect of `frequency` in each `task:stimulus` combination. Then we need to combine the four tests within one object to obtain a familywise error rate correction which we do via `update(..., by = NULL)` (i.e., we revert the effect of the `by` statement from the earlier `emmeans` call) and finally we select the `holm` method for controlling for family wise error rate (the Holm method is uniformly more powerful than the Bonferroni). ```{r} update(pairs(emm_i1), by = NULL, adjust = "holm") ``` We could also use a slightly more powerful method than the Holm method, method `free` from package `multcomp`, which takes the correlation of the model parameters into account (note that due a bug in the current emmenas version this is currently deactivated): ```{r, eval=FALSE} summary(as.glht(update(pairs(emm_i1), by = NULL)), test = adjusted("free")) ``` We see that the results are exactly as expected. In the `nonword` and `naming` condition we have a clear negative effect of frequency while in the other three conditions it is clearly positive. We could now also use the EMMs and retransform them onto the response scale (i.e., RTs) which we could use for plotting. Note that the $p$-values in this ouput are for the $z$ test of whether or not a value is significantly above 0 on the `log_rt`-scale (i.e., above 1 second on the response scale). That seems not the most interesting test, but the output is interesting because of the EMMs and standard errors that could be used for printing. ```{r} emm_i1b <- summary(contrast(emm_i1, by = NULL)) emm_i1b[,c("estimate", "SE")] <- exp(emm_i1b[,c("estimate", "SE")]) emm_i1b ``` ### task:stimulus:density:frequency Interaction As the last example, let us take a look at the significant four-way interaction of `task:stimulus:density:frequency`, $F(1, 111.32) = 10.07$, $p = .002$. Here we might be interested in a slightly more difficult question namely whether the `density:frequency` interaction varies across `task:stimulus` conditions. If we again look at the figures above, it appears that there is a difference between `low:low` and `high:low` in the `nonword` and `lexdec` condition, but not in the other conditions. We again first begin by obtaining the EMMs. However, the actual values are not interesting at the moment, we are basically only interested in the interaction for each `task:stimulus` condition. Therefore, we use the EMMs to create two consecutive contrasts, the first one for `density` and then for `frequency` using the fist contrast. Then we run a joint test conditional on the `task:stimulus` conditions. ```{r} emm_i2 <- emmeans(m2s, c("density", "frequency"), by = c("stimulus", "task")) con1 <- contrast(emm_i2, "trt.vs.ctrl1", by = c("frequency", "stimulus", "task")) # density con2 <- contrast(con1, "trt.vs.ctrl1", by = c("contrast", "stimulus", "task")) test(con2, joint = TRUE, by = c("stimulus", "task")) ``` This test indeed shows that the `density:frequency` interaction is only significant in the `nonword` and `lexdec` condition. Next, let's see if we can unpack this interaction in a meaningful manner. For this we compare `low:low` and `high:low` in each of the four groups. And just for the sake of making the example more complex, we also compare `low:high` and `high:high`. This can simply be done by specifying a list of custom contrasts on the EMMs (or reference grid in `emmeans` parlance) which can be passed again to the `contrast` function. The contrasts are a `list` where each element should sum to one (i.e., be a proper contrast) and be of length equal to the number of EMMs (although we have 16 EMMs in total, we only need to specify it for a length of four due to conditiong by `c("stimulus", "task")`). To control for the family wise error rate across all tests, we again use `update(..., by = NULL)` on the result this time again specifying `by = NULL` to revert the effect of conditiong. Note that although we entered the variables into `emmeans` in the same order as into our plot call above, the order of the four EMMs differs. ```{r} emm_i2 # desired contrats: des_c <- list( ll_hl = c(1, -1, 0, 0), lh_hh = c(0, 0, 1, -1) ) update(contrast(emm_i2, des_c), by = NULL, adjust = "holm") ``` In contrast to our expectation, the results show two significant effects and not only one. In line with our expectations, in the `nonword` and `lexdec` condition the EMM of `low:high` is smaller than the EMM for `high:high`, $z = -6.30$, $p < .0001$. However, in the `nonword` and `naming` condition we found the opposite pattern; the EMM of `low:high` is larger than the EMM for `high:high`, $z = 3.65$, $p = .002$. For all other effects $|z| < 1.3$, $p > .99$. In addition, there is no difference between `low:high` and `high:high` in any condition. ## References * Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. _Journal of Memory and Language_, 68(3), 255-278. https://doi.org/10.1016/j.jml.2012.11.001 * Bretz, F., Hothorn, T., & Westfall, P. H. (2011). _Multiple comparisons using R_. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp * Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. _Journal of Memory and Language_, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004 * Lenth, R. (2017). _emmeans: Estimated Marginal Means, aka Least-Squares Means_. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans * Maxwell, S. E., & Delaney, H. D. (2004). _Designing experiments and analyzing data: a model-comparisons perspective_. Mahwah, N.J.: Lawrence Erlbaum Associates. ```{r, echo=FALSE, eval = FALSE} ### OLD STUFF BELOW. PLEASE IGNORE. load("freeman_models.rda") load("../freeman_models_all.rda") m1lrt$restricted_models <- list(NULL) m2lrt$restricted_models <- list(NULL) m3lrt$restricted_models <- list(NULL) m4lrt$restricted_models <- list(NULL) save(m1lrt, file = "freeman_models1.rda", compress = "xz") save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models.rda", compress = "xz") anovas_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), anova) nice_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), nice) res_lrt <- cbind(nice_lrt[[1]], " " = " ", nice_lrt[[2]][,-(1:2)], " " = " ", nice_lrt[[3]][,-(1:2)], " " = " ", nice_lrt[[4]][,-(1:2)]) colnames(res_lrt)[c(3,4,6,7, 9,10, 12,13)] <- paste0( rep(c("m1_", "m2_", "m3_","m4_"), each =2), colnames(res_lrt)[c(3,4)]) ## warnings: m1s # fails and 1 warning m2s # 1 warning m3s # 0 warnings m4s # 0 warnings m1lrt # 11 warnings m2lrt # 1 nested model(s) provide better, 7 other warnings m3lrt # 7 nested models provide better fit, 9 other warnings m4lrt # 0 warnings cbind(nice_lrt[[1]]$Effect, do.call("cbind", lapply(nice_lrt, function(x) x[,3:4]))) save(m1s, m2s, m3s, m4s, anovas_lrt, nice_lrt,file = "freeman_models.rda", compress = "xz") save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models2.rda", compress = "bzip2") tools::resaveRdaFiles("freeman_models1.rda") ``` afex/NEWS0000644000176200001440000010210213607674426011707 0ustar liggesusers ************************* ** afex VERSION 0.26-x ** ************************* Changes in afex Version 0.26-x Released January 2020 Significant User Visible Changes and New Features o factor_levels argument of afex_plot() now accepts named character vectors which allows: (1) renaming only a subset of factor levels (if only a subset of levels is specified) (2) reordering in which order factor levels are shown in the plot (order of names within a list element determine order that will be used for plotting) Bugfixes o msq data set is now part of psychTools and not of psych. Fixes CRAN check issues. ************************* ** afex VERSION 0.25-x ** ************************* Changes in afex Version 0.25-x Released August 2019 Significant User Visible Changes and New Features o Better error messages for ANOVA in some case in which data shows structural problems (e.g., missing design cells). o afex_plot() now first draws all graphical elements belonging to a specific factor level, before drawing graphical elements belonging to the next factor level in interaction plots (does not apply to data in the background). This avoids inconsistencies in plotting order between error bars and connecting lines. Bugfixes o Correct Type III ANOVA results for character variables if factorize = FALSE. o afex_plot() for mixed or merMod objects uses actual dv on y-axis. o afex_plot() x-labels and legend-title display correctly in case more than one variable is displayed. o The default method for afex_plot() can now aggregate via the id argument even if the corresponding factor is only part if the random effects terms (see rstanarm examples in vignette). o Removed certain non-ASCII characters in examples: https://github.com/singmann/afex/issues/66 ************************* ** afex VERSION 0.24-x ** ************************* Changes in afex Version 0.24-x Released July 2019 Significant User Visible Changes and New Features o Added possibility to suppress calculation of aov object for ANOVAs, via argument 'include_aov' (with default = TRUE). Suppressing the calculation of the aov object can significantly reduce estimation time of ANOVAs for models with large N and within-subjects factors. Even for small models, a speed increase by more than 10% is expected. For ANOVAs without aov object, emmeans are always based on the multivariate or lm model. o Added test_levene() and test_sphercitiy() functions for assumption tests for ANOVA models. Thanks to Mattan S. Ben-Shachar. Addresses #55, https://github.com/singmann/afex/issues/55 o afex now depends on R (>= 3.5.0), as it uses binary/serialized objects version 3. Bugfixes o Sum-to-zero contrasts will now be set to all character variables passed to mixed(). Before, only factor variables were assigned sum-to-zero contrasts and transformation into factors happened only in the call to model.matrix() (which then used the global contrasts). ************************* ** afex VERSION 0.23-x ** ************************* Changes in afex Version 0.23-x Released February 2019 Significant User Visible Changes and New Features o Added afex_plot.default() method which works with a wide variety of fitted objects. See new vignette: vignette("afex_plot_supported_models", package = "afex") o In afex_plot(), renamed 'random' argument to 'id' argument. Bugfixes o Corrected bug in afex_plot() vignette and examples. Correct argument name is factor_levels. o Removed reference to ascii package from documentation, as the package was removed from CRAN. ************************* ** afex VERSION 0.22-x ** ************************* Changes in afex Version 0.22-x Released September 2018 Significant User Visible Changes and New Features o New functions for plotting results (means, error bars, and raw data) using ggplot2, afex_plot(), generic function for afex and lme4::merMod objects. Furthermore added two more functions: - interaction_plot(): workhorse producing interaction plot - oneway_plot(): workhorse producing oneway plot Error bars can display confidence intervals (the default) or standard errors and can be calculated using a variety of different standard errors (e.g., model-based, within-subjects). o Added vignette introducing afex_plot(). o Updated ANOVA vignette to use afex_plot() and the multivariate for follow-up test. o Package emmeans was moved to suggests and needs to be either attached explicitly or called with :: Option 1: emmeans::emmeans() Option 2: library("emmeans") and then just emmeans() o Added call slot to mixed objects holding the matched call. Bugfixes o Error in ANOVA examples using emmeans corrected, see: https://stats.stackexchange.com/q/360900/442 ************************* ** afex VERSION 0.21-x ** ************************* Changes in afex Version 0.21-x Released June 2018 Significant User Visible Changes and New Features o Smaller package footprint: The stringr package is not imported any more, all calls to stringr functions were replaced with calls to base R functions. The coin package (used in compare.2.vectors) was moved from Imports to Suggests. Bugfixes o ANOVA functions produce accurate emmeans even for ANCOVAs, see: https://afex.singmann.science/forums/topic/precise-estimates-from-emmeans-across-lm-and-aov_ez ************************* ** afex VERSION 0.20-x ** ************************* Changes in afex Version 0.20-x Released April 2018 Significant User Visible Changes and New Features o follow-up tests with emmeans for ANOVAs (i.e., objects of class "afex_aov") with repeated-measures factors can now be based on a multivariate model. This provides separate standard errors for each estimate and more adequately accounts for violations of sphericity. To use this model either call emmeans(..., model="multivariate") or set globally via: afex_options(emmeans_model = "multivariate") o ANOVA functions now allow transformations of the dv (thanks to Russell Lenth). o better (i.e., simpler) examples for mixed (use data from MEMSS). Added example showing how to use mixed() with effects package for plotting. o set_data_arg argument of mixed() is now per default controlled via afex_options("set_data_arg"). The default has also changed from TRUE to FALSE. The reason for this change is that FALSE appears to work better with emmeans. o afex_aov objects have received an additional attribute, "incomplete_cases", that contains the IDs of removed participants due to missing values (thanks to Frederik Aust). o afex should now work with the upcoming versions of car (3.0) and lmerTest (3.0). The latter thanks to Rune Haubo Bojesen. Bugfixes o removed bug in mixed that caused a crash if check_contrasts = FALSE and the data contained missing values in the IVs. o removed bug that caused a crash under certain conditions if stringsAsFactors was set to FALSE in the global options and repeated measures factors were present (thanks to Will Hopper for the bug report and simultaneous fix). o set_data_arg now works for lmer_alt and mixed(..., return = "merMod"). This allows to use those objects with e.g., the effects package. o afex should now work with car version 3.0. ************************* ** afex VERSION 0.19-x ** ************************* Changes in afex Version 0.19-0 Released January 2018 Significant User Visible Changes and New Features o afex now works with emmeans (successor of lsmeans pckage). Bugfixes o lsmeans did not work with mixed objects if type=2 and method used nested model comparions (e.g., LRT or PB). o removed warning 'Error() model is singular' when units of observations have missing values for ANOVAs. ************************* ** afex VERSION 0.18-x ** ************************* Changes in afex Version 0.18-0 Released May 2017 Bugfixes o aov_ez did not work with more than one covariate (https://github.com/singmann/afex/issues/29). ************************* ** afex VERSION 0.17-x ** ************************* Changes in afex Version 0.17-x Released April 2017 Significant User Visible Changes and New Features o Added Satterthwaite approximation (method="S") to mixed(), which is implemented via lmerTest. Satterthwaite approximates the degrees-of- freedom of an F-test, similar to the default Kenward-Roger method, but requires less RAM. o mixed() methods "KR" and "S" are now obtained via tests on the full model directly. No restricted models are calculated for these methods. The former KR method is still available: method="nested-KR" o mixed() now per default exports and uses lmerTest::lmer and not lme4::lmer(). This can be changed via calling afex_options(lmer_function = "lme4") o afex does not depend on reshape2 any more. It is only imported. o All arguments with "." in the name have been renamed to use "_". The old names have been deprecated (i.e., still work, but should not be used). check.contrasts = check_contrasts, test.intercept = test_intercept, args.test = args_test, ... o Names of slots of mixed model objects with "." have been renamed to have a "_" instead: full.model = full_model and restricted.models = restricted_models o afex_options() now uses the global R options accessible via options() (with prefix afex.) and allows to reset all options via list (i.e.,: aop <- afex_options(); ...; afex_options(aov); works). o renamed allFit() to all_fit() and argument meth.tab to meth_tab. Added method dfoptim::nmkb() to all_fit(). To use nmkb, dfoptim needs to be loaded explicitly via library (see examples). o Added argument all_fit to mixed(). If TRUE, each model is fitted with all available optimizers and the best fit in each case selected. o mixed objects have an additional slot, "data", that contains the data used for fitting. o Added vignette with extensive mixed model example. o Created forum for providing afex support: http://afex.singmann.science/ Bugfixes o Sphericity correction now correctly displayed as none if all within- factors have only two levels (bug removed by Frederik Aust). o removed bug when calling nice() on afex_aov objects created with explicit effect size. o aov_...(): anova_table = list(intercept = TRUE) now correctly suppresses the intercept (bug removed by Frederik Aust). o aov_...(): return = "nice" did not work (bug removed by Frederik Aust). o aov_...() now supports column names with spaces (using backticks), see: https://github.com/singmann/afex/issues/22 Thx to Jonathan Love for fix. o changed license to GPL >=2 (as it call some function from GPL >=2 packages). o removed bug that mixed() object with type=2 could not be printed. o removed bug that model names for anova.mixed with multiple models were incorrect. o all_fit() now uses a data argument correctly and passes it update(). This again allows to use it for data with suppressed correlations. all_fit(... verbose = TRUE) now correctly signals if a fit failed. ************************* ** afex VERSION 0.16-x ** ************************* Changes in afex Version 0.16-x Released April 2016 Significant User Visible Changes and New Features o added "correction" and "observed" attributes to the anova_table slot of afex_aov objects, which is used per default by nice(). This ensures that nice(object) and object always return the same data.frame. Also added "nice_table" class to data.frame returned by nice which print the value of the slots for information. Both contributed by Frederik Aust (who was also promoted to author). o added return="data" for mixed. This allows to obtain the data set used for fitting a model. Can be useful in combination with expand.re=TRUE and allFit() or for obtaining predictions. See ?allFit for a simple example. Bugfixes o increased required version of R (>= 3.1.0) and the following packages to ensure afex runs with older versions of R: lme4 (>= 1.1-8), pbkrtest (>= 0.4-1), and Matrix (>= 1.1.1). ************************* ** afex VERSION 0.15-x ** ************************* Changes in afex Version 0.15-x Released October 2015 Significant User Visible Changes and New Features o added p.adjust.method argument for ANOVA functions (anova and nice methods). Can be used to control for multiple comparisons in exploratory ANOVAs (see Cramer, et al., 2015; PB&R). Functionality contributed by Frederik Aust (https://github.com/singmann/afex/pull/3). Bugfixes o ANOVA functions work with dplyr data.frames now (data is transformed via as.data.frame). See: https://github.com/singmann/afex/issues/6 o formulas for mixed can now be of a maximum length of 500 characters (was 60 chars previously): https://github.com/singmann/afex/issues/5 o aov_car et al. did not work with within-subject factors that were also included outside the Error term. This was caused by the use of regular expressions not appropriate for the new stringi backend of stringr. Thanks to Tom Wenseleers for reporting this bug. ************************* ** afex VERSION 0.14-x ** ************************* Changes in afex Version 0.14-x Released August 2015 Significant User Visible Changes and New Features o new default return argument for ANOVA functions, afex_aov, an S3 object containing the following: (1) ANOVA table of class "anova" (2) ANOVA fitted with base R's aov (can be passed to lsmeans for post-hoc tests) (3) output from car::Anova (for tests of effects), ANOVA table (1) is based on this model (4) lm object passed to car::Anova (5) data used for estimating (2) and (4) o added support for lsmeans: objects of class afex_aov can be passed to lsmeans directly. afex now depends on lsmeans. o added afex_options() functionality for setting options globally. o added expand_re argument to mixed which, if TRUE, correctly interprets the || notation in random effects with factors (i.e., suppresses estimation of correlation among random effects). lmer_alt is a wrapper for mixed which uses expand_re = TRUE, returns an object of class merMod (i.e., does not calculate p-values), and otherwise behaves like g/lmer (i.e., does not enforce certain contrasts) o added three new data sets (Singmann & Klauer, 2011; Klauer & Singmann, 2013) and a vignette showing how to calculate contrasts after ANOVA. o ANOVA functions renamed to aov_car, aov_ez, and aov_4. Old functions are now deprecated. o first element in mixed object renamed to anova_table. o nice.anova renamed to nice. nice() can be called for afex_aov and mixed objects and returns a nicely formatted (numbers converted to characters) results table (which is also the default print method for both objects). o anova() can be called for afex_aov and mixed objects and returns the numeric anova table (i.e., the first element of each object). There also exists print methods for those data.frames. o summary method for mixed objects now calls summary.merMod on full model. o afex does not depend on car package anymore, it is only imported. o afex is now hosted on github: https://github.com/singmann/afex Bugfixes o ANOVA: for "aov"-objects, contrasts are only set for factors. o compare.2.vector failed when the two means were exactly equal (due to an issue with median_test). This only throws a warning now. o compare.2.vector documentation updated for coin 1-1.0. ************************* ** afex VERSION 0.13-x ** ************************* Changes in afex Version 0.13-x Released January 2015 Significant User Visible Changes and New Features o added ems() function for deriving the expected values of the mean squares for factorial designs (contributed by Jake Westfall). Bugfixes o aov.car et al. stop with error message if a factor has only one level. o aov.car transforms id variable to factor which ensures that return = "aov" provides equivalent results. o changed regex for detecting "observed" variables to work with the new version of stringr which uses stringi. ************************* ** afex VERSION 0.12-x ** ************************* Changes in afex Version 0.12-x Released November 2014 Significant User Visible Changes and New Features o ANOVA functions give informative error if some parameters are not estimable (most likely due to structural missings, i.e. empty cells). Bugfixes o mixed(..., method = "PB") does not fail anymore when only having a single fixed effect (thanks to Kiyoshi Sasaki for reporting it). o aov.car() failed when a within-subject factor had empty levels. Unused factor levels are now dropped. This bug was probably introduced in Rev 126 as part of an attempt to solve a bug. (thanks to Will Bowditch for reporting it). ************************* ** afex VERSION 0.11-x ** ************************* Changes in afex Version 0.11-x Released October 2014 Significant User Visible Changes and New Features o added allFit() function (written by Ben Bolker). o mixed() gives warning if nested model provides worse fit (logLik) than full model (when fitted with ML). o print, summary, and anova method for mixed objects are now identical. o description of returned object from mixed() extended (Thanks to Ben Bolker, see http://stackoverflow.com/a/25612960/289572) o added return = "aov" to aov.car which returns the ANOVA fitted with aov (with correct Error strata) so that it can be passed to lsmeans for post-hoc tests or plotting (lsmip). Bugfixes o all required functions are now correctly imported avoiding CRAN warnings and better functioning. o data argument to lmer calls in mixed set correctly. Note that still contrasts added to the data in mixed may prohibit use of predict.merMod() or similar functions. It is recommended to set the contrasts globally to "contr.sum", e.g., via set_sum_contrasts(), for correct functioning (disable via set.data.arg argument for mixed). ************************ ** afex VERSION 0.10-x ** ************************ Changes in afex Version 0.10-x Released August 2014 Significant User Visible Changes and New Features o afex does not change the global contrasts anymore when loading the package (due to popular demand). o new functions to globally set contrasts: set_sum_contrasts & set_treatment_contrasts (and some more wrappers). o Added more mixed model examples from Maxwell & Delaney, Chapter 15 ("Multilevel Models for within subjects designs"), see ?mixed and ?md_15.1. Thanks to Ulf Mertens. Bugfixes o removed bug when factor levels of within-subject factors contained "+" or "-" and were not converted correctly. Added tests for known bugs in aov.car. ************************ ** afex VERSION 0.9-x ** ************************ Changes in afex Version 0.9-x Released April 2014 Significant User Visible Changes and New Features o added function aov4: another wrapper of car::Anova for ANOVA models specified via lme4::lmer syntax. o added return="marginal" to aov.car which returns the marginal means of all effects (i.e., grand mean and mean of main effects and interactions). Is also returned if return="full". o testing the intercept in mixed models in now only optional. The default is that the new argument test.intercept = FALSE. o removed return="lme4" from aov.car. o added argument intercept to nice.anova (default FALSE) which allows to selective display the intercept in an ANOVA table. o added method = "F" to mixed() which only returns the F-value but no ddf (and hence no p-value). Experimental, not documented. o renamed colname "stat" to "F" when method = "KR" (mixed). o added tests (currently mainly for mixed()) via pkg testthat, see tests/testthat. Bugfixes o increased requirement of R version and lme4 version. o print.mixed should now propagate all warnings from lme4 (i.e., also the new convergence warnings). o lme4 is now loaded at worker nodes for mixed (default, turn of via check.contrasts) ************************ ** afex VERSION 0.8-x ** ************************ Changes in afex Version 0.8-x Released February 2014 Significant User Visible Changes and New Features o removed renaming of within subject factor levels to names with length 1 (which was introduced in 0.6). o helper function round_ps which nicely rounds p-values is now exported. o warning about numerical non-centered variables in mixed is now a message only. o added examples data sets from Maxwell & Delaney (2004) for within-subjects ANOVA and mixed models. o reshape2 is now again in depends but coin only imported. Bugfixes o the default effect size (ges: generalized eta-squared) was calculated wrong (the error term for the intercept was not included). Sorry. This is now corrected (with new examples). o removed bug that aov.car didn't work when running some ANCOVAs (thanks to Gang Chen for reporting this). ************************ ** afex VERSION 0.7-x ** ************************ Changes in afex Version 0.7-x Released December 2013 Significant User Visible Changes and New Features o nicer output of print.mixed Bugfixes o mixed() correctly converts all non-formula arguments to formula correctly to a formula (gave error if formula was a different object and not-available on cluster nodes). Prints message if formula is converted to a formula. o Using multicore for fitting the models prodcued erroneous results (did not use correct contrasts at nodes). Now the current contrasts are also set at the nodes. o mixed() sets REML = FALSE if method = "LRT" and no family argument is present (i.e., for LMMs) as LRTs for models fitted with REML are not recommended. o on the cluster nodes now only the lme4 namespace is loaded (instead of using library) to avoid a CRAN note. ************************ ** afex VERSION 0.6-x ** ************************ Changes in afex Version 0.6-x Released September 2013 Significant User Visible Changes and New Features o added LRT tests to mixed() which should replicate the recommended test by Barr et al. (2013, JML). o multicore estimation of (g)lmer models now available through package parallel (argument cl) for mixed(). o added experimental "lme4" return method for aov.car and ez.glm (which fits the data using lmer). o reshape2 and stringr are not any more loaded when loading afex (are now only imported via Imports) Bugfixes o Type 2 tests of mixed() were implemented incorrectly (i.e., they did not give what they should have given according to the description in the help file). o aov.car() and ez.glm() now convert factor levels of within subjects factors to be of length one so that long levels do not lead to problems when constructing the call to lm. Thanks to Isaac Schwabacher for noticing this, see also: https://bugs.r-project.org/bugzilla3/show_bug.cgi?id=15377 o mixed should now work with missing values as it construes a new data object if the model.matrix from which the different versions are fitted has nrow different to nrow(data) (with warning). Thanks to Daniel Bunker for reporting this. o mixed should work with the newest version of lme4 (>= 1.0.4) and the newst version of pbkrtest (>= 0.3-5.1), but not with older versions (due to CRAN policy to disallow :::). ************************ ** afex VERSION 0.5-x ** ************************ Changes in afex Version 0.5-x Released May 2013 Significant User Visible Changes and New Features o added argument factorize (default: TRUE) to aov.car and ez.glm: all variables are now factorized per default. (now it is necessary to set factorize=FALSE for ANCOVAs!) o added argument per.parameter to mixed() which allows to specify variables for which each parameter is tested (not only the overall effect). Can be useful to test for ordered factors. (only implemented for "Type 3" tests) o added more informative startup message (thanks to Robert Volcic and Lars Konieczny) o mixed, ez.glm and aov.car now check for correct contrasts and set factors to contr.sum if other contrasts are found (can be tunred off via check.contrasts argument). Resetting the default contrast to contr.treatment should therefore not interfere with afex. (this is not intensly tested, so please report anything) o mixed checks numeric variables if they are centered on 0 (and gives warning if not). Bugfixes o checks if observed variable is in the data and throws an error if not (nice.anova) ************************ ** afex VERSION 0.4-x ** ************************ Changes in afex Version 0.4-x Released February 2013 Significant User Visible Changes and New Features o added generalized and partial eta-squared effect sizes to nice.anova (this also included adding observed arguments to aov.car, ez.glm, nice.anova) o added new return arguments to aov.car and ez.glm (nice, lm, data). o changed default return value of aov.car and ez.glm to "nice" which now returns a nice ANOVA table (nice.anova) o mixed has method = "PB" for obtaining parametric bootstrapped p-values (e.g., for GLMMs) o added alternative argument to compare.2.vectors. o aov.car (and ez.glm) now give a warning if observations are missing on within-subject factors. (As before, cases with missing values are simply excluded from the analysis) o had to disable saving of the previous contrasts and resetting those after detaching afex due to CRAN policies (no assignment in global environment). Bugfixes o Bug when running mixed() inside a function and handing the data.frame over as an argument fixed (thanks, again, to Florent Duyme). See bugs/eval.scoping.bug.R o nice.anova did not work with a model with only one within-subjects factor. ************************ ** afex VERSION 0.3-x ** ************************ Changes in afex Version 0.3-x Released August/September 2012 Significant User Visible Changes and New Features o added function compare.2.vectors(). o Name of function univariate() changed to univ(), as a function with this name is part of package multcomp. This may leed to problems. Thanks to Florent Duyme for spotting this. o added return argument to aov.car() and ez.glm(). o added rather dubious Type 2 tests to mixed(). o aov.car checks if each id is only present in one cell of the between subjects design. Bugfixes o aov.car now uses do.call when calling lm() to avoid local variables in the call to lm() which could led to problems when working with the lm model. o mixed() now passes ... (further arguments to lmer) correctly. (Now mixed uses match.call and eval on the call instead of invoking lmer directly.) o corrected bug that was introduced by pbkrtest v3.2 when invoking the print method to an object of class mixed (again thanks to Florent Duyme for spotting this). o removed bug when factor levels of within-subject factors were non-legal names (solution uses make.names). afex/R/0000755000176200001440000000000013531236423011400 5ustar liggesusersafex/R/afex_plot_utils.R0000644000176200001440000002520313607672060014733 0ustar liggesusers afex_plot_internal <- function(x, trace, panel, means, data, error_plot, error_arg, dodge, data_plot, data_geom, data_alpha, data_arg, point_arg, line_arg, mapping, legend_title, return) { if (length(trace) > 0) { means$trace <- interaction(means[trace], sep = "\n") data$trace <- interaction(data[trace], sep = "\n") if (return == "data") { return(list(means = means, data = data)) } else if (return == "plot") { return(interaction_plot(means = means, data = data, error_plot = error_plot, error_arg = error_arg, dodge = dodge, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, line_arg = line_arg, mapping = mapping, legend_title = if (missing(legend_title)) paste(trace, sep = "\n") else legend_title )) } } else { if (return == "data") { return(list(means = means, data = data)) } else if (return == "plot") { return(oneway_plot(means = means, data = data, error_plot = error_plot, error_arg = error_arg, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, mapping = mapping, legend_title = if (missing(legend_title)) paste(x, sep = "\n") else legend_title )) } } } se <- function(x, na.rm = FALSE) sd(x, na.rm = na.rm)/sqrt(length(x)) rename_factor_levels <- function(data, factor_levels, status_message = TRUE) { if (length(factor_levels) > 0) { if (is.null(names(factor_levels))) { stop("factor_levels needs to be a named list.", call. = FALSE) } if (any(!(names(factor_levels) %in% colnames(data)))) { if (status_message) { warning( "factor_levels: No factor named ", paste( paste0("'", names(factor_levels) [!(names(factor_levels) %in% colnames(data))], "'"), collapse = ", "), " in data.", call. = FALSE ) } factor_levels <- factor_levels[names(factor_levels) %in% colnames(data)] } for (i in seq_along(factor_levels)) { if (is.null(names(factor_levels[[i]]))) { if (length(factor_levels[[i]]) != length(levels(data[[names(factor_levels)[i]]]))) { stop("length of new factor_levels for '", names(factor_levels)[i], "' != length of factor levels.", call. = FALSE) } names(factor_levels[[i]]) <- levels(data[[names(factor_levels)[i]]]) } factor_levels[[i]] <- factor_levels[[i]][ names(factor_levels[[i]]) %in% levels(data[[names(factor_levels)[i]]]) ] if (status_message) { message("Renaming/reordering factor levels of '", names(factor_levels)[i], "':\n ", paste( paste( levels(data[[names(factor_levels)[i]]])[ match(names(factor_levels[[i]]), levels(data[[names(factor_levels)[i]]])) ], factor_levels[[i]], sep = " -> "), collapse = "\n ") ) } if (length(factor_levels[[i]]) == length(levels(data[[names(factor_levels)[i]]]))) { data[[names(factor_levels)[i]]] <- factor( x = data[[names(factor_levels)[i]]], levels = names(factor_levels[[i]]), labels = factor_levels[[i]] ) } else { levels(data[[names(factor_levels)[i]]])[ match(names(factor_levels[[i]]), levels(data[[names(factor_levels)[i]]])) ] <- factor_levels[[i]] } } } data } get_emms <- function(object, x, trace, panel, emmeans_arg, factor_levels, level) { if (!requireNamespace("emmeans", quietly = TRUE)) { stop("package emmeans is required.", call. = FALSE) } all_vars <- c(x, trace, panel) emmeans_arg$options$level <- level emms <- as.data.frame(do.call(emmeans::emmeans, args = c(object = list(object), specs = list(all_vars), type = list("response"), emmeans_arg))) emms <- rename_factor_levels( data = emms, factor_levels = factor_levels, status_message = TRUE ) emms$x <- interaction(emms[x], sep = "\n") #col_y <- colnames(emms)[which(colnames(emms) == "SE")-1] if (any(colnames(emms) == "SE")) { colnames(emms)[which(colnames(emms) == "SE")-1] <- "y" } else { colnames(emms)[grep("CL|HPD", colnames(emms))[1]-1] <- "y" } attr(emms, "dv") <- attr(object, "dv") attr(emms, "x") <- paste(x, collapse = " - ") if (length(panel) > 0) { emms$panel <- interaction(emms[panel], sep = "\n") } else { emms$panel <- "1" } emms$all_vars <- interaction(emms[all_vars], sep = ".") return(emms) } prep_data <- function(data, x, trace, panel, factor_levels, dv_col, id) { all_vars <- c(x, trace, panel) data <- rename_factor_levels( data = data, factor_levels = factor_levels, status_message = FALSE ) colnames(data)[colnames(data) == dv_col] <- "y" if (!is.numeric(data$y)) { message("transforming dv to numerical scale") data$y <- as.numeric(data$y) } data <- aggregate(data$y, by = data[c(all_vars,id)], FUN = mean, drop = TRUE) data$y <- data$x data$x <- interaction(data[x], sep = "\n") if (length(panel) > 0) { data$panel <- interaction(data[panel], sep = "\n") } else { data$panel <- "1" } data$all_vars <- interaction(data[all_vars], sep = ".") return(data) } get_plot_var <- function(x) { if (missing(x)) return() if (inherits(x, "formula")) { return(all.vars(x[[2]])) } else { return(x) } } get_data_based_cis <- function(emms, data, error, id, ## colname holding the id/grouping variable all_vars, within_vars, between_vars, error_level, error_ci) { error_plot <- TRUE ## SE/CI calculation: if (error == "model") { emms$error <- emms$SE # emms$lower <- emms$lower.CL # emms$upper <- emms$upper.CL col_cis <- grep("CL|HPD", colnames(emms), value = TRUE) col_cis <- col_cis[!(col_cis %in% all_vars)] emms$lower <- emms[,col_cis[1]] emms$upper <- emms[,col_cis[2]] } else if (error == "mean") { ses <- tapply(data$y, INDEX = list(data$all_vars), FUN = se) sizes <- tapply(data$y, INDEX = list(data$all_vars), FUN = length) stopifnot(emms$all_vars %in% names(ses)) emms$error <- ses[emms$all_vars] emms$lower <- emms$y - qt(1-(1-error_level)/2, sizes - 1) * emms$error emms$upper <- emms$y + qt(1-(1-error_level)/2, sizes - 1) * emms$error } else if (error %in% c("CMO", "within")) { if (length(within_vars) == 0) { stop("within-subject SE only possible if within-subject factors present.", call. = FALSE) } within_fac <- interaction(data[within_vars], sep = ".") indiv_means <- tapply(data$y, INDEX = data[id], FUN = mean) J <- length(levels(within_fac)) ## Cosineau & O'Brien (2014), Equation 2: new_y <- data$y - indiv_means[as.character(data[,id])] + mean(data$y) ## Cosineau & O'Brien (2014), Equation 4: y_bar <- tapply(new_y, INDEX = within_fac, FUN = mean) new_z <- sqrt(J / (J-1)) * (new_y - y_bar[within_fac]) + y_bar[within_fac] ses <- tapply(new_z, INDEX = list(data$all_vars), FUN = se) sizes <- tapply(new_z, INDEX = list(data$all_vars), FUN = length) stopifnot(emms$all_vars %in% names(ses)) emms$error <- ses[emms$all_vars] emms$lower <- emms$y - qt(1-(1-error_level)/2, sizes - 1) * emms$error emms$upper <- emms$y + qt(1-(1-error_level)/2, sizes - 1) * emms$error } else if (error == "between") { if (length(between_vars) > 0) { between_fac <- interaction(data[between_vars], sep = ".") } else { between_fac <- factor(rep("1", nrow(data))) } indiv_means <- aggregate(data$y, by = list( data[,id], between_fac), FUN = mean) ses <- tapply(indiv_means$x, INDEX = indiv_means[["Group.2"]], FUN = se) sizes <- tapply(indiv_means$x, INDEX = indiv_means[["Group.2"]], FUN = length) if (length(between_vars) == 0) { emms$error <- ses emms$lower <- emms$y - qt(1-(1-error_level)/2, sizes - 1) * emms$error emms$upper <- emms$y + qt(1-(1-error_level)/2, sizes - 1) * emms$error } else { emm_between <- interaction(emms[between_vars], sep = ".") emms$error <- ses[emm_between] emms$lower <- emms$y - qt(1-(1-error_level)/2, sizes[emm_between] - 1) * emms$error emms$upper <- emms$y + qt(1-(1-error_level)/2, sizes[emm_between] - 1) * emms$error } } else if (error == "none") { emms$error <- NA_real_ emms$lower <- NA_real_ emms$upper <- NA_real_ error_plot <- FALSE } if (!error_ci) { emms$lower <- emms$y - emms$error emms$upper <- emms$y + emms$error } return(list(emms = emms, error_plot = error_plot)) }afex/R/compare.2.vectors.R0000644000176200001440000002121413351525342014776 0ustar liggesusers#' Compare two vectors using various tests. #' #' Compares two vectors \code{x} and \code{y} using t-test, Welch-test (also known as Satterthwaite), Wilcoxon-test, and a permutation test implemented in \pkg{coin}. #' #' @usage compare.2.vectors(x, y, paired = FALSE, na.rm = FALSE, #' tests = c("parametric", "nonparametric"), coin = TRUE, #' alternative = "two.sided", #' perm.distribution, #' wilcox.exact = NULL, wilcox.correct = TRUE) #' #' @param x a (non-empty) numeric vector of data values. #' @param y a (non-empty) numeric vector of data values. #' @param paired a logical whether the data is paired. Default is \code{FALSE}. #' @param na.rm logical. Should \code{NA} be removed? Default is \code{FALSE}. #' @param tests Which tests to report, parametric or nonparamteric? The default \code{c("parametric", "nonparametric")} reports both. See details. (Arguments may be abbreviated). #' @param alternative a character, the alternative hypothesis must be one of \code{"two.sided"} (default), \code{"greater"} or \code{"less"}. You can specify just the initial letter, will be passed to all functions. #' @param coin logical or character. Should (permutation) tests from the \pkg{coin} package be reported? Default is \code{TRUE} corresponding to all implemented tests. \code{FALSE} calculates no tests from \pkg{coin}. A character vector may include any of the following (potentially abbreviated) implemented tests (see also Details): \code{c("permutation", "Wilcoxon", "median")} #' @param perm.distribution \code{distribution} argument to \pkg{coin}, see \code{\link[coin]{NullDistribution}} or , \code{\link[coin]{IndependenceTest}}. If missing, defaults to \code{coin::approximate(100000)} indicating an approximation of the excat conditional distribution with 100.000 Monte Carlo samples. One can use \code{"exact"} for small samples and if \code{paired = FALSE}. #' @param wilcox.exact \code{exact} argument to \code{\link{wilcox.test}}. #' @param wilcox.correct \code{correct} argument to \code{\link{wilcox.test}}. #' #' @details The \code{parametric} tests (currently) only contain the \emph{t}-test and Welch/Statterwaithe/Smith/unequal variance \emph{t}-test implemented in \code{\link{t.test}}. The latter one is only displayed if \code{paired = FALSE}. #' #' The \code{nonparametric} tests (currently) contain the Wilcoxon test implemented in \code{\link{wilcox.test}} (\code{stats::Wilcoxon}) and (if \code{coin = TRUE}) the following tests implemented in \pkg{coin}: #' #' \itemize{ #' \item a \code{permutation} test \code{\link[coin]{oneway_test}} (the only test in this selction not using a rank transformation), #' \item the \code{Wilcoxon} test \code{\link[coin]{wilcox_test}} (\code{coin::Wilcoxon}), and #' \item the \code{median} test \code{\link[coin]{median_test}}. #' } #' Note that the two implementations of the Wilcoxon test probably differ. This is due to differences in the calculation of the Null distributions. #' #' @return a list with up to two elements (i.e., \code{paramteric} and/or \code{nonparamteric}) each containing a \code{data.frame} with the following columns: \code{test}, \code{test.statistic}, \code{test.value}, \code{test.df}, \code{p}. #' #' @export compare.2.vectors # @importFrom coin oneway_test wilcox_test median_test approximate statistic pvalue #' @importFrom stats t.test wilcox.test #' @example examples/examples.compare.R #' #' @encoding UTF-8 #' compare.2.vectors <- function(x, y, paired = FALSE, na.rm = FALSE, tests = c("parametric", "nonparametric"), coin = TRUE, alternative = "two.sided", perm.distribution, wilcox.exact = NULL, wilcox.correct = TRUE) { tests <- match.arg(tests, c("parametric", "nonparametric"), several.ok = TRUE) if (na.rm) { x <- x[!is.na(x)] y <- y[!is.na(y)] } else if (any(is.na(x), is.na(y))) stop("NAs in data, use na.rm = TRUE.", call. = FALSE) out <- list() if (paired) if (!length(x) == length(y)) stop("length(x) needs to be equal to length(y) when paired is TRUE!", call. = FALSE) if ("parametric" %in% tests) { res.t <- t.test(x, y, paired = paired, var.equal = TRUE, alternative = alternative) parametric <- data.frame(test = "t", test.statistic = "t", test.value = res.t[["statistic"]], test.df = res.t[["parameter"]], p = res.t[["p.value"]], stringsAsFactors = FALSE) if (!paired) { res.welch <- t.test(x, y, paired = paired, var.equal = FALSE, alternative = alternative) parametric <- rbind(parametric, data.frame(test = "Welch", test.statistic = "t", test.value = res.welch[["statistic"]], test.df = res.welch[["parameter"]], p = res.welch[["p.value"]], stringsAsFactors = FALSE)) } rownames(parametric) <- NULL out <- c(out, list(parametric = parametric)) } if ("nonparametric" %in% tests) { implemented.tests <- c("permutation", "Wilcoxon", "median") res.wilcox <- wilcox.test(x, y, paired = paired, exact = wilcox.exact, correct = wilcox.correct, alternative = alternative) nonparametric <- data.frame(test = "stats::Wilcoxon", test.statistic = if (paired) "V" else "W", test.value = res.wilcox[["statistic"]], test.df = NA, p = res.wilcox[["p.value"]], stringsAsFactors = FALSE) if (!(coin == FALSE) && !requireNamespace("coin", quietly = TRUE)) { warning("package coin necessary if coin != FALSE.") coin <- FALSE } if (!(coin == FALSE)) { dv <- c(x, y) iv <- factor(rep(c("A", "B"), c(length(x), length(y)))) if (missing(perm.distribution)) { perm.distribution <- coin::approximate(100000) } if (paired) { id <- factor(rep(1:length(x), 2)) formula.coin <- as.formula(dv ~ iv | id) } else formula.coin <- as.formula(dv ~ iv) if (isTRUE(coin)) coin <- implemented.tests else coin <- match.arg(coin, implemented.tests, several.ok = TRUE) tryCatch(if ("permutation" %in% coin) { res.perm <- coin::oneway_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "permutation", test.statistic = "Z", test.value = coin::statistic(res.perm), test.df = NA, p = coin::pvalue(res.perm)[1], stringsAsFactors = FALSE)) }, error = function(e) warning(paste("coin::permutation test failed:", e))) tryCatch(if ("Wilcoxon" %in% coin) { res.coin.wilcox <- coin::wilcox_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "coin::Wilcoxon", test.statistic = "Z", test.value = coin::statistic(res.coin.wilcox), test.df = NA, p = coin::pvalue(res.coin.wilcox)[1], stringsAsFactors = FALSE)) }, error = function(e) warning(paste("coin::Wilcoxon test failed:", e))) tryCatch(if ("median" %in% coin) { res.median <- coin::median_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "median", test.statistic = "Z", test.value = coin::statistic(res.median), test.df = NA, p = coin::pvalue(res.median)[1], stringsAsFactors = FALSE)) }, error = function(e) warning(paste("coin::median test failed:", e))) } rownames(nonparametric) <- NULL out <- c(out, nonparametric = list(nonparametric)) } out } afex/R/ks2013.3-data.R0000644000176200001440000000643213351525342013524 0ustar liggesusers#' Data from Klauer & Singmann (2013, Experiment 3) #' #' Klauer and Singmann (2013) attempted to replicate an hypothesis of Morsanyi and Handley (2012) according to which individuals have an intuitive sense of logicality. Specifically, Morsanyi and Handley apparently provided evidence that the logical status of syllogisms (i.e., valid or invalid) affects participants liking ratings of the conclusion of syllogisms. Conclusions from valid syllogisms (e.g., Some snakes are poisonous. No poisonous animals are obbs. Some snakes are not obbs.) received higher liking ratings than conclusions from invalid syllogisms (e.g., No ice creams are vons. Some vons are hot. Some ice creams are not hot.). It is important to noted that in the experiments participants were simply shown the premises and conclusion in succession, they were not asked whether or not the conclusion follows or to generate their own conclusion. Their task was simply to judge how much they liked the "final" statement (i.e., the conclusion). #' #' In their Experiment 3 Klauer and Singmann (2013) tested the idea that this finding was a consequence of the materials used and not an effect intuitive logic. More specifically, they observed that in the original study by Morsanyi and Handley (2012) a specific content always appeared with the same logical status. For example, the "ice-cream" content only ever appeared as an invalid syllogism as in the example above but never in a valid syllogism. In other words, content was perfectly confounded with logical status in the original study. To test this they compared a condition in which the logical status was confounded with the content (the "fixed" condition) with a condition in which the contents were randomly assigned to a logical status across participants (the "random" condition). For example, the ice-cream content was, across participants, equally like to appear in the invalid form as given above or in the following valid form: No hot things are vons. Some vons are ice creams. Conclusion Some ice creams are not hot. #' #' The data.frame contains the raw responses of all 60 participants (30 per condition) reported in Klauer & Singmann (2013). Each participants provided 24 responses, 12 to valid and 12 to invalid syllogisms. Furthermore, 8 syllogisms had a believable conclusion (e.g., Some ice creams are not hot.), 8 had an abstract conclusion (e.g., Some snakes are not obbs.), and 8 had an unbelievable conclusion (e.g., Some animals are not monkeys.). The number of the contents corresponds to the numbering given in Morsanyi and Handley (2012, p. 616). #' #' #' @docType data #' @keywords dataset #' @name ks2013.3 #' @usage ks2013.3 #' @format A data.frame with 1440 rows and 6 variables. #' @source Klauer, K. C., & Singmann, H. (2013). Does logic feel good? Testing for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39(4), 1265-1273. http://doi.org/10.1037/a0030530 #' #' Morsanyi, K., & Handley, S. J. (2012). Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(3), 596-616. http://doi.org/10.1037/a0026099 #' #' #' #' #' @encoding UTF-8 #' #' @example examples/examples.ks2013.3.R NULL afex/R/md_12.1-data.R0000644000176200001440000000515713351525342013504 0ustar liggesusers#' Data 12.1 from Maxwell & Delaney #' #' Hypothetical Reaction Time Data for 2 x 3 Perceptual Experiment: Example data for chapter 12 of Maaxwell and Delaney (2004, Table 12.1, p. 574) in long format. Has two within.subjects factors: angle and noise. #' #' Description from pp. 573: #' #' Suppose that a perceptual psychologist studying the visual system was interested in determining the #' extent to which interfering visual stimuli slow the ability to recognize letters. Subjects are #' brought into a laboratory and seated in front of a tachistoscope. Subjects are told that they will #' see either the letter T or the letter I displayed on the screen. In some trials, the letter appears #' by itself, but in other trials, the target letter is embedded in a group of other letters. This #' variation in the display constitutes the first factor, which is referred to as noise. The noise #' factor has two levels?absent and present. The other factor varied by the experimenter is where in #' the display the target letter appears. This factor, which is called angle, has three levels. The #' target letter is either shown at the center of the screen (i.e., 0° off-center, where the subject #' has been instructed to fixate), 4° off-center or 8° off-center (in each case, the deviation from the #' center varies randomly between left and right). Table 12.1 presents hypothetical data for 10 #' subjects. As usual, the sample size is kept small to make the calculations easier to follow. The #' dependent measure is reaction time (latency), measured in milliseconds (ms), required by a subject #' to identify the correct target letter. Notice that each subject has six scores, one for each #' combination of the 2 x 3 design. In an actual perceptual experiment, each of these six scores would #' itself be the mean score for that subject across a number of trials in the particular condition. #' Although "trials" could be used as a third within-subjects factor in such a situation, more #' typically trials are simply averaged over to obtain a more stable measure of the individual's #' performance in each condition. #' #' @docType data #' @keywords dataset #' @name md_12.1 #' @usage md_12.1 #' @format A data.frame with 60 rows and 4 variables. #' @source Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 #' #' @encoding UTF-8 #' #' @examples #' data(md_12.1) #' #' # Table 12.5 (p. 578): #' aov_ez("id", "rt", md_12.1, within = c("angle", "noise"), #' args.return=list(correction = "none", es = "none")) #' #' NULL afex/R/utils.R0000644000176200001440000000445613351525342012675 0ustar liggesusers ## paste function that can replace stringr::str_c and differs from the way # paste handles NULL arguments as last arguments. # It checks whether the first or last char of the string is equal to sep and # removes it in this case. mypaste <- function(..., sep) { tmp <- paste(..., sep = sep) if (substr(tmp, nchar(tmp), nchar(tmp)) == sep) { tmp <- substr(tmp, 1, nchar(tmp)-1) } if (substr(tmp, 1, 1) == sep) { tmp <- substr(tmp, 2, nchar(tmp)) } tmp } escape_vars <- function(names) { if (length(names) == 0) return(names) names <- vapply(names, function(name) { if (make.names(name) != name) { name <- gsub('\\', '\\\\', name, fixed=TRUE) name <- gsub('`', '\\`', name, fixed=TRUE) name <- paste0('`', name, '`') } name }, FUN.VALUE='', USE.NAMES=FALSE) names } # decompose functions from jmvcore decomposeTerm <- function(term) { chars <- strsplit(term, '')[[1]] components <- character() componentChars <- character() inQuote <- FALSE i <- 1 n <- length(chars) while (i <= n) { char <- chars[i] if (char == '`') { inQuote <- ! inQuote } else if (char == '\\') { i <- i + 1 char <- chars[i] componentChars <- c(componentChars, char) } else if (char == ':' && inQuote == FALSE) { component <- paste0(componentChars, collapse='') components <- c(components, component) componentChars <- character() } else { componentChars <- c(componentChars, char) } i <- i + 1 } component <- paste0(componentChars, collapse='') components <- c(components, component) components } print_legend <- function(x) { sig_symbols <- as.character(attr(x, "sig_symbols")) if(length(sig_symbols) > 0 & !all(sig_symbols == rep("", 4))) { sleg <- attr(stats::symnum(0, cutpoints = c(0, 0.001, 0.01, 0.05, 0.1, 1), symbols = rev(c(" " , trimws(sig_symbols)))), "legend") width <- getOption("width") if(width < nchar(sleg)) { sleg <- strwrap(sleg, width = width - 2, prefix = " ") } cat("---\nSignif. codes: ", sleg, sep = "", fill = getOption("width") + 4 + max(nchar(sleg, "bytes") - nchar(sleg))) } } afex/R/zzz.R0000644000176200001440000000460013531236423012360 0ustar liggesusers ## set default options for afex_options: .onLoad <- function(libname, pkgname) { op <- options() op.afex <- list( afex.type = 3, afex.set_data_arg = FALSE, afex.check_contrasts = TRUE, afex.method_mixed = "KR", afex.return_aov = "afex_aov", afex.es_aov = "ges", afex.correction_aov = "GG", afex.factorize = TRUE, afex.lmer_function = "lmerTest", afex.sig_symbols = c(" +", " *", " **", " ***"), afex.emmeans_model = c("univariate"), afex.include_aov = TRUE ) toset <- !(names(op.afex) %in% names(op)) if(any(toset)) options(op.afex[toset]) if (requireNamespace("emmeans", quietly = TRUE)) { emmeans::.emm_register(c("mixed", "afex_aov"), pkgname) } invisible() } .onAttach <- function(libname, pkgname) { #assign(".oldContrasts", options("contrasts"), envir = .GlobalEnv) packageStartupMessage("************\nWelcome to afex. For support visit: http://afex.singmann.science/") packageStartupMessage("- Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()\n- Methods for calculating p-values with mixed(): 'KR', 'S', 'LRT', and 'PB'\n- 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests\n- NEWS: library('emmeans') now needs to be called explicitly!\n- Get and set global package options with: afex_options()\n- Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()\n- For example analyses see: browseVignettes(\"afex\")\n************") #if (options("contrasts")[[1]][1] != "contr.sum") { #packageStartupMessage("Setting contrasts to effects coding: options(contrasts=c('contr.sum', 'contr.poly'))\nThis affects all functions using contrasts (e.g., lmer, lm, aov, ...).\nTo reset default settings run: options(contrasts=c('contr.treatment', 'contr.poly')) (all afex functions should be unaffected by this)\n") # \nPrevious contrasts saved in '.oldContrasts'. #options(contrasts=c('contr.sum', 'contr.poly')) #} else packageStartupMessage("Contrasts already set to effects coding: options(contrasts=c('contr.sum', '...'))\n") #packageStartupMessage("afex loads the required packages (e.g., lme4, car, pbkrtest) in an order that should not lead to problems.\nLoading any of the packages (specifically lme4) beforehand can lead to problems (especially with older versions of either).\nLoading nlme in addition to afex (before or after loading it), may especially lead to problems.\n************") } afex/R/afex-package.R0000644000176200001440000000026013351525342014036 0ustar liggesusers#' \packageDescription{afex} #' #' The DESCRIPTION file: #' \packageDESCRIPTION{afex} #' #' @title #' \packageTitle{afex} #' #' Maintainer: \packageMaintainer{afex} "_PACKAGE" afex/R/obk.long-data.R0000644000176200001440000000554313351525342014153 0ustar liggesusers#' O'Brien Kaiser's Repeated-Measures Dataset with Covariate #' #' This is the long version of the \code{OBrienKaiser} dataset from the \pkg{car} pakage adding a random covariate \code{age}. Originally the dataset ist taken from O'Brien and Kaiser (1985). The description from \code{\link[carData]{OBrienKaiser}} says: "These contrived repeated-measures data are taken from O'Brien and Kaiser (1985). The data are from an imaginary study in which 16 female and male subjects, who are divided into three treatments, are measured at a pretest, postest, and a follow-up session; during each session, they are measured at five occasions at intervals of one hour. The design, therefore, has two between-subject and two within-subject factors." #' #' @docType data #' @keywords dataset #' @name obk.long #' @usage obk.long #' @format A data frame with 240 rows and 7 variables. #' @source O'Brien, R. G., & Kaiser, M. K. (1985). MANOVA method for analyzing repeated measures designs: An extensive primer. \emph{Psychological Bulletin}, 97, 316-333. doi:10.1037/0033-2909.97.2.316 #' #' @encoding UTF-8 #' #' @examples #' # The dataset is constructed as follows: #' data("OBrienKaiser", package = "carData") #' set.seed(1) #' OBrienKaiser2 <- within(OBrienKaiser, { #' id <- factor(1:nrow(OBrienKaiser)) #' age <- scale(sample(18:35, nrow(OBrienKaiser), replace = TRUE), scale = FALSE)}) #' attributes(OBrienKaiser2$age) <- NULL # needed or resahpe2::melt throws an error. #' OBrienKaiser2$age <- as.numeric(OBrienKaiser2$age) #' obk.long <- reshape2::melt(OBrienKaiser2, id.vars = c("id", "treatment", "gender", "age")) #' obk.long[,c("phase", "hour")] <- lapply(as.data.frame(do.call(rbind, #' strsplit(as.character(obk.long$variable), "\\."),)), factor) #' obk.long <- obk.long[,c("id", "treatment", "gender", "age", "phase", "hour", "value")] #' obk.long <- obk.long[order(obk.long$id),] #' rownames(obk.long) <- NULL #' str(obk.long) #' ## 'data.frame': 240 obs. of 7 variables: #' ## $ id : Factor w/ 16 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ... #' ## $ treatment: Factor w/ 3 levels "control","A",..: 1 1 1 1 1 1 1 1 1 1 ... #' ## $ gender : Factor w/ 2 levels "F","M": 2 2 2 2 2 2 2 2 2 2 ... #' ## $ age : num -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 -4.75 ... #' ## $ phase : Factor w/ 3 levels "fup","post","pre": 3 3 3 3 3 2 2 2 2 2 ... #' ## $ hour : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ... #' ## $ value : num 1 2 4 2 1 3 2 5 3 2 ... #' head(obk.long) #' ## id treatment gender age phase hour value #' ## 1 1 control M -4.75 pre 1 1 #' ## 2 1 control M -4.75 pre 2 2 #' ## 3 1 control M -4.75 pre 3 4 #' ## 4 1 control M -4.75 pre 4 2 #' ## 5 1 control M -4.75 pre 5 1 #' ## 6 1 control M -4.75 post 1 3 NULL afex/R/helpers.R0000644000176200001440000001077513506224623013200 0ustar liggesusers#' Set/get global afex options #' #' Global afex options are used, for example, by \code{\link{aov_car}} (et al.) #' and \code{\link{mixed}}. But can be changed in each functions directly using #' an argument (which has precedence over the global options). #' #' @param ... One of four: (1) nothing, then returns all options as a list; (2) #' a name of an option element, then returns its' value; (3) a name-value pair #' which sets the corresponding option to the new value (and returns nothing), #' (4) a list with option-value pairs which sets all the corresponding #' arguments. The example show all possible cases. #' #' @details The following arguments are currently set: #' \itemize{ #' \item \code{check_contrasts} should contrasts be checked and changed to #' sum-to-zero contrasts? Default is \code{TRUE}. #' \item \code{type} type of sums-of-squares to be used for testing effects, #' default is 3 which reports Type 3 tests. #' \item \code{method_mixed}: Method used to obtain p-values in #' \code{\link{mixed}}, default is \code{"KR"} (which will change to #' \code{"LRT"} soon). (\code{mixed()} only) #' \item \code{es_aov}: Effect size reported for ANOVAs (see #' \code{\link{aov_car}}), default is \code{"ges"} (generalized eta-squared). #' \item \code{correction_aov}: Correction used for within-subjects factors with #' more than two levels for ANOVAs (see \code{\link{aov_car}} or #' \code{\link{nice}}), default is \code{"GG"} (Greenhouse-Geisser correction). #' (ANOVA functions only) #' \item \code{emmeans_model}: Which model should be used by \pkg{emmeans} for #' follow-up analysis of ANOVAs (i.e., objects pf class \code{"afex_aov"})? #' Default is \code{"univariate"} which uses the \code{aov} model object (if #' present). The other option is \code{"multivariate"} which uses the \code{lm} #' model object (which is an object of class \code{"mlm"} in case #' repeated-measures factors are present). #' \item \code{include_aov}: Should the \code{aov} model be included into ANOVA objects of class \code{"afex_aov"}? Setting this to \code{FALSE} can lead to considerable speed improvements. #' \item \code{factorize}: Should between subject factors be factorized (with #' note) before running the analysis? Default is \code{TRUE}. (ANOVA functions #' only) #' \item \code{sig_symbols}: Default significant symbols used for ANOVA and #' \code{mixed} printing. Default is\code{c(" +", " *", " **", " ***")}. #' \item \code{lmer_function}: Which \code{lmer} function should \code{mixed} or #' \code{lmer_alt} use. The default is \code{"lmerTest"} which uses #' \code{\link[lmerTest]{lmer}}, \code{"lme4"} is also possible which uses #' \code{\link[lme4]{lmer}}. Note that \code{mixed} methods \code{"KR"} and #' \code{"S"} only work with \code{"lmerTest"}. For the other methods, #' \code{"lme4"} could be minimally faster, but does not allow to use #' \code{lmerTest::anova()}. #' \item \code{return_aov}: Return value of the ANOVA functions (see #' \code{\link{aov_car}}), default is \code{"nice"}. #' } #' #' @note All options are saved in the global R \code{\link{options}} with prefix #' \code{afex.} #' #' @return depends on input, see above. #' #' @example examples/examples.helpers.R #' #' @export # afex_options <- function(...) # { # dots <- list(...) # if (length(dots) == 0) return(ls.str(envir = .afexEnv)) # else { # if (!is.null(names(dots))) { # if (length(dots) > 1) stop("afex_options can only return a single element.") # for (i in seq_along(dots)) { # assign(names(dots)[i], dots[[i]], envir = .afexEnv) # } # } else return(get(dots[[1]], envir = .afexEnv)) # } # } afex_options <- function(...) { dots <- list(...) #browser() if (length(dots) == 0) { # branch to get all afex options op <- options() afex_op <- op[grepl("^afex.", names(op))] names(afex_op) <- sub("^afex.", "", names(afex_op)) return(afex_op) } else if (is.list(dots[[1]])) { # set several afex options as a list: newop <- dots[[1]] names(newop) <- paste0("afex.", names(newop)) options(newop) } else if (!is.null(names(dots))) { newop <- dots names(newop) <- paste0("afex.", names(newop)) options(newop) } else if (is.null(names(dots))) { # get a single afex options if (length(dots) > 1) stop("afex_options() can only return the value of a single option.", call. = FALSE) return(getOption(paste0("afex.", unlist(dots)))) } else { warning("Unsopported command to afex_options(), nothing done.", call. = FALSE) } } afex/R/deprecated.R0000644000176200001440000000206013351525342013622 0ustar liggesusers#' Deprecated functions #' #' These functions have been renamed and deprecated in \pkg{afex}: #' \code{aov.car()} (use \code{\link{aov_car}()}), #' \code{ez.glm()} (use \code{\link{aov_ez}()}), #' \code{aov4()} (use \code{\link{aov_4}()}). #' @rdname deprecated #' @keywords internal #' @aliases afex-deprecated #' @param ... arguments passed from the old functions of the style #' \code{foo.bar()} to the new functions \code{foo_bar()} #' @export aov.car <- function(...) { .Deprecated("aov_car", "afex", "aov.car was renamed to aov_car and is now deprecated.") aov_car(...) } #' @rdname deprecated #' @export ez.glm <- function(...) { .Deprecated("aov_ez", "afex", "ez.glm was renamed to aov_ez and is now deprecated.") aov_ez(...) } #' @rdname deprecated #' @export aov4 <- function(...) { .Deprecated("aov_4", "afex", "aov4 was renamed to aov_4 and is now deprecated.") aov_4(...) } warn_deprecated_arg <- function(name, instead) { warning(gettextf("'%s' is deprecated; use '%s' instead", name, instead), call.=FALSE, domain=NA) } afex/R/round_ps.R0000644000176200001440000000137213351525342013360 0ustar liggesusers#' Helper function which rounds p-values #' #' p-values are rounded in a sane way: .99 - .01 to two digits, < .01 to three digits, < .001 to four digits. #' #' @usage round_ps(x) #' #' @param x a numeric vector #' #' @return A character vector with the same length of x. #' #' @author Henrik Singmann #' #' @encoding UTF-8 #' #' @export round_ps #' @examples #' round_ps(runif(10)) #' #' round_ps(runif(10, 0, .01)) #' #' round_ps(runif(10, 0, .001)) #' #' round_ps(0.0000000099) #' round_ps <- function(x) { substr(as.character(ifelse(x < 0.0001, " <.0001", ifelse(x < 0.001, formatC(x, digits = 4, format = "f"), ifelse(x < 0.01, formatC(x, digits = 3, format = "f"), ifelse(round(x, 2) == 1, " >.99", formatC(x, digits = 2, format = "f")))))), 2, 7) } afex/R/lmerTest_utils.R0000644000176200001440000000666713351525342014562 0ustar liggesusers #' @importFrom utils packageVersion #' @importFrom methods as #' @importFrom stats anova lmerTest_anova <- function(object, ...) { # Produce lmerTest-anova table for lmer-model fits (lme4 or lmerTest) with old # as well as new lmerTest package. # Standard method dispatch for all non-lmerMod objects. pkg_version <- "2.0-37.9005" if(!inherits(object, "lmerMod")) return(anova(object, ...)) # non-lmer objects if(requireNamespace("lmerTest", quietly=TRUE) && packageVersion("lmerTest") < pkg_version) { stop("Newer version of lmerTest is required.") } if(requireNamespace("lmerTest", quietly=TRUE) && packageVersion("lmerTest") >= pkg_version) { if(inherits(object, "lmerModLmerTest")) return(anova(object, ...)) else # lmerTest object return(anova(lmerTest::as_lmerModLmerTest(object), ...)) # lme4 object } return(anova(object, ...)) # *merModLmerTest objects and/or 'lmerTest' is not available } lmerTest_summary <- function(object, ...) { # Produce lmerTest-summary for lmer-model fits (lme4 or lmerTest) with old # as well as new lmerTest package. # Standard method dispatch for all non-lmerMod objects. pkg_version <- "2.0-37.9005" if(!inherits(object, "lmerMod")) return(summary(object, ...)) # non-lmer objects if(requireNamespace("lmerTest", quietly=TRUE) && packageVersion("lmerTest") < pkg_version) { stop("Newer version of lmerTest is required.") } if(requireNamespace("lmerTest", quietly=TRUE) && packageVersion("lmerTest") >= pkg_version) { if(inherits(object, "lmerModLmerTest")) return(summary(object, ...)) else # lmerTest object return(summary(lmerTest::as_lmerModLmerTest(object), ...)) # lme4 object } return(summary(object, ...)) # *merModLmerTest objects and/or 'lmerTest' is not available } is_lmerTest_class <- function(object) # Check if an object is of class merModLmerTest or lmerModLmerTest # Bridges across versions of lmerTest inherits(object, "merModLmerTest") || inherits(object, "lmerModLmerTest") # anova_lmerTest <- function(object, ...) { # # Dispatch the right anova method across lmerTest versions # if(is_lmerTest_class(object) && requireNamespace("lmerTest", quietly = TRUE)) { # if(packageVersion("lmerTest") < "2.0.37.90012") # return(lmerTest::anova(object, ...)) else return(anova(object, ...)) # } else if(inherits(object, "merMod") && requireNamespace("lmerTest", quietly = TRUE)) { # if(packageVersion("lmerTest") < "2.0.37.90012") # return(lmerTest::anova(as(object, "merModLmerTest"), ...)) else # return(anova(lmerTest::as_lmerModLmerTest(object), ...)) # } # Default: # anova(object, ...) # } # # summary_lmerTest <- function(object, ...) { # # Dispatch the right summary method across lmerTest versions # if(is_lmerTest_class(object) && requireNamespace("lmerTest", quietly = TRUE)) { # if(packageVersion("lmerTest") < "2.0.37.90012") # return(lmerTest::summary(object, ...)) else return(summary(object, ...)) # } else if(inherits(object, "merMod") && requireNamespace("lmerTest", quietly = TRUE)) { # if(packageVersion("lmerTest") < "2.0.37.90012") # return(lmerTest::summary(as(object, "merModLmerTest"), ...)) else # return(summary(lmerTest::as_lmerModLmerTest(object), ...)) # } # Default: # summary(object, ...) # } # afex/R/md_15.1-data.R0000644000176200001440000000635513351525342013510 0ustar liggesusers#' Data 15.1 / 11.5 from Maxwell & Delaney #' #' Hypothetical IQ Data from 12 children at 4 time points: Example data for chapter 11/15 of Maxwell and Delaney (2004, Table 15.1, p. 766) in long format. Has two one within-subjects factor: time. #' #' Description from pp. 534: #' #' The data show that 12 subjects have been observed in each of 4 conditions. To make the example easier to discuss, let's suppose that the 12 subjects are children who have been observed at 30, 36, 42, and 48 months of age. In each case, the dependent variable is the child's age-normed general cognitive score on the McCarthy Scales of Children's Abilities. Although the test is normed so that the mean score is independent of age for the general population, our 12 children may come from a population in which cognitive abilities are either growing more rapidly or less rapidly than average. Indeed, this is the hypothesis our data allow us to address. In other words, although the sample means suggest that the children's cognitive abilities are growing, a significance test is needed if we want to rule out sampling error as a likely explanation for the observed differences. #' #' To replicate the results in chapter 15 several different contrasts need to be applied, see Examples. #' #' \code{time} is time in months (centered at 0) and \code{timecat} is the same as a categorical variable. #' #' @docType data #' @keywords dataset #' @name md_15.1 #' @usage md_15.1 #' @format A data.frame with 48 rows and 4 variables. #' @source Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 766 #' @author R code for examples written by Ulf Mertens and Henrik Singmann #' #' @examples #' ### replicate results from Table 15.2 to 15.6 (Maxwell & Delaney, 2004, pp. 774) #' data(md_15.1) #' #' ### ANOVA results (Table 15.2) #' aov_4(iq ~ timecat + (timecat|id),data=md_15.1, anova_table=list(correction = "none")) #' #' ### Table 15.3 (random intercept only) #' # we need to set the base level on the last level: #' contrasts(md_15.1$timecat) <- contr.treatment(4, base = 4) #' # "Type 3 Tests of Fixed Effects" #' (t15.3 <- mixed(iq ~ timecat + (1|id),data=md_15.1, check.contrasts=FALSE)) #' # "Solution for Fixed Effects" and "Covariance Parameter Estimates" #' summary(t15.3$full.model) #' #' ### make Figure 15.2 #' plot(NULL, NULL, ylim = c(80, 140), xlim = c(30, 48), ylab = "iq", xlab = "time") #' plyr::d_ply(md_15.1, plyr::.(id), function(x) lines(as.numeric(as.character(x$timecat)), x$iq)) #' #' ### Table 15.4, page 789 #' # random intercept plus slope #' (t15.4 <- mixed(iq ~ timecat + (1+time|id),data=md_15.1, check.contrasts=FALSE)) #' summary(t15.4$full.model) #' #' ### Table 15.5, page 795 #' # set up polynomial contrasts for timecat #' contrasts(md_15.1$timecat) <- contr.poly #' # fit all parameters separately #' (t15.5 <- mixed(iq ~ timecat + (1+time|id), data=md_15.1, check.contrasts=FALSE, #' per.parameter="timecat")) #' # quadratic trend is considerably off, conclusions stay the same. #' #' #' ### Table 15.6, page 797 #' # growth curve model #' (t15.6 <- mixed(iq ~ time + (1+time|id),data=md_15.1)) #' summary(t15.6$full.model) #' #' @encoding UTF-8 #' NULL afex/R/fhch2010-data.R0000644000176200001440000000561713351525342013657 0ustar liggesusers#' Data from Freeman, Heathcote, Chalmers, & Hockley (2010) #' #' Lexical decision and word naming latencies for 300 words and 300 nonwords presented in Freeman, Heathcote, Chalmers, and Hockley (2010). The study had one between-subjects factors, \code{"task"} with two levels (\code{"naming"} or \code{"lexdec"}), and four within-subjects factors: \code{"stimulus"} type with two levels (\code{"word"} or \code{"nonword"}), word \code{"density"} and word \code{"frequency"} each with two levels (\code{"low"} and \code{"high"}) and stimulus \code{"length"} with three levels (4, 5, and 6). #' #' In the lexical-decision condition (N = 25), subjects indicated whether each item was a word or a nonword, by pressing either the left (labeled word) or right (labeled nonword) outermost button on a 6-button response pad. The next study item appeared immediately after the lexical decision response was given. In the naming condition (N = 20), subjects were asked to name each item aloud, and items remained on screen for 3 s. Naming time was recorded by a voice key. #' #' Items consisted of 300 words, 75 in each set making up a factorial combination of high and low density and frequency, and 300 nonwords, with equal numbers of 4, 5, and 6 letter items in each set. #' #' #' @docType data #' @keywords dataset #' @name fhch2010 #' @usage fhch2010 #' @format A \code{data.frame} with 13,222 obs. of 9 variables: #' \describe{ #' \item{id}{participant id, \code{factor}} #' \item{task}{\code{factor} with two levels indicating which task was performed: \code{"naming"} or \code{"lexdec"}} #' \item{stimulus}{\code{factor} indicating whether the shown stimulus was a \code{"word"} or \code{"nonword"}} #' \item{density}{\code{factor} indicating the neighborhood density of presented items with two levels: \code{"low"} and \code{"high"}. Density is defined as the number of words that differ from a base word by one letter or phoneme.} #' \item{frequency}{\code{factor} indicating the word frequency of presented items with two levels: \code{"low"} (i.e., words that occur less often in natural language) and \code{"high"} (i.e., words that occur more often in natural language).} #' \item{length}{\code{factor} with 3 levels (4, 5, or 6) indicating the number of characters of presented stimuli.} #' \item{item}{\code{factor} with 600 levels: 300 words and 300 nonwords} #' \item{rt}{response time in seconds} #' \item{log_rt}{natural logarithm of response time in seconds} #' \item{correct}{boolean indicating whether or not the response in the lexical decision task was correct or incorrect (incorrect responses of the naming task are not part of the data).} #' } #' @source Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. Journal of Memory and Language, 62(1), 1-18. http://doi.org/10.1016/j.jml.2009.09.004 #' #' @encoding UTF-8 #' #' @example examples/examples.fhch2010.R NULL afex/R/reexport.R0000644000176200001440000000010313351525342013366 0ustar liggesusers### lme4 #' @importFrom lmerTest lmer #' @export lmerTest::lmer afex/R/ems.R0000644000176200001440000001171513351525342012315 0ustar liggesusers#' Expected values of mean squares for factorial designs #' #' Implements the Cornfield-Tukey algorithm for deriving the expected values of the mean squares for factorial designs. #' #' @param design A \code{formula} object specifying the factors in the design (except residual error, which is always implicitly included). The left hand side of the \code{~} is the symbol that will be used to denote the number of replications per lowest-level factor combination (I usually use "r" or "n"). The right hand side should include all fixed and random factors separated by \code{*}. Factor names should be single letters. #' @param nested A \code{character} vector, where each element is of the form \code{"A/B"}, indicating that the levels of factor B are nested under the levels of factor A. #' @param random A \code{character} string indicating, without spaces or any separating characters, which of the factors specified in the design are random. #' #' @return The returned value is a formatted table where the rows represent the mean squares, the columns represent the variance components that comprise the various mean squares, and the entries in each cell represent the terms that are multiplied and summed to form the expectation of the mean square for that row. Each term is either the lower-case version of one of the experimental factors, which indicates the number of levels for that factor, or a "1", which means the variance component for that column is contributes to the mean square but is not multiplied by anything else. #' #' @note Names for factors or parameters should only be of length 1 as they are simply concatenated in the returned table. #' #' @author Jake Westfall #' #' @seealso A detailed description with explanation of the example can be found \href{http://www.talkstats.com/showthread.php/18603-Share-your-functions-amp-code?p=82050&viewfull=1\#post82050}{elsewhere} (note that the \code{design} argument of the function described at the link behaves slightly different). #' #' Example applications of this function can be found here: \url{http://stats.stackexchange.com/a/122662/442}. #' #' #' @example examples/examples.ems.R #' @export ems <- function(design, nested=NULL, random=""){ # modify design formula based on nested factors specified if(!is.null(nested)){ terms <- attr(terms(design), "term.labels") # for each nested, get indices of all terms not involving their interaction keeps <- lapply(strsplit(nested, "/"), function(x){ which(apply(sapply(x, grepl, terms), 1, function(x) !all(x))) }) terms <- terms[Reduce(intersect, keeps)] formula <- paste(c(as.character(design)[2:1], paste(terms, collapse="+")), collapse="") design <- eval(parse(text=formula)) } # build two-way table mat <- t(attr(terms(design), "factors")) terms <- tolower(as.character(attr(terms(design), "variables"))[-1]) # resolve fixed/random dummies if (!is.null(random)){ random <- unlist(strsplit(random,split="")) mat[,which(colnames(mat) %in% random)][mat[, which(colnames(mat) %in% random)]==1] <- "" mat[,which(!colnames(mat) %in% random)][mat[, which(!colnames(mat) %in% random)]==1] <- "fix" } # insert 1 in nested rows subs <- strsplit(rownames(mat), split=":") if(!is.null(nested)){ nested <- strsplit(nested, split="/") for(term in nested){ rows <- unlist(lapply(subs, function(x) term[2] %in% x)) cols <- colnames(mat)==term[1] mat[rows,cols] <- "1" } } mat <- rbind(mat, e=rep("1", ncol(mat))) # insert numbers of levels for remaining cells for(row in seq(nrow(mat))){ mat[row,][mat[row,]=="0"] <- tolower(colnames(mat)[mat[row,]=="0"]) } # construct EMS table ems <- matrix(nrow=nrow(mat), ncol=nrow(mat), dimnames=list(Effect=rownames(mat), VarianceComponent=rev(rownames(mat)))) # add nesting information to subscripts if (!is.null(nested)){ subs <- lapply(subs, function(x){ new <- x for (nest in seq(length(nested))){ if (nested[[nest]][2] %in% x) new <- c(new, nested[[nest]][1]) } return(new) }) } subs[["e"]] <- colnames(mat)[-1] names(subs) <- rownames(mat) # rename #-of-reps variable to 'e' invisibly colnames(mat)[1] <- "e" # fill in EMS table for(effect in rownames(ems)){ for(varcomp in colnames(ems)){ effectVec <- unlist(strsplit(effect, ":")) ans <- mat[varcomp,-1*which(colnames(mat) %in% effectVec)] if ("fix" %in% ans) ans <- "" if (all(ans=="1")) ans <- "1" if (("1" %in% ans | "2" %in% ans) & !all(ans=="1")){ ans <- ans[!ans %in% c("1","2")] } varcompVec <- unlist(strsplit(varcomp, ":")) if (!all(effectVec %in% subs[[varcomp]])) ans <- "" if (effect=="e" & varcomp=="e") ans <- "1" ems[effect,varcomp] <- paste(ans, collapse="") } } attr(ems, "terms") <- terms return(noquote(ems)) } afex/R/md_16.4-data.R0000644000176200001440000000473413351525342013513 0ustar liggesusers#' Data 16.4 from Maxwell & Delaney #' #' Data from a hypothetical inductive reasoning study. #' #' #' Description from pp. 841: #' #' Suppose an educational psychologist has developed an intervention to teach inductive reasoning skills to school children. She decides to test the efficacy of her intervention by conducting a randomized design. Three classrooms of students are randomly assigned to the treatment condition, and 3 other classrooms are assigned to the control. #' #' Table 16.4 shows hypothetical data collected from 29 children who participated in the study assessing the effectiveness of the intervention to increase inductive reasoning skills. We want to call your attention to several aspects of the data. First, the 15 children with condition values of 0 received the control, whereas the 14 children with condition values of 1 received the treatment. Second, 4 of the children in the control condition were students in control Classroom 1, 6 of them were students in control Classroom 2, and 5 were students in control Classroom 3. Along similar lines, 3 of the children in the treatment condition were students in treatment Classroom 1, 5 were students in treatment Classroom 2, and 6 were students in treatment Classroom 3. It is essential to understand that there are a total of six classrooms here; we have coded classroom from 1 to 3 for control as well as treatment, because we will indicate to PROC MIXED that classroom is nested under treatment. Third, scores on the dependent variable appear in the rightmost column under the variable label "induct." #' #' Note that it would make a lot more sense to change the labeling of room from 1 to 3 nested within cond to 1 to 6. However, I keep this in line with the original. The random effects term in the call to mixed is therefore a little bit uncommon.#' #' #' @docType data #' @keywords dataset #' @name md_16.4 #' @usage md_16.4 #' @format A data.frame with 24 rows and 3 variables. #' @source Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 #' #' @encoding UTF-8 #' #' @examples #' # data for next examples (Maxwell & Delaney, Table 16.4) #' data(md_16.4) #' str(md_16.4) #' #' ### replicate results from Table 16.6 (Maxwell & Delaney, 2004, p. 845) #' # p-values (almost) hold: #' (mixed2 <- mixed(induct ~ cond + (1|room:cond), md_16.4)) #' # (1|room:cond) is needed because room is nested within cond. #' #' NULL afex/R/afex_plot.R0000644000176200001440000012613113607673763013530 0ustar liggesusers#' m-way Plot with Error Bars and Raw Data #' #' @description Plots results from factorial experiments. Estimated marginal #' means and error bars are plotted in the foreground, raw data is plotted in #' the background. Error bars can be based on different standard errors (e.g., #' model-based, within-subjects, between-subjects). Functions described here #' return a \pkg{ggplot2} plot object, thus allowing further customization of #' the plot. #' #' \code{afex_plot} is the user friendly function that does data preparation #' and plotting. It also allows to only return the prepared data (\code{return #' = "data"}). #' #' \code{interaction_plot} does the plotting when a \code{trace} factor is #' present. \code{oneway_plot} does the plotting when a \code{trace} factor is #' absent. #' #' @param object \code{afex_aov}, \code{mixed}, \code{merMod} or other model #' object supported by \pkg{emmeans} (for further examples see: #' \code{vignette("afex_plot_supported_models")}). #' @param x A \code{character} vector or one-sided \code{formula} specifying the #' factor names of the predictors displayed on the x-axis. \code{mapping} #' specifies further mappings for these factors if \code{trace} is missing. #' @param trace An optional \code{character} vector or one-sided \code{formula} #' specifying the factor names of the predictors connected by the same line. #' \code{mapping} specifies further mappings for these factors. #' @param panel An optional \code{character} vector or one-sided \code{formula} #' specifying the factor names of the predictors shown in different panels. #' @param mapping A \code{character} vector specifying which aesthetic mappings #' should be applied to either the \code{trace} factors (if \code{trace} is #' specified) or the \code{x} factors. Useful options are any combination of #' \code{"shape"}, \code{"color"}, \code{"linetype"}, or also \code{"fill"} #' (see examples). The default (i.e., missing) uses \code{c("shape", #' "linetype")} if \code{trace} is specified and \code{""} otherwise (i.e., no #' additional aesthetic). If specific mappings should not be applied to #' specific graphical elements, one can override those via the corresponding #' further arguments. For example, for \code{data_arg} the default is #' \code{list(color = "darkgrey")} which prevents that \code{"color"} is #' mapped onto points in the background. #' @param error A scalar \code{character} vector specifying on which standard #' error the error bars should be based. Default is \code{"model"}, which #' plots model-based standard errors. Further options are: \code{"none"} (or #' \code{NULL}), \code{"mean"}, \code{"within"} (or \code{"CMO"}), and #' \code{"between"}. See details. #' @param id An optional \code{character} vector specifying over which variables #' the raw data should be aggregated. Only relevant for \code{mixed}, #' \code{merMod}, and \code{default} method. The default (missing) uses all #' random effects grouping factors (for \code{mixed} and \code{merMod} method) #' or assumes all data points are independent. This can lead to many data #' points. \code{error = "within"} or \code{error = "between"} require that #' \code{id} is of length 1. See examples. #' @param dv An optional scalar \code{character} vector giving the name of the #' column containing the dependent variable for the \code{afex_plot.default} #' method. If missing, the function attempts to take it from the \code{call} #' slot of \code{object}. This is also used as y-axis label. #' @param error_ci Logical. Should error bars plot confidence intervals #' (=\code{TRUE}, the default) or standard errors (=\code{FALSE})? #' @param error_level Numeric value between 0 and 1 determing the width of the #' confidence interval. Default is .95 corresponding to a 95\% confidence #' interval. #' @param error_arg A \code{list} of further arguments passed to #' \code{\link[ggplot2]{geom_errorbar}}, which draws the errorsbars. Default #' is \code{list(width = 0)} which suppresses the vertical bars at the end of #' the error bar. #' @param data_plot \code{logical}. Should raw data be plotted in the #' background? Default is \code{TRUE}. #' @param data_geom Geom \code{function} used for plotting data in background. #' The default (missing) uses \code{\link[ggplot2]{geom_point}} if #' \code{trace} is specified, otherwise #' \code{\link[ggbeeswarm]{geom_beeswarm}}. See examples fo further options. #' @param data_alpha numeric \code{alpha} value between 0 and 1 passed to #' \code{data_geom}. Default is \code{0.5} which correspond to semitransparent #' data points in the background such that overlapping data points are plotted #' darker. #' @param data_arg A \code{list} of further arguments passed to #' \code{data_geom}. Default is \code{list(color = "darkgrey")}, which plots #' points in the background in grey. #' @param point_arg,line_arg A \code{list} of further arguments passed to #' \code{\link[ggplot2]{geom_point}} or \code{\link[ggplot2]{geom_line}} which #' draw the points and lines in the foreground. Default is \code{list()}. #' \code{line_arg} is only used if \code{trace} is specified. #' @param emmeans_arg A \code{list} of further arguments passed to #' \code{\link[emmeans]{emmeans}}. Of particular importance for ANOVAs is #' \code{model}, see \code{\link{afex_aov-methods}}. #' @param dodge Numerical amount of dodging of factor-levels on x-axis. Default #' is \code{0.5}. #' @param return A scalar \code{character} specifying what should be returned. #' The default \code{"plot"} returns the \pkg{ggplot2} plot. The other option #' \code{"data"} returns a list with two \code{data.frame}s containing the #' data used for plotting: \code{means} contains the means and standard errors #' for the foreground, \code{data} contains the raw data in the background. #' @param factor_levels A \code{list} of new factor levels that should be used #' in the plot. The name of each list entry needs to correspond to one of the #' factors in the plot. Each list element can optionally be a named character #' vector where the name corresponds to the old factor level and the value to #' the new factor level. Named vectors allow two things: (1) updating only a #' subset of factor levels (if only a subset of levels is specified) and (2) #' reordering (and renaming) the factor levels, as order of names within a #' list element are the order that will be used for plotting. If specified, #' emits a \code{message} with \code{old -> new} factor levels. #' @param legend_title A scalar \code{character} vector with a new title for the #' legend. #' @param data For the \code{afex_plot.default} method, an optional #' \code{data.frame} containing the raw data used for fitting the model and #' which will be used as basis for the data points in the background. If #' missing, it will be attempted to obtain it from the model via #' \code{\link[emmeans]{recover_data}}. For the plotting functions, a #' \code{data.frame} with the data that has to be passed and contains the #' background data points. #' @param within_vars,between_vars For the \code{afex_plot.default} method, an #' optional \code{character} vector specifying which variables should be #' treated as within-subjects (or repeated-measures) factors and which as #' between-subjects (or independen-sampels) factors. If one of the two #' arguments is given, all other factors are assumed to fall into the other #' category. #' @param means \code{data.frame}s used for plotting of the plotting #' functions. #' @param col_y,col_x,col_trace,col_panel A scalar \code{character} string #' specifying the name of the corresponding column containing the information #' used for plotting. Each column needs to exist in both the \code{means} and #' the \code{data} \code{data.frame}. #'@param col_lower,col_upper A scalar \code{character} string specifying the #' name of the columns containing lower and upper bounds for the error bars. #' These columns need to exist in \code{means}. #' @param error_plot \code{logical}. Should error bars be plotted? Only used in #' plotting functions. To suppress plotting of error bars use \code{error = #' "none"} in \code{afex_plot}. #' @param ... currently ignored. #' #' @details \code{afex_plot} obtains the estimated marginal means via #' \code{\link[emmeans]{emmeans}} and aggregates the raw data to the same #' level. It then calculates the desired confidence interval or standard error #' (see below) and passes the prepared data to one of the two plotting #' functions: \code{interaction_plot} when \code{trace} is specified and #' \code{oneway_plot} otherwise. #' #' \subsection{Error Bars}{Error bars provide a grahical representation of the #' variability of the estimated means and should be routinely added to results #' figures. However, there exist several possibilities which particular #' measure of variability to use. Because of this, any figure depicting error #' bars should be accompanied by a note detailing which measure the error bars #' shows. The present functions allow plotting of different types of #' confidence intervals (if \code{error_ci = TRUE}, the default) or standard #' errors (if \code{error_ci = FALSE}). #' #' A further complication is that readers routinely misinterpret confidence #' intervals. The most common error is to assume that non-overlapping error #' bars indicate a significant difference (e.g., Belia et al., 2005). This is #' rarely the case (see e.g., Cumming & Finch, 2005; Knol et al., 2011; #' Schenker & Gentleman, 2005). For example, in a fully between-subjects design #' in which the error bars depict 95\% confidence intervals and groups are of #' approximately equal size and have equal variance, even error bars that #' overlap by as much as 50\% still correspond to \emph{p} < .05. Error bars #' that are just touching roughly correspond to \emph{p} = .01. #' #' In the case of designs involving repeated-measures factors the usual #' confidence intervals or standard errors (i.e., model-based confidence #' intervals or intervals based on the standard error of the mean) cannot be #' used to gauge significant differences as this requires knowledge about the #' correlation between measures. One popular alternative in the psychological #' literature are intervals based on within-subjects standard #' errors/confidence intervals (e.g., Cousineau & O'Brien, 2014). These #' attempt to control for the correlation across individuals and thereby allow #' judging differences between repeated-measures condition. As a downside, #' when using within-subjects intervals no comparisons across between-subjects #' conditions or with respect to a fixed-value are possible anymore. #' #' In the case of a mixed-design, no single type of error bar is possible that #' allows comparison across all conditions. Likewise, for mixed models #' involving multiple \emph{crossed} random effects, no single set of error #' bars (or even data aggregation) adequately represent the true varibility in #' the data and adequately allows for "inference by eye". Therefore, special #' care is necessary in such cases. One possiblity is to avoid error bars #' altogether and plot only the raw data in the background (with \code{error = #' "none"}). The raw data in the background still provides a visual impression #' of the variability in the data and the precision of the mean estimate, but #' does not as easily suggest an incorrect inferences. Another possibility is #' to use the model-based standard error and note in the figure caption that #' it does not permit comparisons across repeated-measures factors. #' #' The following "rules of eye" (Cumming and Finch, 2005) hold, when permitted #' by design (i.e., within-subjects bars for within-subjects comparisons; #' other variants for between-subjects comparisons), and groups are #' approximately equal in size and variance. Note that for more complex #' designs ususally analyzed with mixed models, such as designs involving #' complicated dependencies across data points, these rules of thumbs may be #' highly misleading. #' \itemize{ #' \item \emph{p} < .05 when the overlap of the 95\% confidence intervals #' (CIs) is no more than about half the average margin of error, that is, #' when proportion overlap is about .50 or less. #' \item \emph{p} < .01 when the two CIs do not overlap, that is, when #' proportion overlap is about 0 or there is a positive gap. #' \item \emph{p} < .05 when the gap between standard error (SE) bars is at #' least about the size of the average SE, that is, when the proportion gap #' is about 1 or greater. #' \item \emph{p} < .01 when the proportion gap between SE bars is about 2 #' or more. #' } #' } #' \subsection{Implemented Standard Errors}{The following lists the #' implemented approaches to calculate confidence intervals (CIs) and standard #' errors (SEs). CIs are based on the SEs using the \emph{t}-distribution with #' degrees of freedom based on the cell or group size. For ANOVA models, #' \code{afex_plot} attempts to warn in case the chosen approach is misleading #' given the design (e.g., model-based error bars for purely #' within-subjects plots). For \code{mixed} models, no such warnings are #' produced, but users should be aware that all options beside \code{"model"} #' are not actually appropriate and have only heuristic value. But then again, #' \code{"model"} based error bars do not permit comparisons for factors #' varying within one of the random-effects grouping factors (i.e., factors #' for which random-slopes should be estimated). #' \describe{ #' \item{\code{"model"}}{Uses model-based CIs and SEs. For ANOVAs, the #' variant based on the \code{lm} or \code{mlm} model (i.e., #' \code{emmeans_arg = list(model = "multivariate")}) seems generally #' preferrable.} #' \item{\code{"mean"}}{Calculates the standard error of the mean for #' each cell ignoring any repeated-measures factors.} #' \item{\code{"within"} or \code{"CMO"}}{Calculates within-subjects SEs #' using the Cosineau-Morey-O'Brien (Cousineau & O'Brien, 2014) method. This #' method is based on a double normalization of the data. SEs and CIs are #' then calculated independently for each cell (i.e., if the desired output #' contains between-subjects factors, SEs are calculated for each cell #' including the between-subjects factors).} #' \item{\code{"between"}}{First aggregates the data per participant and #' then calculates the SEs for each between-subjects condition. Results in #' one SE and \emph{t}-quantile for all conditions in purely within-subjects #' designs.} #' \item{\code{"none"} or \code{NULL}}{Suppresses calculation of SEs and #' plots no error bars.} #' } #' For \code{mixed} models, the within-subjects/repeated-measures factors are #' relative to the chosen \code{id} effects grouping factor. They are #' automatically detected based on the random-slopes of the random-effects #' grouping factor in \code{id}. All other factors are treated as #' independent-samples or between-subjects factors. #' } #' #' @return Returns a \pkg{ggplot2} plot (i.e., object of class \code{c("gg", #' "ggplot")}) unless \code{return = "data"}. #' #' @references Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). #' Researchers Misunderstand Confidence Intervals and Standard Error Bars. #' \emph{Psychological Methods}, 10(4), 389-396. #' https://doi.org/10.1037/1082-989X.10.4.389 #' #' Cousineau, D., & O'Brien, F. (2014). Error bars in within-subject designs: #' a comment on Baguley (2012). \emph{Behavior Research Methods}, 46(4), #' 1149-1151. https://doi.org/10.3758/s13428-013-0441-z #' #' Cumming, G., & Finch, S. (2005). Inference by Eye: Confidence Intervals and #' How to Read Pictures of Data. \emph{American Psychologist}, 60(2), 170-180. #' https://doi.org/10.1037/0003-066X.60.2.170 #' #' Knol, M. J., Pestman, W. R., & Grobbee, D. E. (2011). The (mis)use of #' overlap of confidence intervals to assess effect modification. #' \emph{European Journal of Epidemiology}, 26(4), 253-254. #' https://doi.org/10.1007/s10654-011-9563-8 #' #' Schenker, N., & Gentleman, J. F. (2001). On Judging the Significance of #' Differences by Examining the Overlap Between Confidence Intervals. #' \emph{The American Statistician}, 55(3), 182-186. #' https://doi.org/10.1198/000313001317097960 #' #' #' @importFrom stats aggregate sd qt formula #' #' @example examples/examples.afex_plot.R #' #' @export afex_plot <- function(object, ...) UseMethod("afex_plot", object) # @method afex_plot afex_aov #' @rdname afex_plot #' @export afex_plot.afex_aov <- function(object, x, trace, panel, mapping, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ...) { return <- match.arg(return, c("plot", "data")) error <- match.arg(error, c("none", "model", "mean", "within", "CMO", "between")) dots <- list(...) if (length(dots) > 0) { warning("Additional arguments ignored: ", paste(names(dots), collapse = ", "), call. = FALSE) } x <- get_plot_var(x) trace <- get_plot_var(trace) panel <- get_plot_var(panel) all_vars <- c(x, trace, panel) emms <- get_emms(object = object, x = x, trace = trace, panel = panel, emmeans_arg = emmeans_arg, factor_levels = factor_levels, level = error_level) ## prepare raw (i.e., participant by cell) data data <- prep_data(object$data$long, x = x, trace = trace, panel = panel, factor_levels = factor_levels, dv_col = attr(object, "dv"), id = attr(object, "id")) ### prepare variables for SE/CI calculation within_vars <- all_vars[all_vars %in% names(attr(object, "within"))] between_vars <- all_vars[all_vars %in% names(attr(object, "between"))] ### check if error bars are consistent with panel(s) and warn otherwise if (error %in% c("model", "mean", "between") && all(c(x, trace) %in% within_vars)) { warning("Panel(s) show within-subjects factors, ", "but not within-subjects error bars.\n", 'For within-subjects error bars use: error = "within"', call. = FALSE) } else if (error %in% c("within", "CMO") && all(c(x, trace) %in% between_vars)) { warning("Panel(s) show between-subjects factors, ", "but within-subjects error bars.\n", 'For between-subjects error bars use e.g.,: ', 'error = "model" or error = "mean"', call. = FALSE) } else if (any(between_vars %in% c(x, trace)) && any(within_vars %in% c(x, trace)) && error != "none") { warning("Panel(s) show a mixed within-between-design.\n", "Error bars do not allow comparisons across all means.\n", 'Suppress error bars with: error = "none"', call. = FALSE) } tmp <- get_data_based_cis(emms = emms, data = data, error = error, id = attr(object, "id"), ## colname holding the id/grouping variable all_vars = all_vars, within_vars = within_vars, between_vars = between_vars, error_level = error_level, error_ci = error_ci) emms <- tmp$emms error_plot <- tmp$error_plot return(afex_plot_internal(x = x, trace = trace, panel = panel, means = emms, data = data, error_plot = error_plot, error_arg = error_arg, dodge = dodge, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, line_arg = line_arg, mapping = mapping, legend_title = legend_title, return = return )) } # @method afex_plot afex_aov #' @rdname afex_plot #' @export afex_plot.mixed <- function(object, x, trace, panel, mapping, id, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ...) { return <- match.arg(return, c("plot", "data")) error <- match.arg(error, c("none", "model", "mean", "within", "CMO", "between")) dots <- list(...) if (length(dots) > 0) { warning("Additional arguments ignored: ", paste(names(dots), collapse = ", "), call. = FALSE) } x <- get_plot_var(x) trace <- get_plot_var(trace) panel <- get_plot_var(panel) all_vars <- c(x, trace, panel) if (missing(id)) { id <- unique(names(lme4::ranef(object$full_model))) message("Aggregating data over: ", paste(id, collapse = ", ")) } ## prepare raw (i.e., participant by cell) data data <- prep_data(object$data, x = x, trace = trace, panel = panel, factor_levels = factor_levels, dv_col = deparse(object$full_model@call[["formula"]][[2]]), id = id) data$afex_id <- interaction(data[id], sep = ".") if (!(error %in% c("none" ,"model", "mean")) & (length(id) > 1)) { stop("When aggregating over multiple random effects,\n", ' error has to be in: c("model", "mean", "none")', call. = FALSE) } emms <- get_emms(object = object, x = x, trace = trace, panel = panel, emmeans_arg = emmeans_arg, factor_levels = factor_levels, level = error_level) attr(emms, "dv") <- deparse(object$full_model@call[["formula"]][[2]]) if (length(id) == 1) { all_within <- lapply(lme4::findbars(object$call), all.vars) all_within <- unique(unlist( all_within[vapply(all_within, function(x) id %in% x, NA)] )) all_within <- all_within[all_within != id] within_vars <- all_vars[all_vars %in% all_within] between_vars <- all_vars[!(all_vars %in% within_vars)] } ### prepare variables for SE/CI calculation tmp <- get_data_based_cis(emms = emms, data = data, error = error, id = "afex_id", ## colname holding the id/grouping variable all_vars = all_vars, within_vars = within_vars, between_vars = between_vars, error_level = error_level, error_ci = error_ci) emms <- tmp$emms error_plot <- tmp$error_plot return(afex_plot_internal(x = x, trace = trace, panel = panel, means = emms, data = data, error_plot = error_plot, error_arg = error_arg, dodge = dodge, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, line_arg = line_arg, mapping = mapping, legend_title = legend_title, return = return )) } #' @rdname afex_plot #' @export afex_plot.merMod <- function(object, x, trace, panel, mapping, id, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ...) { return <- match.arg(return, c("plot", "data")) error <- match.arg(error, c("none", "model", "mean", "within", "CMO", "between")) dots <- list(...) if (length(dots) > 0) { warning("Additional arguments ignored: ", paste(names(dots), collapse = ", "), call. = FALSE) } x <- get_plot_var(x) trace <- get_plot_var(trace) panel <- get_plot_var(panel) all_vars <- c(x, trace, panel) if (missing(id)) { id <- unique(names(lme4::ranef(object))) message("Aggregating data over: ", paste(id, collapse = ", ")) } ## prepare raw (i.e., participant by cell) data data <- prep_data( data = emmeans::recover_data( object = object, trms = terms(object, fixed.only = FALSE) ), x = x, trace = trace, panel = panel, factor_levels = factor_levels, dv_col = deparse(object@call[["formula"]][[2]]), id = id) data$afex_id <- interaction(data[id], sep = ".") if (!(error %in% c("none" ,"model", "mean")) & (length(id) > 1)) { stop("When aggregating over multiple random effects,\n", ' error has to be in: c("model", "mean", "none")', call. = FALSE) } emms <- get_emms(object = object, x = x, trace = trace, panel = panel, emmeans_arg = emmeans_arg, factor_levels = factor_levels, level = error_level) attr(emms, "dv") <- deparse(object@call[["formula"]][[2]]) if (length(id) == 1) { all_within <- lapply(lme4::findbars(object@call), all.vars) all_within <- unique(unlist( all_within[vapply(all_within, function(x) id %in% x, NA)] )) all_within <- all_within[all_within != id] within_vars <- all_vars[all_vars %in% all_within] between_vars <- all_vars[!(all_vars %in% within_vars)] } ### prepare variables for SE/CI calculation tmp <- get_data_based_cis(emms = emms, data = data, error = error, id = "afex_id", ## colname holding the id/grouping variable all_vars = all_vars, within_vars = within_vars, between_vars = between_vars, error_level = error_level, error_ci = error_ci) emms <- tmp$emms error_plot <- tmp$error_plot return(afex_plot_internal(x = x, trace = trace, panel = panel, means = emms, data = data, error_plot = error_plot, error_arg = error_arg, dodge = dodge, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, line_arg = line_arg, mapping = mapping, legend_title = legend_title, return = return )) } #' @rdname afex_plot #' @export afex_plot.default <- function(object, x, trace, panel, mapping, id, dv, data, within_vars, between_vars, error = "model", error_ci = TRUE, error_level = 0.95, error_arg = list(width = 0), data_plot = TRUE, data_geom, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), emmeans_arg = list(), dodge = 0.5, return = "plot", factor_levels = list(), legend_title, ...) { return <- match.arg(return, c("plot", "data")) error <- match.arg(error, c("none", "model", "mean", "within", "CMO", "between")) dots <- list(...) if (length(dots) > 0) { warning("Additional arguments ignored: ", paste(names(dots), collapse = ", "), call. = FALSE) } x <- get_plot_var(x) trace <- get_plot_var(trace) panel <- get_plot_var(panel) all_vars <- c(x, trace, panel) if (missing(dv)) { formula_name <- names(object$call)[2] message("dv column detected: ", deparse(object$call[[formula_name]][[2]])) dv <- deparse(object$call[[formula_name]][[2]]) } ## prepare raw (i.e., participant by cell) data if missing if (missing(data)) { data <- tryCatch(emmeans::recover_data( object = object, #trms = terms(object) trms = terms(lme4::subbars(formula(object))) ), error = function(e) emmeans::recover_data( object = object, trms = terms(object) )) } if (missing(id)) { message("No id column passed. ", "Assuming all rows are independent samples.") data$id <- factor(seq_len(nrow(data))) id <- "id" } data <- prep_data( data = data, x = x, trace = trace, panel = panel, factor_levels = factor_levels, dv_col = dv, id = id) data$afex_id <- interaction(data[id], sep = ".") if (!(error %in% c("none" ,"model", "mean")) & (length(id) > 1)) { stop("When aggregating over multiple ids,\n", ' error has to be in: c("model", "mean", "none")', call. = FALSE) } emms <- get_emms(object = object, x = x, trace = trace, panel = panel, emmeans_arg = emmeans_arg, factor_levels = factor_levels, level = error_level) attr(emms, "dv") <- dv if (missing(within_vars) & !missing(between_vars)) { within_vars <- all_vars[!(all_vars %in% within_vars)] } if (!missing(within_vars) & missing(between_vars)) { between_vars <- all_vars[!(all_vars %in% between_vars)] } ### prepare variables for SE/CI calculation tmp <- get_data_based_cis(emms = emms, data = data, error = error, id = "afex_id", ## colname holding the id/grouping variable all_vars = all_vars, within_vars = within_vars, between_vars = between_vars, error_level = error_level, error_ci = error_ci) emms <- tmp$emms error_plot <- tmp$error_plot return(afex_plot_internal(x = x, trace = trace, panel = panel, means = emms, data = data, error_plot = error_plot, error_arg = error_arg, dodge = dodge, data_plot = data_plot, data_geom = data_geom, data_alpha = data_alpha, data_arg = data_arg, point_arg = point_arg, line_arg = line_arg, mapping = mapping, legend_title = legend_title, return = return )) } ###if(getRversion() >= "2.15.1") utils::globalVariables(c("error", "y", "x")) #' @rdname afex_plot #' @export interaction_plot <- function(means, data, mapping = c("shape", "lineytpe"), error_plot = TRUE, error_arg = list(width = 0), data_plot = TRUE, data_geom = ggplot2::geom_point, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), line_arg = list(), dodge = 0.5, legend_title, col_x = "x", col_y = "y", col_trace = "trace", col_panel = "panel", col_lower = "lower", col_upper = "upper") { if (!requireNamespace("ggplot2", quietly = TRUE)) { stop("package ggplot2 is required.", call. = FALSE) } if (missing(mapping)) { mapping <- c('shape', 'linetype') } else if (length(mapping) == 0) { stop("mapping cannot be empty. Possible values: 'shape', 'color', 'linetype'.", call. = FALSE) } tmp_list <- as.list(rep(col_trace, length(mapping))) names(tmp_list) <- mapping error_mapping <- mapping[!(mapping %in% c("linetype", "shape", "fill"))] tmp_list_error <- as.list(rep(col_trace, length(error_mapping))) names(tmp_list_error) <- error_mapping plot_out <- ggplot2::ggplot(data = means, mapping = do.call( what = ggplot2::aes_string, args = c(list( y = col_y, x = col_x, group = col_trace), tmp_list))) if (data_plot) { if (missing(data_geom)) { data_geom <- ggplot2::geom_point } data_arg$alpha <- data_alpha if (!("position" %in% names(data_arg)) & ("position" %in% names(formals(data_geom)))) { data_arg$position = ggplot2::position_dodge(width = dodge) } plot_out <- plot_out + do.call(what = data_geom, args = c( #mapping = list(ggplot2::aes(group = interaction(x, trace))), mapping = list( ggplot2::aes_string( group = paste0("interaction(", paste0(c(col_x, col_trace), collapse = ", "), ")") )), data = list(data), data_arg ) ) } for (i in levels(data$trace)) { tmp_means <- means tmp_means[means$trace != i, c(col_y, col_lower, col_upper)] <- NA #tmp_means <- tmp_means[means$trace == i,] plot_out <- plot_out + do.call(what = ggplot2::geom_point, args = c( data = list(tmp_means), position = list( ggplot2::position_dodge(width = dodge) ), point_arg, na.rm = list(TRUE) )) + do.call(what = ggplot2::geom_line, args = c( data = list(tmp_means), position = list( ggplot2::position_dodge(width = dodge) ), line_arg, na.rm = list(TRUE) )) if (error_plot) { plot_out <- plot_out + do.call(what = ggplot2::geom_errorbar, args = c( data = list(tmp_means), mapping = list(do.call( what = ggplot2::aes_string, args = c(list( x = col_x, ymin = col_lower, ymax = col_upper, group = col_trace), tmp_list_error))), position = list(ggplot2::position_dodge(width = dodge)), error_arg, na.rm = list(TRUE), inherit.aes = list(FALSE) )) } } if (length(unique(means$panel)) > 1) { plot_out <- plot_out + ggplot2::facet_wrap(facets = "panel") } ## add labels if (!is.null(attr(means, "dv"))) { plot_out <- plot_out + ggplot2::ylab(attr(means, "dv")) } if (!is.null(attr(means, "x"))) { plot_out <- plot_out + ggplot2::xlab(attr(means, "x")) } if (!missing(legend_title)) { legend_title <- paste(legend_title, collapse = "\n") tmp_list <- rep(list(ggplot2::guide_legend(title = legend_title)), length(mapping)) names(tmp_list) <- mapping plot_out <- plot_out + do.call(what = ggplot2::guides, args = tmp_list) } return(plot_out) } #' @rdname afex_plot #' @export oneway_plot <- function(means, data, mapping = "", error_plot = TRUE, error_arg = list(width = 0), data_plot = TRUE, data_geom = ggbeeswarm::geom_beeswarm, data_alpha = 0.5, data_arg = list(color = "darkgrey"), point_arg = list(), legend_title, col_x = "x", col_y = "y", col_panel = "panel", col_lower = "lower", col_upper = "upper") { if (!requireNamespace("ggplot2", quietly = TRUE)) { stop("package ggplot2 is required.", call. = FALSE) } if (missing(mapping)) { mapping <- "" } if (length(mapping) > 1 || mapping[1] != "") { tmp_list <- as.list(rep(col_x, length(mapping))) names(tmp_list) <- mapping error_mapping <- mapping[!(mapping %in% c("linetype", "shape", "fill"))] tmp_list_error <- as.list(rep(col_x, length(error_mapping))) names(tmp_list_error) <- error_mapping } else { tmp_list <- list() tmp_list_error <- list() } plot_out <- ggplot2::ggplot(data = means, mapping = do.call( what = ggplot2::aes_string, args = c(list( y = col_y, x = col_x, group = col_x), tmp_list))) if (data_plot) { if (missing(data_geom)) { if (!requireNamespace("ggbeeswarm", quietly = TRUE)) { stop("package ggbeeswarm is required.", call. = FALSE) } data_geom <- ggbeeswarm::geom_beeswarm } data_arg$alpha <- data_alpha plot_out <- plot_out + do.call(what = data_geom, args = c( data = list(data), data_arg ) ) } plot_out <- plot_out + do.call(what = ggplot2::geom_point, args = point_arg) if (error_plot) { plot_out <- plot_out + do.call(what = ggplot2::geom_errorbar, args = c( mapping = list(do.call( what = ggplot2::aes_string, args = c(list( x = col_x, ymin = col_lower, ymax = col_upper), tmp_list_error))), error_arg, inherit.aes = list(FALSE) )) } if (length(unique(means$panel)) > 1) { plot_out <- plot_out + ggplot2::facet_wrap(facets = "panel") } ## add labels if (!is.null(attr(means, "dv"))) { plot_out <- plot_out + ggplot2::ylab(attr(means, "dv")) } if (!is.null(attr(means, "x"))) { plot_out <- plot_out + ggplot2::xlab(attr(means, "x")) } if (!missing(legend_title)) { legend_title <- paste(legend_title, collapse = "\n") tmp_list <- rep(list(ggplot2::guide_legend(title = legend_title)), length(mapping)) names(tmp_list) <- mapping plot_out <- plot_out + do.call(what = ggplot2::guides, args = tmp_list) } return(plot_out) } afex/R/allFit.R0000644000176200001440000001217613432626233012747 0ustar liggesusers#' Refit \code{lmer} model using multiple optimizers #' #' Attempt to re-fit a [g]lmer model with a range of optimizers. #' The default is to use all known optimizers for R that satisfy the #' requirements (do not require explicit gradients, allow #' box constraints), in four categories; (i) built-in #' (\code{minqa::bobyqa}, \code{lme4::Nelder_Mead}), (ii) wrapped via optimx #' (most of optimx's optimizers that allow box constraints require #' an explicit gradient function to be specified; the two provided #' here are really base R functions that can be accessed via optimx, #' (iii) wrapped via nloptr, (iv) \code{dfoptim::nmkb}. #' #' @param m a fitted model with \code{lmer} #' @param meth_tab a matrix (or data.frame) with columns #' - method the name of a specific optimization method to pass to the optimizer #' (leave blank for built-in optimizers) #' - optimizer the \code{optimizer} function to use #' @param verbose print progress messages? #' @param maxfun number of iterations to allow for the optimization rountine. #' @param ... further arguments passed to \code{\link{update.merMod}} such as \code{data}. #' @param fn needed for \code{dfoptim::nmkb} #' @param par needed for \code{dfoptim::nmkb} #' @param lower needed for \code{dfoptim::nmkb} #' @param upper needed for \code{dfoptim::nmkb} #' @param control needed for \code{dfoptim::nmkb} #' #' @details Needs packages \pkg{nloptr}, \pkg{optimx}, and \code{dfoptim} to try out all optimizers. \pkg{optimx} needs to be loaded explicitly using \code{library} or \code{require} (see examples). #' #' \code{nmkbw} is a simple wrapper function for fitting models with the corresponding optimizer. It needs to be exported for \code{lme4}, but should not be called directly by the user. #' #' @note Very similar to the function of the same name that is part of \pkg{lme4}. The present function will be removed eventually in favor of the \pkg{lme4} function. #' #' @return a list of fitted \code{merMod} objects #' @seealso slice, slice2D in the bbmle package #' @author Ben Bolker, minor changes by Henrik Singmann #' @export #' @importFrom lme4 isGLMM lmerControl glmerControl #' @importFrom stats setNames update optim #' #' @example examples/examples.allFit.R #' all_fit <- function(m, meth_tab = cbind( optimizer=rep(c("bobyqa","Nelder_Mead", "optimx", "nloptwrap", "nmkbw"), c( 1, 1, 2, 2, 1)), method= c("", "", "nlminb","L-BFGS-B","NLOPT_LN_NELDERMEAD", "NLOPT_LN_BOBYQA", "") ), verbose=TRUE,maxfun=1e6, ...) { stopifnot(length(dm <- dim(meth_tab)) == 2, dm[1] >= 1, dm[2] >= 2, is.character(optimizer <- meth_tab[,"optimizer"]), is.character(method <- meth_tab[,"method"])) fit.names <- paste(optimizer, method, sep=".") res <- setNames(as.list(fit.names), fit.names) dots <- list(...) for (i in seq_along(fit.names)) { if (verbose) cat(fit.names[i],": ") ctrl <- list(optimizer=optimizer[i]) ctrl$optCtrl <- switch(optimizer[i], optimx = list(method = method[i]), nloptWrap = list(algorithm= method[i]), list(maxfun=maxfun)) ctrl <- do.call(if(isGLMM(m)) glmerControl else lmerControl, ctrl) if ("data" %in% names(dots)) { tt <- system.time(rr <- tryCatch( update(m, control = ctrl, data = dots$data, ...), error = function(e) e)) } else { tt <- system.time(rr <- tryCatch( update(m, control = ctrl, ...), error = function(e) e)) } attr(rr, "optCtrl") <- ctrl$optCtrl # contains crucial info here attr(rr, "time") <- tt # store timing info res[[i]] <- rr if (verbose) { if (inherits(rr, "merMod")) cat("[OK]\n") else cat("[ERROR]\n") } } ## res } #' @rdname all_fit #' @export nmkbw <- function(fn,par,lower,upper,control) { if (length(par)==1) { res <- optim(fn=fn,par=par,lower=lower,upper=100*par, method="Brent") } else { if (!is.null(control$maxfun)) { control$maxfeval <- control$maxfun control$maxfun <- NULL } res <- dfoptim::nmkb(fn=fn,par=par,lower=lower,upper=upper,control=control) } res$fval <- res$value res } # #' @export # summary.allfit <- function(object, ...) { # which.OK <- !sapply(object,is,"error") # msgs <- lapply(object[which.OK],function(x) x@optinfo$conv$lme4$messages) # fixef <- t(sapply(object[which.OK],fixef)) # llik <- sapply(object[which.OK],logLik) # times <- t(sapply(object[which.OK],attr,"time")) # feval <- sapply(object[which.OK],function(x) x@optinfo$feval) # sdcor <- t(sapply(object[which.OK],function(x) { # aa <- as.data.frame(VarCorr(x)) # setNames(aa[,"sdcor"],c(lme4:::tnames(object[which.OK][[1]]), # if (isLMM(object[[1]])) "sigma" else NULL)) # })) # namedList(which.OK,msgs,fixef,llik,sdcor,times,feval) # } # # #' @export # print.summary.allfit <- function(object,...) { # if (!which.OK==seq(length(object))) { # cat("some optimizers failed: ", # paste(names(object)[!which.OK],collapse=","),"\n") # } # }afex/R/aov_car.R0000644000176200001440000011353313520615175013146 0ustar liggesusers#' Convenient ANOVA estimation for factorial designs #' #' These functions allow convenient specification of any type of ANOVAs (i.e., #' purely within-subjects ANOVAs, purely between-subjects ANOVAs, and mixed #' between-within or split-plot ANOVAs) for data in the \strong{long} format #' (i.e., one observation per row). If the data has more than one observation #' per individual and cell of the design (e.g., multiple responses per #' condition), the data will by automatically aggregated. The default settings #' reproduce results from commercial statistical packages such as SPSS or SAS. #' \code{aov_ez} is called specifying the factors as character vectors, #' \code{aov_car} is called using a formula similar to \code{\link{aov}} #' specifying an error strata for the within-subject factor(s), and \code{aov_4} #' is called with a \pkg{lme4}-like formula (all ANOVA functions return #' identical results). The returned object contains the ANOVA also fitted via #' base R's \code{\link{aov}} which can be passed to e.g., \pkg{emmeans} for #' further analysis (e.g., follow-up tests, contrasts, plotting, etc.). These #' functions employ \code{\link[car]{Anova}} (from the \pkg{car} package) to #' provide test of effects avoiding the somewhat unhandy format of #' \code{car::Anova}. #' #' #' @param id \code{character} vector (of length 1) indicating the subject #' identifier column in \code{data}. #' @param dv \code{character} vector (of length 1) indicating the column #' containing the \strong{dependent variable} in \code{data}. #' @param between \code{character} vector indicating the #' \strong{between}-subject(s) factor(s)/column(s) in \code{data}. Default is #' \code{NULL} indicating no between-subjects factors. #' @param within \code{character} vector indicating the #' \strong{within}-subject(s)(or repeated-measures) factor(s)/column(s) in #' \code{data}. Default is \code{NULL} indicating no within-subjects factors. #' @param covariate \code{character} vector indicating the between-subject(s) #' covariate(s) (i.e., column(s)) in \code{data}. Default is \code{NULL} #' indicating no covariates. Please note that \code{factorize} needs to be set #' to \code{FALSE} in case the covariate is numeric and should be treated as #' such. #' @param observed \code{character} vector indicating which of the variables are #' observed (i.e, measured) as compared to experimentally manipulated. The #' default effect size reported (generalized eta-squared) requires correct #' specification of the obsered (in contrast to manipulated) variables. #' @param formula A formula specifying the ANOVA model similar to #' \code{\link{aov}} (for \code{aov_car} or similar to \code{lme4:lmer} for #' \code{aov_4}). Should include an error term (i.e., \code{Error(id/...)} for #' \code{aov_car} or \code{(...|id)} for \code{aov_4}). Note that the #' within-subject factors do not need to be outside the Error term (this #' contrasts with \code{aov}). See Details. #' @param data A \code{data.frame} containing the data. Mandatory. #' @param fun_aggregate The function for aggregating the data before running the #' ANOVA if there is more than one observation per individual and cell of the #' design. The default \code{NULL} issues a warning if aggregation is #' necessary and uses \code{\link{mean}}. Pass \code{mean} directly to avoid #' the warning. #' @param transformation In \code{aov_ez}, a \code{character} vector (of length #' 1) indicating the name of a transformation to apply to \code{dv} before #' fitting the model. If missing, no transformation is applied. In #' \code{aov_car} and \code{aov_4}, a response transformation may be #' incorporated in the left-hand side of \code{formula}. #' @param type The type of sums of squares for the ANOVA. The default is given #' by \code{afex_options("type")}, which is \strong{initially set to 3}. #' Passed to \code{\link[car]{Anova}}. Possible values are \code{"II"}, #' \code{"III"}, \code{2}, or \code{3}. #' @param factorize logical. Should between subject factors be factorized (with #' note) before running the analysis. The default is given by #' \code{afex_options("factorize")}, which is initially \code{TRUE}. If one #' wants to run an ANCOVA, this needs to be set to \code{FALSE} (in which case #' centering on 0 is checked on numeric variables). #' @param check_contrasts \code{logical}. Should contrasts for between-subject #' factors be checked and (if necessary) changed to be \code{"contr.sum"}. See #' details. The default is given by \code{afex_options("check_contrasts")}, #' which is initially \code{TRUE}. #' @param print.formula \code{aov_ez} and \code{aov_4} are wrapper for #' \code{aov_car}. This boolean argument indicates whether the formula in the #' call to \code{car.aov} should be printed. #' @param anova_table \code{list} of further arguments passed to function #' producing the ANOVA table. Arguments such as \code{es} (effect size) or #' \code{correction} are passed to either \code{anova.afex_aov} or #' \code{nice}. Note that those settings can also be changed once an object of #' class \code{afex_aov} is created by invoking the \code{anova} method #' directly. #' @param include_aov Boolean. Allows suppressing the calculation of the aov #' object, which is per default part of the returned \code{afex_aov} object. #' \code{FALSE} prevents this potentially costly calculation. Especially for #' designs with larger N and within-subjects factors, this is highly #' advisable. Follow-up analyses using \pkg{emmeans} are then always based on #' the multivariate or \code{lm} model. #' @param ... Further arguments passed to \code{fun_aggregate}. #' @param return What should be returned? The default is given by #' \code{afex_options("return_aov")}, which is initially \code{"afex_aov"}, #' returning an S3 object of class \code{afex_aov} for which various #' \link[=afex_aov-methods]{methods} exist (see there and below for more #' details). Other values are currently still supported for backward #' compatibility. # To avoid the (potentially costly) computation via \code{aov} set # \code{return} to \code{"nice"} in which case only the nice ANOVA table is # returned (produced by \code{\link{nice}}, this was the previous default # return value). # Possible values are \code{c("Anova", "lm", "data", "nice", "full", "all", # "univariate", "marginal", "aov")} (possibly abbreviated). #' #' @return \code{aov_car}, \code{aov_4}, and \code{aov_ez} are wrappers for #' \code{\link[car]{Anova}} and \code{\link{aov}}, the return value is #' dependent on the \code{return} argument. Per default, an S3 object of class #' \code{"afex_aov"} is returned containing the following slots: #' #' \describe{ #' \item{\code{"anova_table"}}{An ANOVA table of class \code{c("anova", #' "data.frame")}.} #' \item{\code{"aov"}}{\code{aov} object returned from \code{\link{aov}} #' (should not be used to evaluate significance of effects, but can be passed #' to \code{emmeans} for post-hoc tests).} #' \item{\code{"Anova"}}{object returned from \code{\link[car]{Anova}}, an #' object of class \code{"Anova.mlm"} (if within-subjects factors are present) #' or of class \code{c("anova", "data.frame")}.} #' \item{\code{"lm"}}{the object fitted with \code{lm} and passed to #' \code{Anova} (i.e., an object of class \code{"lm"} or \code{"mlm"}). Also #' returned if \code{return = "lm"}.} #' \item{\code{"data"}}{a list containing: (1) \code{long} (the possibly #' aggregated data in long format used for \code{aov}), \code{wide} (the data #' used to fit the \code{lm} object), and \code{idata} (if within-subject #' factors are present, the \code{idata} argument passed to #' \code{car::Anova}). Also returned if \code{return = "data"}.} #' } #' In addition, the object has the following attributes: \code{"dv"}, #' \code{"id"}, \code{"within"}, \code{"between"}, and \code{"type"}. #' #' The \link[=afex_aov-methods]{print} method for \code{afex_aov} objects #' (invisibly) returns (and prints) the same as if \code{return} is #' \code{"nice"}: a nice ANOVA table (produced by \code{\link{nice}}) with the #' following columns: \code{Effect}, \code{df}, \code{MSE} (mean-squared #' errors), \code{F} (potentially with significant symbols), \code{ges} #' (generalized eta-squared), \code{p}. #' #' @details #' #' \subsection{Details of ANOVA Specification}{ \code{aov_ez} will concatenate #' all between-subject factors using \code{*} (i.e., producing all main effects #' and interactions) and all covariates by \code{+} (i.e., adding only the main #' effects to the existing between-subject factors). The within-subject factors #' do fully interact with all between-subject factors and covariates. This is #' essentially identical to the behavior of SPSS's \code{glm} function. #' #' The \code{formula}s for \code{aov_car} or \code{aov_4} must contain a single #' \code{Error} term specifying the \code{ID} column and potential #' within-subject factors (you can use \code{\link{mixed}} for running #' mixed-effects models with multiple error terms). Factors outside the #' \code{Error} term are treated as between-subject factors (the within-subject #' factors specified in the \code{Error} term are ignored outside the #' \code{Error} term; in other words, it is not necessary to specify them #' outside the \code{Error} term, see Examples).\cr Suppressing the intercept #' (i.e, via \code{0 +} or \code{- 1}) is ignored. Specific specifications of #' effects (e.g., excluding terms with \code{-} or using \code{^}) could be okay #' but is not tested. Using the \code{\link{I}} or \code{\link{poly}} function #' within the formula is not tested and not supported! #' #' To run an ANCOVA you need to set \code{factorize = FALSE} and make sure that #' all variables have the correct type (i.e., factors are factors and numeric #' variables are numeric and centered). #' #' Note that the default behavior is to include calculation of the effect size #' generalized eta-squared for which \strong{all non-manipluated (i.e., #' observed)} variables need to be specified via the \code{observed} argument to #' obtain correct results. When changing the effect size to \code{"pes"} #' (partial eta-squared) or \code{"none"} via \code{anova_table} this becomes #' unnecessary. #' #' If \code{check_contrasts = TRUE}, contrasts will be set to \code{"contr.sum"} #' for all between-subject factors if default contrasts are not equal to #' \code{"contr.sum"} or \code{attrib(factor, "contrasts") != "contr.sum"}. #' (within-subject factors are hard-coded \code{"contr.sum"}.) } #' #' \subsection{Statistical Issues}{ \strong{Type 3 sums of squares are default #' in \pkg{afex}.} While some authors argue that so-called type 3 sums of #' squares are dangerous and/or problematic (most notably Venables, 2000), they #' are the default in many commercial statistical application such as SPSS or #' SAS. Furthermore, statisticians with an applied perspective recommend type 3 #' tests (e.g., Maxwell and Delaney, 2004). Consequently, they are the default #' for the ANOVA functions described here. For some more discussion on this #' issue see \href{http://stats.stackexchange.com/q/6208/442}{here}. #' #' Note that lower order effects (e.g., main effects) in type 3 ANOVAs are only #' meaningful with #' \href{http://www.ats.ucla.edu/stat/mult_pkg/faq/general/effect.htm}{effects #' coding}. That is, contrasts should be set to \code{\link{contr.sum}} to #' obtain meaningful results. This is imposed automatically for the functions #' discussed here as long as \code{check_contrasts} is \code{TRUE} (the #' default). I nevertheless recommend to set the contrasts globally to #' \code{contr.sum} via running \code{\link{set_sum_contrasts}}. For a #' discussion of the other (non-recommended) coding schemes see #' \href{http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm}{here}. } #' #' \subsection{Follow-Up Contrasts and Post-Hoc Tests}{ The S3 object returned #' per default can be directly passed to \code{emmeans::emmeans} for further #' analysis. This allows to test any type of contrasts that might be of interest #' independent of whether or not this contrast involves between-subject #' variables, within-subject variables, or a combination thereof. The general #' procedure to run those contrasts is the following (see Examples for a full #' example): #' #' \enumerate{ #' \item Estimate an \code{afex_aov} object with the function returned here. For example: \code{x <- aov_car(dv ~ a*b + (id/c), d)} #' \item Obtain a \code{\link[emmeans]{emmGrid-class}} object by running \code{\link[emmeans]{emmeans}} on the \code{afex_aov} object from step 1 using the factors involved in the contrast. For example: \code{r <- emmeans(x, ~a:c)} #' \item Create a list containing the desired contrasts on the reference grid object from step 2. For example: \code{con1 <- list(a_x = c(-1, 1, 0, 0, 0, 0), b_x = c(0, 0, -0.5, -0.5, 0, 1))} #' \item Test the contrast on the reference grid using \code{\link[emmeans]{contrast}}. For example: \code{contrast(r, con1)} #' \item To control for multiple testing p-value adjustments can be specified. For example the Bonferroni-Holm correction: \code{contrast(r, con1, adjust = "holm")} #' } #' #' Note that \pkg{emmeans} allows for a variety of advanced settings and #' simplifiations, for example: all pairwise comparison of a single factor #' using one command (e.g., \code{emmeans(x, "a", contr = "pairwise")}) or #' advanced control for multiple testing by passing objects to \pkg{multcomp}. #' A comprehensive overview of the functionality is provided in the #' accompanying vignettes (see #' \href{https://CRAN.R-project.org/package=emmeans}{here}). #' #' A caveat regarding the use of \pkg{emmeans} concerns the assumption of #' sphericity for ANOVAs including within-subjects/repeated-measures factors #' (with more than two levels). The current default for follow-up tests uses a #' univariate model (\code{model = "univariate"} in the call to #' \code{emmeans}), which does not adequately control for violations of #' sphericity. This may result in anti-conservative tests and contrasts #' somewhat with the default ANOVA table which reports results based on the #' Greenhousse-Geisser correction. An alternative is to use a multivariate #' model (\code{model = "multivariate"} in the call to \code{emmeans}) which #' should handle violations of sphericity better. The default will likely #' change to multivariate tests in one of the next versions of the package. #' #' Starting with \pkg{afex} version 0.22, \pkg{emmeans} is \emph{not} #' loaded/attached automatically when loading \pkg{afex}. Therefore, #' \pkg{emmeans} now needs to be loaded by the user via #' \code{library("emmeans")} or \code{require("emmeans")}. #' } #' #' \subsection{Methods for \code{afex_aov} Objects}{ A full overview over the #' methods provided for \code{afex_aov} objects is provided in the corresponding #' help page: \code{\link{afex_aov-methods}}. The probably most important ones #' for end-users are \code{summary}, \code{anova}, and \code{\link{nice}}. #' #' The \code{summary} method returns, for ANOVAs containing within-subject #' (repeated-measures) factors with more than two levels, the complete #' univariate analysis: Results without df-correction, the Greenhouse-Geisser #' corrected results, the Hyunh-Feldt corrected results, and the results of the #' Mauchly test for sphericity. #' #' The \code{anova} method returns a \code{data.frame} of class \code{"anova"} #' containing the ANOVA table in numeric form (i.e., the one in slot #' \code{anova_table} of a \code{afex_aov}). This method has arguments such as #' \code{correction} and \code{es} and can be used to obtain an ANOVA table with #' different correction than the one initially specified. #' #' The \code{\link{nice}} method also returns a \code{data.frame}, but rounds #' most values and transforms them into characters for nice printing. Also has #' arguments like \code{correction} and \code{es} which can be used to obtain an #' ANOVA table with different correction than the one initially specified. } #' #' @author Henrik Singmann #' #' The design of these functions was influenced by \code{\link[ez]{ezANOVA}} #' from package \pkg{ez}. #' #' @note Calculation of ANOVA models via \code{aov} (which is done per default) #' can be comparatively slow and produce comparatively large objects for #' ANOVAs with many within-subjects factors or levels. To avoid this #' calculation set \code{include_aov = FALSE}. You can also disable this #' globally with: \code{afex_options(include_aov = FALSE)} #' #' The id variable and variables entered as within-subjects (i.e., #' repeated-measures) factors are silently converted to factors. Levels of #' within-subject factors are converted to valid variable names using #' \code{\link{make.names}(...,unique=TRUE)}. Unused factor levels are #' silently dropped on all variables. #' #' Contrasts attached to a factor as an attribute are probably not preserved #' and not supported. #' #' The workhorse is \code{aov_car}. \code{aov_4} and \code{aov_ez} only #' construe and pass an appropriate formula to \code{aov_car}. Use #' \code{print.formula = TRUE} to view this formula. #' #' In contrast to \code{\link{aov}} \code{aov_car} assumes that all factors to #' the right of \code{/} in the \code{Error} term are belonging together. #' Consequently, \code{Error(id/(a*b))} and \code{Error(id/a*b)} are identical #' (which is not true for \code{\link{aov}}). #' #' @seealso Various methods for objects of class \code{afex_aov} are available: #' \code{\link{afex_aov-methods}} #' #' \code{\link{nice}} creates the nice ANOVA tables which is by default printed. #' See also there for a slightly longer discussion of the available effect #' sizes. #' #' \code{\link{mixed}} provides a (formula) interface for obtaining p-values for #' mixed-models via \pkg{lme4}. The functions presented here do not estimate #' mixed models. #' #' @references Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, #' H., Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). #' Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies. #' \emph{Psychonomic Bulletin & Review}, 1-8. #' doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} #' #' #' Maxwell, S. E., & Delaney, H. D. (2004). \emph{Designing Experiments and #' Analyzing Data: A Model-Comparisons Perspective}. Mahwah, N.J.: Lawrence #' Erlbaum Associates. #' #' Venables, W.N. (2000). \emph{Exegeses on linear models}. Paper presented to #' the S-Plus User's Conference, Washington DC, 8-9 October 1998, Washington, #' DC. Available from: \url{http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf} #' #' @importFrom car Anova #' @importFrom reshape2 dcast #' @importFrom lme4 findbars nobars #' @importFrom stats terms as.formula xtabs contrasts<- coef #' #' @example examples/examples.aov_car.R #' #' #' @encoding UTF-8 #' @export aov_car <- function(formula, data, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), observed = NULL, anova_table = list(), include_aov = afex_options("include_aov"), return = afex_options("return_aov"), ...) { return <- match.arg(return, c("Anova", "lm", "data", "nice", "afex_aov", "univariate", "marginal", "aov")) dots <- list(...) ### deprercate old argument names: if("check.contrasts" %in% names(dots)) { warn_deprecated_arg("check.contrasts", "check_contrasts") check_contrasts <- dots$check.contrasts dots <- dots[names(dots) != "check.contrasts"] } if("fun.aggregate" %in% names(dots)) { warn_deprecated_arg("fun.aggregate", "fun_aggregate") fun_aggregate <- dots$fun.aggregate dots <- dots[names(dots) != "fun.aggregate"] } # transform to data.frame if necessary (e.g., when using dplyr) data <- as.data.frame(data) # stuff copied from aov: Terms <- terms(formula, "Error", data = data) indError <- attr(Terms, "specials")$Error if (length(indError) > 1L) stop(sprintf(ngettext(length(indError), "there are %d Error terms: only 1 is allowed", "there are %d Error terms: only 1 is allowed"), length(indError)), domain = NA) # from here, code by Henrik Singmann: vars <- all.vars(formula) #--- Russ Lenth added/modified code to detect transformed responses: lhs <- all.names(formula[[2]]) transf <- setdiff(lhs, all.vars(formula[[2]])) if (length(transf) == 0) transf = NULL if (!is.null(transf)) { origdv <- setdiff(lhs, transf) dv <- paste0(transf[1], ".", origdv) data[[dv]] <- eval(formula[[2]], envir = data) # add transformed version vars <- vars[!(vars %in% lhs)] } else { dv <- vars[1] if (!is.numeric(data[,dv])) stop("dv needs to be numeric.") #check if dv is numeric vars <- vars[-1] } #--- end RL changes parts <- attr(terms(formula, "Error", data = data), "term.labels") error.term <- parts[grepl("^Error\\(", parts)] id <- all.vars(parse(text = error.term))[1] within <- all.vars(parse(text = error.term))[-1] between <- vars[!(vars %in% c(id, within))] dv.escaped <- escape_vars(dv) id.escaped <- escape_vars(id) within.escaped <- escape_vars(within) between.escaped <- escape_vars(between) effect.parts <- parts[!grepl("^Error\\(", parts)] if (length(within) > 0) { effect.parts.no.within <- character() for (term in effect.parts) { components <- decomposeTerm(term) if ( ! any(within %in% components)) effect.parts.no.within <- c(effect.parts.no.within, term) } } else { effect.parts.no.within <- effect.parts } data <- droplevels(data) #remove empty levels. # make id and within variables to factors: if (!(is.factor(data[,id]))) data[,id] <- factor(data[,id]) # factorize if necessary if (factorize) { if (any(!vapply(data[, between, drop = FALSE], is.factor, TRUE))) { to.factor <- between[!vapply(data[,between, drop = FALSE], is.factor, TRUE)] message(paste0("Converting to factor: ", paste0(to.factor, collapse = ", "))) for (tmp.c in to.factor) { data[,tmp.c] <- factor(data[,tmp.c]) } } } else { # check if numeric variables are centered. c.ns <- between[vapply(data[, between, drop = FALSE], is.numeric, TRUE)] if (length(c.ns) > 0) { non.null <- c.ns[!abs(vapply(data[, c.ns, drop = FALSE], mean, 0)) < .Machine$double.eps ^ 0.5] if (length(non.null) > 0) warning(paste0( "Numerical variables NOT centered on 0 (i.e., likely bogus results): ", paste0(non.null, collapse = ", ")), call. = FALSE) } } for (i in c(between, within)) { if (is.factor(data[,i]) && length(unique(data[,i])) == 1) stop(paste0("Factor \"", i, "\" consists of one level only. Remove factor from model?")) } # make formulas rh2 <- if (length(between.escaped) > 0) paste0(effect.parts.no.within, collapse = "+") else "1" lh1 <- mypaste(id, if (length(between.escaped) > 0) paste0(between.escaped, collapse = "+") else NULL, sep = "+") rh1 <- paste0(within.escaped, collapse = "+") rh3 <- paste0(within.escaped, collapse = "*") # converting all within subject factors to factors and # add a leading charcter (x) if starting with a digit. for (within.factor in within) { if (is.factor(data[,within.factor])) levels(data[,within.factor]) <- make.names(levels(data[,within.factor]), unique = TRUE) else data[,within.factor] <- factor(as.character(data[,within.factor]), levels = unique(as.character(data[,within.factor])), labels = make.names(unique(as.character(data[,within.factor])), unique=TRUE)) } # Check if each id is in only one between subjects cell. between.factors <- between[vapply(data[, between, drop = FALSE], is.factor, TRUE)] if (length(between.factors) > 0) { split.data <- split(data, lapply(between.factors, function(x) data[,x])) ids.per.condition <- lapply(split.data, function(x) unique(as.character(x[,id]))) ids.in.more.condition <- unique(unlist( lapply(seq_along(ids.per.condition), function(x) unique(unlist( lapply(ids.per.condition[-x], function(y, z = ids.per.condition[[x]]) intersect(z, y))))))) if (length(ids.in.more.condition) > 0) { stop( paste0("Following ids are in more than one between subjects condition:\n", paste0(ids.in.more.condition, collapse = ", "))) } } ## check for structurally missing data # within-subjects if ((length(within) > 0) && any(table(data[within]) == 0)) { stop("Empty cells in within-subjects design ", " (i.e., bad data structure).\n", "", paste0("table(data[", deparse(within), "])"), "\n# ", paste(utils::capture.output(table(data[within])), collapse = "\n# "), call. = FALSE) } # between-subjects between_nn <- between[!vapply(data[between], is.numeric, NA)] if (length(between_nn) > 0 && any(table(data[between_nn]) == 0)) { stop("Empty cells in between-subjects design ", " (i.e., bad data structure).\n", "", paste0("table(data[", deparse(between_nn), "])"), "\n# ", paste(utils::capture.output(table(data[between_nn])), collapse = "\n# "), call. = FALSE) } # Is fun_aggregate NULL and aggregation necessary? if (is.null(fun_aggregate)) { if (any(xtabs( as.formula(paste0("~", id.escaped, if (length(within) > 0) "+", rh1)), data = data) > 1)) { warning("More than one observation per cell, aggregating the data using mean (i.e, fun_aggregate = mean)!", call. = FALSE) fun_aggregate <- mean } } # prepare the data: tmp.dat <- do.call( dcast, args = c(data = list(data), formula = as.formula(paste(lh1, if (length(within) > 0) rh1 else ".", sep = "~")), fun.aggregate = fun_aggregate, dots, value.var = dv)) # check for missing values: if (any(is.na(tmp.dat))) { missing.values <- apply(tmp.dat, 1, function(x) any(is.na(x))) missing_ids <- unique(tmp.dat[missing.values,1]) warning(paste0("Missing values for following ID(s):\n", paste0(missing_ids, collapse = ", "), "\nRemoving those cases from the analysis."), call. = FALSE) tmp.dat <- tmp.dat[!missing.values,] data <- data[ !(data[,id] %in% missing_ids),] } else { missing_ids <- NULL } # if (length(between) > 0) { # n_data_points <- xtabs(as.formula(paste("~", paste(between, collapse = "+"))), data = tmp.dat) # if (any(n_data_points == 0)) warning("Some cells of the fully crossed between-subjects design are empty. A full model might not be estimable.") # } # marginals: (disabled in April 2015), dat.ret is now used for aov() dat.ret <- do.call( dcast, args = c(data = list(data), formula = as.formula(paste0(mypaste(lh1, if (length(within) > 0) rh1 else NULL, sep = "+"), "~.")), fun.aggregate = fun_aggregate, dots, value.var = dv)) colnames(dat.ret)[length(colnames(dat.ret))] <- dv if (length(between) > 0) { if (check_contrasts) { resetted <- NULL for (i in between) { if (is.character(tmp.dat[,i])) { tmp.dat[,i] <- factor(tmp.dat[,i]) } if (is.factor(tmp.dat[,i])) { if (is.null(attr(tmp.dat[,i], "contrasts")) & (options("contrasts")[[1]][1] != "contr.sum")) { contrasts(tmp.dat[,i]) <- "contr.sum" resetted <- c(resetted, i) } else if (!is.null(attr(tmp.dat[,i], "contrasts")) && attr(tmp.dat[,i], "contrasts") != "contr.sum") { contrasts(tmp.dat[,i]) <- "contr.sum" resetted <- c(resetted, i) } } } if (!is.null(resetted)) message(paste0("Contrasts set to contr.sum for the following variables: ", paste0(resetted, collapse=", "))) } else { non_sum_contrast <- c() for (i in between) { if (is.factor(tmp.dat[,i])) { if (is.null(attr(tmp.dat[,i], "contrasts")) & (options("contrasts")[[1]][1] != "contr.sum")) { non_sum_contrast <- c(non_sum_contrast, between) } else if (!is.null(attr(tmp.dat[,i], "contrasts")) && attr(tmp.dat[,i], "contrasts") != "contr.sum") { non_sum_contrast <- c(non_sum_contrast, between) } } } if((type == 3 | type == "III") && (length(non_sum_contrast)>0)) warning( paste0("Calculating Type 3 sums with contrasts != 'contr.sum' for: ", paste0(non_sum_contrast, collapse=", "), "\n Results likely bogus or not interpretable!\n You probably want check_contrasts = TRUE or options(contrasts=c('contr.sum','contr.poly'))"), call. = FALSE) } } if (return %in% c("aov")) include_aov <- TRUE if(include_aov){ if (check_contrasts) { factor_vars <- vapply(dat.ret[,c(within, between), drop = FALSE], is.factor, NA) contrasts <- as.list(rep("contr.sum", sum(factor_vars))) names(contrasts) <- c(within, between)[factor_vars] } tmp_formula <- formula(paste(dv.escaped, "~", if (length(within) > 0) { paste( if (rh2 == "1") { paste(within.escaped, collapse="*") } else { paste("(" ,rh2, ")*(", paste(within.escaped, collapse="*"), ")") }, "+Error(", id.escaped, "/(", paste(within.escaped, collapse="*"), "))") } else rh2)) aov <- aov(tmp_formula, data=dat.ret, contrasts = contrasts) } else { aov <- NULL } if(return == "aov") return(aov) data.l <- list(long = dat.ret, wide = tmp.dat) if (return == "data") return(tmp.dat) # branching based on type of ANOVA if (length(within) > 0) { # if within-subject factors are present: # make idata argument if (length(within) > 1) { within.levels <- lapply(lapply(data[,within], levels), factor) idata <- rev(expand.grid(rev(within.levels))) } else { idata <- data.frame(levels(data[,within]), stringsAsFactors = TRUE) colnames(idata) <- within } tmp.lm <- do.call( "lm", list(formula = as.formula(paste0("cbind(", paste0(colnames( tmp.dat[-(seq_along(c(id, between)))]), collapse = ", "), ") ~ ", rh2)), data = tmp.dat)) if (any(is.na(coef(tmp.lm)))) stop("Some parameters are not estimable, most likely due to empty cells of the design (i.e., structural missings). Check your data.") if (return == "lm") return(tmp.lm) Anova.out <- Anova(tmp.lm, idata = idata, idesign = as.formula(paste0("~", rh3)), type = type) data.l <- c(data.l, idata = list(idata)) } else { # if NO within-subjetc factors are present (i.e., purley between ANOVA): colnames(tmp.dat)[ncol(tmp.dat)] <- "dv" tmp.lm <- do.call("lm", list(formula = as.formula(paste0("dv ~ ", rh2)), data = tmp.dat)) if (return == "lm") return(tmp.lm) Anova.out <- Anova(tmp.lm, type = type) } if (return == "afex_aov") { afex_aov <- list( anova_table = NULL, aov = aov, Anova = Anova.out, lm = tmp.lm, data = data.l ) class(afex_aov) <- "afex_aov" attr(afex_aov, "dv") <- dv attr(afex_aov, "id") <- id attr(afex_aov, "within") <- if (length(within) > 0) lapply(data[, within, drop = FALSE], levels) else list() attr(afex_aov, "between") <- if (length(between) > 0) lapply(data[, between, drop = FALSE], levels) else list() attr(afex_aov, "type") <- type attr(afex_aov, "transf") <- transf attr(afex_aov, "incomplete_cases") <- missing_ids afex_aov$anova_table <- do.call("anova", args = c(object = list(afex_aov), observed = list(observed), anova_table)) return(afex_aov) } if (return == "Anova") return(Anova.out) else if (return == "univariate") { if (inherits(Anova.out, "Anova.mlm")) return(summary(Anova.out, multivariate = FALSE)) else return(Anova.out) } else if (return == "nice") { afex_aov <- list( anova_table = NULL, Anova = Anova.out ) class(afex_aov) <- "afex_aov" attr(afex_aov, "dv") <- dv attr(afex_aov, "id") <- id attr(afex_aov, "within") <- if (length(within) > 0) lapply(data[,within, drop = FALSE], levels) else list() attr(afex_aov, "between") <- if (length(between) > 0) lapply(data[,between,drop=FALSE], levels) else list() attr(afex_aov, "type") <- type afex_aov$anova_table <- do.call("anova", args = c(object = list(afex_aov), observed = list(observed), anova_table)) return(do.call("nice", args = c(object = list(afex_aov), observed = list(observed), anova_table))) } } #' @describeIn aov_car Allows definition of ANOVA-model using #' \code{lme4::lmer}-like Syntax (but still fits a standard ANOVA). #' @export aov_4 <- function(formula, data, observed = NULL, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), anova_table = list(), include_aov = afex_options("include_aov"), ..., print.formula = FALSE) { barterms <- findbars(formula) if (length(barterms) > 1) stop("aov_4 only allows one random effect term") within <- all.vars(barterms[[1]][[2]]) id <- all.vars(barterms[[1]][[3]]) id <- escape_vars(id) within <- escape_vars(within) error <- paste0(" + Error(", id, if (length(within) > 0) "/(" else "", paste0(within, collapse = " * "), if (length(within) > 0) ")" else "", ")") lh <- as.character(nobars(formula)) if (length(lh) == 1) { dv <- lh rh <- "1" } else { dv <- lh[2] rh <- lh[3] } formula <- paste0(dv, " ~ ", rh, error) if (print.formula) message(paste0("Formula send to aov_car: ", formula)) aov_car(formula = as.formula(formula), data = data, fun_aggregate = fun_aggregate, type = type, return = return, factorize = factorize, check_contrasts = check_contrasts, observed = observed, anova_table = anova_table, include_aov = include_aov, ...) } #' @describeIn aov_car Allows definition of ANOVA-model using character strings. #' @export aov_ez <- function(id, dv, data, between = NULL, within = NULL, covariate = NULL, observed = NULL, fun_aggregate = NULL, transformation, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), anova_table = list(), include_aov = afex_options("include_aov"), ..., print.formula = FALSE) { if (is.null(between) & is.null(within)) stop("Either between or within need to be non-NULL!") if (!is.null(covariate)) { covariate <- escape_vars(covariate) covariate <- paste0(covariate, collapse = "+") } id <- escape_vars(id) dv <- escape_vars(dv) between <- escape_vars(between) within <- escape_vars(within) rh <- if (!is.null(between) || !is.null(covariate)) mypaste(if (!is.null(between)) paste0(between, collapse = " * ") else NULL, covariate, sep = "+") else "1" error <- paste0(" + Error(", id, if (!is.null(within)) "/(" else "", paste0(within, collapse = " * "), if (length(within) > 0) ")" else "", ")") if (!missing(transformation)) dv <- paste0(transformation, "(", dv, ")") formula <- paste0(dv, " ~ ", rh, error) if (print.formula) message(paste0("Formula send to aov_car: ", formula)) aov_car(formula = as.formula(formula), data = data, fun_aggregate = fun_aggregate, type = type, return = return, factorize = factorize, check_contrasts = check_contrasts, observed = observed, anova_table = anova_table, include_aov = include_aov, ...) } afex/R/set_contrasts.R0000644000176200001440000000266113351525342014424 0ustar liggesusers#' Set global contrasts #' #' These functions are simple wrappers to set contrasts globally via \code{options(contrasts = ...)}. #' #' @usage set_sum_contrasts() #' #' set_deviation_contrasts() #' #' set_effects_contrasts() #' #' set_default_contrasts() #' #' set_treatment_contrasts() #' #' #' @details \code{set_deviation_contrasts} and \code{set_effects_contrasts} are wrappers for \code{set_sum_contrasts}. Likewise, \code{set_default_contrasts} is a wrapper to \code{set_treatment_contrasts()}. #' #' @return nothing. These functions are called for their side effects to change the global options. #' #' @name set_sum_contrasts #' @aliases set_sum_contrasts set_deviation_contrasts set_effects_contrasts set_treatment_contrasts set_default_contrasts #' @export set_sum_contrasts set_deviation_contrasts set_effects_contrasts set_treatment_contrasts set_default_contrasts set_sum_contrasts <- function() { message("setting contr.sum globally: options(contrasts=c('contr.sum', 'contr.poly'))") options(contrasts=c('contr.sum', 'contr.poly')) } set_deviation_contrasts <- function() { set_sum_contrasts() } set_effects_contrasts <- function() { set_sum_contrasts() } set_treatment_contrasts <- function() { message("setting contr.treatment globally: options(contrasts=c('contr.treatment', 'contr.poly'))") options(contrasts=c('contr.treatment', 'contr.poly')) } set_default_contrasts <- function() { set_treatment_contrasts() } afex/R/test_assumption.R0000644000176200001440000000265213506224623014772 0ustar liggesusers#' Assumption Tests for ANOVAs #' #' \code{test_levene} computes Levene's test for homogeneity of variances across #' groups via \code{car::leveneTest}. \code{test_sphericity} computes Mauchly #' test of sphericity via \code{car::Anova}. #' #' @param afex_aov \code{afex_aov} object. #' @param center Function to compute the center of each group; \code{mean} (the #' default) gives the original Levene's test. #' @param ... passed to \code{\link[car]{leveneTest}} #' #' @author Mattan S. Ben-Shachar and Henrik Singmann #' #' #' @example examples/examples.test_assumptions.R #' #' @rdname test_assumptions #' @export test_levene <- function(afex_aov, center = mean, ...){ if (length(attr(afex_aov,'between')) == 0) { stop("Levene test is only aplicable to ANOVAs with between-subjects factors.") } data <- afex_aov$data$long dv <- attr(afex_aov,'dv') id <- attr(afex_aov,'id') between <- names(attr(afex_aov,'between')) form <- stats::formula(paste0(dv,'~',paste0(between,collapse = '*'))) ag_data <- aggregate(data[,dv],data[,c(between,id)],mean) colnames(ag_data)[length(c(between,id))+1] <- dv car::leveneTest(form,ag_data, center = center, ...) } #' @export #' @rdname test_assumptions test_sphericity<- function(afex_aov){ if (length(attr(afex_aov,'within')) == 0) { stop("Mauchly Test of Sphericity is only aplicable to ANOVAs with within-subjects factors.") } summary(afex_aov)$sphericity.tests } afex/R/sk2011.2-data.R0000644000176200001440000000565113351525342013523 0ustar liggesusers#' Data from Singmann & Klauer (2011, Experiment 2) #' #' Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and type of the problem. Problem type consistent of three levels: prological problems (i.e., problems in which background knowledge suggested to accept valid but reject invalid conclusions), neutral problems (i.e., in which background knowledge suggested to reject all problems), and counterlogical problems (i.e., problems in which background knowledge suggested to reject valid but accept invalid conclusions). #' #' This data set contains 63 participants in contrast to the originally reported 56 participants. The additional participants were not included in the original studies as they did not meet the inclusion criteria (i.e., no students, prior education in logic, or participated in a similar experiment). The IDs of those additional participants are: 7, 8, 9, 12, 17, 24, 30. The excluded participant reported in the paper has ID 16. #' #' content has the following levels (C = content/conditional):\cr #' 1 = Wenn eine Person in ein Schwimmbecken gefallen ist, dann ist sie nass.\cr #' 2 = Wenn ein Hund Flöhe hat, dann kratzt er sich hin und wieder.\cr #' 3 = Wenn eine Seifenblase mit einer Nadel gestochen wurde, dann platzt sie.\cr #' 4 = Wenn ein Mädchen Geschlechtsverkehr vollzogen hat, dann ist es schwanger.\cr #' 5 = Wenn eine Pflanze ausreichend gegossen wird, dann bleibt sie grün.\cr #' 6 = Wenn sich eine Person die Zähne putzt, dann bekommt sie KEIN Karies.\cr #' 7 = Wenn eine Person viel Cola trinkt, dann nimmt sie an Gewicht zu.\cr #' 8 = Wenn eine Person die Klimaanlage angeschaltet hat, dann fröstelt sie.\cr #' 9 = Wenn eine Person viel lernt, dann wird sie in der Klausur eine gute Note erhalten. #' #' @docType data #' @keywords dataset #' @name sk2011.2 #' @usage sk2011.2 #' @format A data.frame with 2268 rows and 9 variables. #' @source Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. Thinking & Reasoning, 17(3), 247-281. doi:10.1080/13546783.2011.572718 #' #' @encoding UTF-8 #' #' @example examples/examples.sk2011.2.R NULL afex/R/sk2011.1-data.R0000644000176200001440000000564313351525342013523 0ustar liggesusers#' Data from Singmann & Klauer (2011, Experiment 1) #' #' Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and plausibility of the problem (inferences which were consisted with the background knowledge versus problems that were inconsistent with the background knowledge). The critical comparison across the two conditions was among problems which were valid and implausible with problems that were invalid and plausible. For example, the next problem was invalid and plausible: #' #' If a person is wet, then the person fell into a swimming pool. \cr #' A person fell into a swimming pool. \cr #' How valid is the conclusion/How likely is it that the person is wet? #' #' For those problems we predicted that under deductive instructions responses should be lower (as the conclusion does not necessarily follow from the premises) as under probabilistic instructions. For the valid but implausible problem, an example is presented next, we predicted the opposite pattern: #' #' If a person is wet, then the person fell into a swimming pool. \cr #' A person is wet. \cr #' How valid is the conclusion/How likely is it that the person fell into a swimming pool? #' #' Our study also included valid and plausible and invalid and implausible problems. #' #' Note that the factor `plausibility` is not present in the original manuscript, there it is a results of a combination of other factors. #' #' #' @docType data #' @keywords dataset #' @name sk2011.1 #' @usage sk2011.1 #' @format A data.frame with 640 rows and 9 variables. #' @source Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. Thinking & Reasoning, 17(3), 247-281. doi:10.1080/13546783.2011.572718 #' #' @encoding UTF-8 #' #' @examples #' data(sk2011.1) #' #' # Table 1 (p. 264): #' aov_ez("id", "response", sk2011.1[ sk2011.1$what == "affirmation",], #' within = c("inference", "type"), between = "instruction", #' anova_table=(es = "pes")) #' aov_ez("id", "response", sk2011.1[ sk2011.1$what == "denial",], #' within = c("inference", "type"), between = "instruction", #' anova_table=(es = "pes")) #' #' NULL afex/R/methods.afex_aov.R0000644000176200001440000003064313506224623014764 0ustar liggesusers#' Methods for afex_aov objects #' #' Methods defined for objects returned from the ANOVA functions \code{\link{aov_car}} et al. of class \code{afex_aov} containing both the ANOVA fitted via \code{car::Anova} and base R's \code{aov}. #' #' @param object,x object of class \code{afex_aov} as returned from \code{\link{aov_car}} and related functions. #' @param p_adjust_method \code{character} indicating if p-values for individual effects should be adjusted for multiple comparisons (see \link[stats]{p.adjust} and details). #' @param ... further arguments passed through, see description of return value for details. #' @param trms,xlev,grid same as for \code{\link[emmeans]{emm_basis}}. #' @param model argument for \code{\link[emmeans]{emmeans}()} and rlated functions that allows to choose on which model the follow-up tests for ANOVAs with repeated-measures factors are based. \code{"univariate"} uses the \code{aov} model and \code{"multivariate"} uses the \code{lm} model. Default given by \code{afex_options("emmeans_mode")}. Multivariate tests likely provide a better correction for violations of sphericity. #' #' @return #' \describe{ #' \item{\code{anova}}{Returns an ANOVA table of class \code{c("anova", "data.frame")}. Information such as effect size (\code{es}) or df-correction are calculated each time this method is called.} #' \item{\code{summary}}{For ANOVAs containing within-subject factors it returns the full output of the within-subject tests: the uncorrected results, results containing Greenhousse-Geisser and Hyunh-Feldt correction, and the results of the Mauchly test of sphericity (all achieved via \code{summary.Anova.mlm}). For other ANOVAs, the \code{anova} table is simply returned.} #' \item{\code{print}}{Prints (and invisibly returns) the ANOVA table as constructed from \code{\link{nice}} (i.e., as strings rounded nicely). Arguments in \code{...} are passed to \code{nice} allowing to pass arguments such as \code{es} and \code{correction}.} #' \item{\code{recover_data} and \code{emm_basis}}{Provide the backbone for using \code{\link[emmeans]{emmeans}} and related functions from \pkg{emmeans} directly on \code{afex_aov} objects by returning a \code{\link[emmeans]{emmGrid-class}} object. Should not be called directly but through the functionality provided by \pkg{emmeans}.} #' #' } #' #' @details #' Exploratory ANOVA, for which no detailed hypotheses have been specified a priori, harbor a multiple comparison problem (Cramer et al., 2015). To avoid an inflation of familywise Type I error rate, results need to be corrected for multiple comparisons using \code{p_adjust_method}. #' \code{p_adjust_method} defaults to the method specified in the call to \code{\link{aov_car}} in \code{anova_table}. If no method was specified and \code{p_adjust_method = NULL} p-values are not adjusted. #' #' @references #' Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies. \emph{Psychonomic Bulletin & Review}, 1-8. doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} #' #' @name afex_aov-methods #' @importFrom stats p.adjust NULL #### methods for afex_aov #' @rdname afex_aov-methods #' @inheritParams nice #' @method anova afex_aov #' @export anova.afex_aov <- function(object, es = afex_options("es_aov"), observed = NULL, correction = afex_options("correction_aov"), MSE = TRUE, intercept = FALSE, p_adjust_method = NULL, sig_symbols = attr(object$anova_table, "sig_symbols"), ...) { # internal functions: # check arguments dots <- list(...) if("p.adjust.method" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("p.adjust.method", "p_adjust_method") p_adjust_method <- dots$p.adjust.method } es <- match.arg(es, c("none", "ges", "pes"), several.ok = TRUE) correction <- match.arg(correction, c("GG", "HF", "none")) if (inherits(object$Anova, "Anova.mlm")) { tmp <- suppressWarnings(summary(object$Anova, multivariate = FALSE)) t.out <- tmp[["univariate.tests"]] #browser() #t.out <- cbind(t.out, orig_den_df = t.out[, "den Df"]) if (correction[1] == "GG") { tmp[["pval.adjustments"]] <- tmp[["pval.adjustments"]][ !is.na(tmp[["pval.adjustments"]][,"GG eps"]),, drop = FALSE] t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] * tmp[["pval.adjustments"]][,"GG eps"] t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] * tmp[["pval.adjustments"]][,"GG eps"] t.out[row.names(tmp[["pval.adjustments"]]), "Pr(>F)"] <- tmp[["pval.adjustments"]][,"Pr(>F[GG])"] } else { if (correction[1] == "HF") { try(if (any(tmp[["pval.adjustments"]][,"HF eps"] > 1)) warning("HF eps > 1 treated as 1", call. = FALSE), silent = TRUE) tmp[["pval.adjustments"]] <- tmp[["pval.adjustments"]][ !is.na(tmp[["pval.adjustments"]][,"HF eps"]),, drop = FALSE] t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] * pmin(1, tmp[["pval.adjustments"]][,"HF eps"]) t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] * pmin(1, tmp[["pval.adjustments"]][,"HF eps"]) t.out[row.names(tmp[["pval.adjustments"]]), "Pr(>F)"] <- tmp[["pval.adjustments"]][,"Pr(>F[HF])"] } else { if (correction[1] == "none") { TRUE } else stop("None supported argument to correction.") } } tmp.df <- t.out tmp2 <- as.data.frame(unclass(tmp.df)) #} else if (class(object$Anova)[1] == "anova") { } else if (inherits(object$Anova, "anova")) { #browser() tmp.df <- cbind(object$Anova[-nrow(object$Anova),], data.frame("Error SS" = object$Anova[nrow(object$Anova), "Sum Sq"], "den Df" = object$Anova[nrow(object$Anova), "Df"], check.names = FALSE)) colnames(tmp.df)[1:3] <- c("SS", "num Df", "F") #tmp.df$orig_den_df <- tmp.df[, "den Df"] tmp2 <- as.data.frame(tmp.df) } else stop("Non-supported object passed. Slot 'Anova' needs to be of class 'Anova.mlm' or 'anova'.") tmp2[,"MSE"] <- tmp2[,"Error SS"]/tmp2[,"den Df"] ## provision for car 3.0 (March 2018), for calculation of es if ("Sum Sq" %in% colnames(tmp2)) { tmp2$SS <- tmp2[,"Sum Sq"] } # calculate es es_df <- data.frame(row.names = rownames(tmp2)) if ("pes" %in% es) { es_df$pes <- tmp2$SS/(tmp2$SS + tmp2[,"Error SS"]) } if ("ges" %in% es) { # This code is basically a copy from ezANOVA by Mike Lawrence! if(!is.null(observed) & length(observed) > 0){ obs <- rep(FALSE,nrow(tmp2)) for(i in observed){ if (!any(grepl(paste0("\\b",i,"\\b"), rownames(tmp2)))) stop(paste0("Observed variable not in data: ", i)) obs <- obs | grepl(paste0("\\b",i,"\\b"), rownames(tmp2)) } obs_SSn1 <- sum(tmp2$SS*obs) obs_SSn2 <- tmp2$SS*obs } else { obs_SSn1 <- 0 obs_SSn2 <- 0 } es_df$ges <- tmp2$SS/(tmp2$SS+sum(unique(tmp2[,"Error SS"])) + obs_SSn1-obs_SSn2) } colname_f <- grep("^F", colnames(tmp2), value = TRUE) anova_table <- cbind(tmp2[,c("num Df", "den Df", "MSE")], F = tmp2[,colname_f], es_df, "Pr(>F)" = tmp2[,c("Pr(>F)")]) #browser() if (!MSE) anova_table$MSE <- NULL if (!intercept) if (row.names(anova_table)[1] == "(Intercept)") anova_table <- anova_table[-1,, drop = FALSE] # Correct for multiple comparisons if(is.null(p_adjust_method)) p_adjust_method <- ifelse(is.null(attr(object$anova_table, "p_adjust_method")), "none", attr(object$anova_table, "p_adjust_method")) anova_table[,"Pr(>F)"] <- p.adjust(anova_table[,"Pr(>F)"], method = p_adjust_method) class(anova_table) <- c("anova", "data.frame") p_adj_heading <- if(p_adjust_method != "none") paste0(", ", p_adjust_method, "-adjusted") else NULL attr(anova_table, "heading") <- c(paste0("Anova Table (Type ", attr(object, "type"), " tests", p_adj_heading, ")\n"), paste("Response:", attr(object, "dv"))) attr(anova_table, "p_adjust_method") <- p_adjust_method attr(anova_table, "es") <- es attr(anova_table, "correction") <- if(length(attr(object, "within")) > 0 && any( vapply(object$data$long[, names(attr(object, "within")), drop = FALSE], nlevels, 0) > 2)) correction else "none" attr(anova_table, "observed") <- if(!is.null(observed) & length(observed) > 0) observed else character(0) attr(anova_table, "incomplete_cases") <- attr(object, "incomplete_cases") attr(anova_table, "sig_symbols") <- if(!is.null(sig_symbols)) sig_symbols else afex_options("sig_symbols") anova_table } #' @rdname afex_aov-methods #' @method print afex_aov #' @importFrom stats symnum #' @export print.afex_aov <- function(x, ...) { out <- nice(x$anova_table, ...) print(out) invisible(out) } #' @rdname afex_aov-methods #' @method summary afex_aov #' @export summary.afex_aov <- function(object, ...) { if (inherits(object$Anova, "Anova.mlm")) { #if (class(object$Anova)[1] == "Anova.mlm") { if(attr(object$anova_table, "p_adjust_method") != "none") message("Note, results are NOT adjusted for multiple comparisons as requested\n(p_adjust_method = '", attr(object$anova_table, "p_adjust_method"), "')\nbecause the desired method of sphericity correction is unknown.\nFor adjusted p-values print the object (to see object$anova_table), or call\none of anova.afex_aov() or nice().") return(summary(object$Anova, multivariate = FALSE)) #} else if (class(object$Anova)[1] == "anova") { } else if (inherits(object$Anova, "anova")) { return(object$anova_table) } else stop("Non-supported object passed. Slot 'Anova' needs to be of class 'Anova.mlm' or 'anova'.") } #-------------------------------------------------------------- ### afex package - mixed objects ### # just need to provide an 'emmeans' method here #' @rdname afex_aov-methods ## @importFrom emmeans recover_data emm_basis #' @importFrom utils packageVersion ## @method recover.data afex_aov ## @export recover_data.afex_aov = function(object, ..., model = afex_options("emmeans_model")) { model <- match.arg(model, c("univariate", "multivariate")) if (model == "univariate" & is.null(object$aov)) { message("Substituting multivariate/lm model, as aov object missing.") model <- "multivariate" } if (model == "univariate") { emmeans::recover_data(object = object$aov, ...) } else if (model == "multivariate") { if (packageVersion("emmeans") < "1.1.2") stop("emmeans version >= 1.1.2 required for multivariate tests") out <- emmeans::recover_data(object$lm, ...) if (length(attr(object, "within")) > 0) { out$misc$ylevs <- rev(attr(object, "within")) } return(out) } } #' @rdname afex_aov-methods ## @method lsm.basis afex_aov ## @export emm_basis.afex_aov = function(object, trms, xlev, grid, ..., model = afex_options("emmeans_model")) { model <- match.arg(model, c("univariate", "multivariate")) if (model == "univariate" & is.null(object$aov)) { #message("Substituting multivariate/lm model, as aov object missing.") model <- "multivariate" } if (model == "univariate") { out <- emmeans::emm_basis(object$aov, trms, xlev, grid, ...) } else if (model == "multivariate") { out <- emmeans::emm_basis(object$lm, trms, xlev, grid, ...) if (length(attr(object, "within")) > 0) { out$misc$ylevs <- rev(attr(object, "within")) } } out$misc$tran = attr(object, "transf") return(out) } afex/R/mixed.R0000644000176200001440000015277313506224623012651 0ustar liggesusers#' p-values for fixed effects of mixed-model via lme4::lmer() #' #' @description Estimates mixed models with \pkg{lme4} and calculates p-values #' for all fixed effects. The default method \code{"KR"} (= Kenward-Roger) as #' well as \code{method="S"} (Satterthwaite) support LMMs and estimate the #' model with \code{\link[lmerTest]{lmer}} and then pass it to the #' \code{\link[lmerTest]{lmerTest}} \code{anova} method (or #' \code{\link[car]{Anova}}). The other methods (\code{"LRT"} = #' likelihood-ratio tests and \code{"PB"} = parametric bootstrap) support both #' LMMs (estimated via \code{\link[lme4]{lmer}}) and GLMMs (i.e., with #' \code{family} argument which invokes estimation via #' \code{\link[lme4]{glmer}}) and estimate a full model and restricted models #' in which the parameters corresponding to one effect (i.e., model term) are #' withhold (i.e., fixed to 0). Per default tests are based on Type 3 sums of #' squares. \code{print}, \code{nice}, \code{anova}, and \code{summary} #' methods for the returned object of class \code{"mixed"} are available. #' \code{summary} invokes the default \pkg{lme4} summary method and shows #' parameters instead of effects. #' #' \code{lmer_alt} is simply a wrapper for mixed that only returns the #' \code{"lmerModLmerTest"} or \code{"merMod"} object and correctly uses the #' \code{||} notation for removing correlations among factors. This function #' otherwise behaves like \code{g/lmer} (as for \code{mixed}, it calls #' \code{glmer} as soon as a \code{family} argument is present). Use #' \code{\link{afex_options}}\code{("lmer_function")} to set which function #' for estimation should be used. This option determines the class of the #' returned object (i.e., \code{"lmerModLmerTest"} or \code{"merMod"}). #' #' #' @param formula a formula describing the full mixed-model to be fitted. As #' this formula is passed to \code{lmer}, it needs at least one random term. #' @param data \code{data.frame} containing the data. Should have all the #' variables present in \code{fixed}, \code{random}, and \code{dv} as columns. #' @param type type of test on which effects are based. Default is to use type 3 #' tests, taken from \code{\link{afex_options}}. #' @param method character vector indicating which methods for obtaining #' p-values should be used: \code{"KR"} corresponds to the Kenward-Roger #' approximation for degrees of freedom (only LMMs), \code{"S"} corresponds to #' the Satterthwaite approximation for degrees of freedom (via #' \code{\link{lmerTest}}, only LMMs), \code{"PB"} calculates p-values based #' on parametric bootstrap, \code{"LRT"} calculates p-values via the #' likelihood ratio tests implemented in the \code{anova} method for #' \code{merMod} objects (only recommended for models with many [i.e., > 50] #' levels for the random factors). The default (currently \code{"KR"}) is #' taken from \code{\link{afex_options}}. For historical compatibility #' \code{"nested-KR"} is also supported which was the default KR-method in #' previous versions. #' @param per_parameter \code{character} vector specifying for which variable #' tests should be run for each parameter (instead for the overall effect). #' Can be useful e.g., for testing ordered factors. Uses \code{\link{grep}} #' for selecting parameters among the fixed effects so regular expressions #' (\code{\link{regex}}) are possible. See Examples. #' @param args_test \code{list} of arguments passed to the function calculating #' the p-values. See Details. #' @param test_intercept logical. Whether or not the intercept should also be #' fitted and tested for significance. Default is \code{FALSE}. Only relevant #' if \code{type = 3}. #' @param check_contrasts \code{logical}. Should contrasts be checked and (if #' necessary) changed to \code{"contr.sum"}? See Details. The default #' (\code{"TRUE"}) is taken from \code{\link{afex_options}}. #' @param expand_re logical. Should random effects terms be expanded (i.e., #' factors transformed into numerical variables) before fitting with #' \code{(g)lmer}? Allows to use "||" notation with factors. #' @param all_fit logical. Should \code{\link{all_fit}} be used to fit each #' model with each available optimization algorithm and the results that #' provided the best fit in each case be used? Warning: This can dramatically #' increase the optimization time. Adds two new attributes to the returned #' object designating which algorithm was selected and the log-likelihoods for #' each algorithm. Note that only warnings from the initial fit are emitted #' during fitting. The warnings of the chosen models are emitted when printing #' the returned object. #' @param set_data_arg \code{logical}. Should the data argument in the slot #' \code{call} of the \code{merMod} object returned from \code{lmer} be set to #' the passed data argument? If \code{FALSE} (currently the default) the name #' will be \code{data}. \code{TRUE} may be helpful when fitted objects are #' used afterwards (e.g., compared using \code{anova} or when using the #' \code{effects} package, see examples). \pkg{emmeans} functions appear to #' work better with \code{FALSE}. Default is given by #' afex_options("set_data_arg"). #' @param progress if \code{TRUE}, shows progress with a text progress bar and #' other status messages during estimation #' @param cl A vector identifying a cluster; used for distributing the #' estimation of the different models using several cores (if seveal models #' are calculated). See examples. If \code{ckeck_contrasts = TRUE}, mixed sets #' the current contrasts (\code{getOption("contrasts")}) at the nodes. Note #' this does \emph{not} distribute calculation of p-values (e.g., when using #' \code{method = "PB"}) across the cluster. Use \code{args_test} for this. #' @param return the default is to return an object of class \code{"mixed"}. #' \code{return = "merMod"} will skip the calculation of all submodels and #' p-values and simply return the full model estimated with \code{lmer} (note #' that somewhat unintuiviely, the returned object can either be of class #' \code{"lmerModLmerTest"} or of class \code{"merMod"}, depending on the #' value of \code{\link{afex_options}}\code{("lmer_function")}). Can be useful #' in combination with \code{expand_re = TRUE} which allows to use "||" with #' factors. \code{return = "data"} will not fit any models but just return the #' data that would have been used for estimating the model (note that the data #' is also part of the returned object). #' @param sig_symbols Character. What should be the symbols designating #' significance? When entering an vector with \code{length(sig.symbol) < 4} #' only those elements of the default (\code{c(" +", " *", " **", " ***")}) #' will be replaced. \code{sig_symbols = ""} will display the stars but not #' the \code{+}, \code{sig_symbols = rep("", 4)} will display no symbols. The #' default is given by \code{afex_options("sig_symbols")}. #' @param ... further arguments (such as \code{weights}, \code{family}, or #' \code{control}) passed to \code{\link{lmer}}/\code{\link{glmer}}. Note that #' additional data (e.g., \code{weights}) need to be passed fully and not only #' by name (e.g., \code{weights = df$weights} and not \code{weights = #' weights}). #' #' #' @return An object of class \code{"mixed"} (i.e., a list) with the following #' elements: #' #' \enumerate{ #' \item \code{anova_table} a data.frame containing the statistics returned #' from \code{\link[pbkrtest]{KRmodcomp}}. The \code{stat} column in this #' data.frame gives the value of the test statistic, an F-value for #' \code{method = "KR"} and a chi-square value for the other two methods. #' \item \code{full_model} the \code{"lmerModLmerTest"} or \code{"merMod"} #' object returned from estimating the full model. Use #' \code{\link{afex_options}}\code{("lmer_function")} for setting which #' function for estimation should be used. The possible options are #' \code{"lmerTest"} (the default returning an object of class #' \code{"lmerModLmerTest"}) and \code{"lme4"} returning an object of class #' (\code{"merMod"}). Note that in case a \code{family} argument is present #' an object of class \code{"glmerMod"} is always returned. #' \item \code{restricted_models} a list of \code{"g/lmerMod"} (or #' \code{"lmerModLmerTest"}) objects from estimating the restricted models #' (i.e., each model lacks the corresponding effect) #' \item \code{tests} a list of objects returned by the function for #' obtaining the p-values. #' \item \code{data} The data used for estimation (i.e., after excluding #' missing rows and applying expand_re if requested). #' \item \code{call} The matched call. #' } #' #' It also has the following attributes, \code{"type"} and \code{"method"}. And #' the attributes \code{"all_fit_selected"} and \code{"all_fit_logLik"} if #' \code{all_fit=TRUE}. #' #' Two similar methods exist for objects of class \code{"mixed"}: \code{print} #' and \code{anova}. They print a nice version of the \code{anova_table} element #' of the returned object (which is also invisibly returned). This methods omit #' some columns and nicely round the other columns. The following columns are #' always printed: #' \enumerate{ #' \item \code{Effect} name of effect #' \item \code{p.value} estimated p-value for the effect #' } #' #' For LMMs with \code{method="KR"} or \code{method="S"} the following further #' columns are returned (note: the Kenward-Roger correction does two separate #' things: (1) it computes an effective number for the denominator df; (2) it #' scales the statistic by a calculated amount, see also #' \url{http://stackoverflow.com/a/25612960/289572}): #' \enumerate{ #' \item \code{F} computed F statistic #' \item \code{ndf} numerator degrees of freedom (number of parameters used #' for the effect) #' \item \code{ddf} denominator degrees of freedom (effective residual #' degrees of freedom for testing the effect), computed from the #' Kenward-Roger correction using \code{pbkrtest::KRmodcomp} #' \item \code{F.scaling} scaling of F-statistic computing from Kenward-Roger #' approximation (only printed if \code{method="nested-KR"}) #' } #' #' For models with \code{method="LRT"} the following further columns are #' returned: #' \enumerate{ #' \item \code{df.large} degrees of freedom (i.e., estimated paramaters) for #' full model (i.e., model containing the corresponding effect) #' \item \code{df.small} degrees of freedom (i.e., estimated paramaters) for #' restricted model (i.e., model without the corresponding effect) #' \item \code{chisq} 2 times the difference in likelihood (obtained with #' \code{logLik}) between full and restricted model #' \item \code{df} difference in degrees of freedom between full and #' restricted model (p-value is based on these df). #' } #' #' For models with \code{method="PB"} the following further column is returned: #' \enumerate{ #' \item \code{stat} 2 times the difference in likelihood (obtained with #' \code{logLik}) between full and restricted model (i.e., a chi-square #' value). #' } #' #' Note that \code{anova} can also be called with additional mixed and/or #' \code{merMod} objects. In this casethe full models are passed on to #' \code{anova.merMod} (with \code{refit=FALSE}, which differs from the default #' of \code{anova.merMod}) which produces the known LRT tables. #' #' The \code{summary} method for objects of class \code{mixed} simply calls #' \code{\link{summary.merMod}} on the full model. #' #' If \code{return = "merMod"} (or when invoking \code{lmer_alt}), an object of #' class \code{"lmerModLmerTest"} or of class \code{"merMod"} (depending on the #' value of \code{\link{afex_options}}\code{("lmer_function")}), as returned #' from \code{g/lmer}, is returned. The default behavior is to return an object #' of class \code{"lmerModLmerTest"} estimated via \code{\link[lmerTest]{lmer}}. #' #'@details For an introduction to mixed-modeling for experimental designs see #' our chapter #' (\href{http://singmann.org/download/publications/singmann_kellen-introduction-mixed-models.pdf}{Singmann #' & Kellen, in press}) or Barr, Levy, Scheepers, & Tily (2013). Arguments for #' using the Kenward-Roger approximation for obtaining p-values are given by #' Judd, Westfall, and Kenny (2012). Further introductions to mixed-modeling #' for experimental designs are given by Baayen and colleagues (Baayen, 2008; #' Baayen, Davidson & Bates, 2008; Baayen & Milin, 2010). Specific #' recommendations on which random effects structure to specify for #' confirmatory tests can be found in Barr and colleagues (2013) and Barr #' (2013), but also see Bates et al. (2015). #' #' \subsection{p-value Calculations}{ #' #' When \code{method = "KR"} (the default, implemented via #' \code{\link[pbkrtest]{KRmodcomp}}), the Kenward-Roger approximation for #' degrees-of-freedom is calculated using \code{\link[lmerTest]{lmerTest}} (if #' \code{test_intercept=FALSE}) or \code{\link[car]{Anova}} (if #' \code{test_intercept=TRUE}), which is only applicable to linear-mixed models #' (LMMs). The test statistic in the output is an F-value (\code{F}). A similar #' method that requires less RAM is \code{method = "S"} which calculates the #' Satterthwaite approximation for degrees-of-freedom via #' \code{\link[lmerTest]{lmerTest}} and is also only applicable to LMMs. #' \code{method = "KR"} or \code{method = "S"} provide the best control for #' Type 1 errors for LMMs (Luke, 2017). #' #' \code{method = "PB"} calculates p-values using parametric bootstrap using #' \code{\link[pbkrtest]{PBmodcomp}}. This can be used for linear and also #' generalized linear mixed models (GLMMs) by specifying a #' \code{\link[stats]{family}} argument to \code{mixed}. Note that you should #' specify further arguments to \code{PBmodcomp} via \code{args_test}, #' especially \code{nsim} (the number of simulations to form the reference #' distribution) or \code{cl} (for using multiple cores). For other arguments #' see \code{\link[pbkrtest]{PBmodcomp}}. Note that \code{REML} (argument to #' \code{[g]lmer}) will be set to \code{FALSE} if method is \code{PB}. #' #' \code{method = "LRT"} calculates p-values via likelihood ratio tests #' implemented in the \code{anova} method for \code{"merMod"} objects. This is #' the method recommended by Barr et al. (2013; which did not test the other #' methods implemented here). Using likelihood ratio tests is only recommended #' for models with many levels for the random effects (> 50), but can be pretty #' helpful in case the other methods fail (due to memory and/or time #' limitations). The #' \href{http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html}{lme4 faq} also #' recommends the other methods over likelihood ratio tests. } #' #' \subsection{Implementation Details}{ #' #' For methods \code{"KR"} and \code{"S"} type 3 and 2 tests are implemented as #' in \code{\link[car]{Anova}}. #' #' For all other methods, type 3 tests are obtained by comparing a model in #' which only the tested effect is excluded with the full model (containing all #' effects). For method \code{"nested-KR"} (which was the default in previous #' versions) this corresponds to the (type 3) Wald tests given by #' \code{car::Anova} for \code{"lmerMod"} models. The submodels in which the #' tested effect is excluded are obtained by manually creating a model matrix #' which is then fitted in \code{"lme4"}. #' #' Type 2 tests are truly sequential. They are obtained by comparing a model in #' which the tested effect and all higher oder effect (e.g., all three-way #' interactions for testing a two-way interaction) are excluded with a model in #' which only effects up to the order of the tested effect are present and all #' higher order effects absent. In other words, there are multiple full models, #' one for each order of effects. Consequently, the results for lower order #' effects are identical of whether or not higher order effects are part of the #' model or not. This latter feature is not consistent with classical ANOVA #' type 2 tests but a consequence of the sequential tests (and #' \href{https://stat.ethz.ch/pipermail/r-sig-mixed-models/2012q3/018992.html}{I #' didn't find a better way} of implementing the Type 2 tests). This #' \strong{does not} correspond to the (type 2) Wald test reported by #' \code{car::Anova}. #' #' If \code{check_contrasts = TRUE}, contrasts will be set to #' \code{"contr.sum"} for all factors in the formula if default contrasts are #' not equal to \code{"contr.sum"} or \code{attrib(factor, "contrasts") != #' "contr.sum"}. Furthermore, the current contrasts (obtained via #' \code{getOption("contrasts")}) will be set at the cluster nodes if \code{cl} #' is not \code{NULL}. } #' #' \subsection{Expand Random Effects}{ \code{expand_re = TRUE} allows to expand #' the random effects structure before passing it to \code{lmer}. This allows #' to disable estimation of correlation among random effects for random effects #' term containing factors using the \code{||} notation which may aid in #' achieving model convergence (see Bates et al., 2015). This is achieved by #' first creating a model matrix for each random effects term individually, #' rename and append the so created columns to the data that will be fitted, #' replace the actual random effects term with the so created variables #' (concatenated with +), and then fit the model. The variables are renamed by #' prepending all variables with rei (where i is the number of the random #' effects term) and replacing ":" with "_by_". #' #' \code{lmer_alt} is simply a wrapper for \code{mixed} that is intended to #' behave like \code{lmer} (or \code{glmer} if a \code{family} argument is #' present), but also allows the use of \code{||} with factors (by always using #' \code{expand_re = TRUE}). This means that \code{lmer_alt} per default does #' not enforce a specific contrast on factors and only returns the #' \code{"lmerModLmerTest"} or \code{"merMod"} object without calculating any #' additional models or p-values (this is achieved by setting \code{return = #' "merMod"}). Note that it most likely differs from \code{g/lmer} in how it #' handles missing values so it is recommended to only pass data without #' missing values to it! #' #' One consequence of using \code{expand_re = TRUE} is that the data that is #' fitted will not be the same as the passed data.frame which can lead to #' problems with e.g., the \code{predict} method. However, the actual data used #' for fitting is also returned as part of the \code{mixed} object so can be #' used from there. Note that the \code{set_data_arg} can be used to change #' whether the \code{data} argument in the call to \code{g/lmer} is set to #' \code{data} (the default) or the name of the data argument passed by the #' user. } #' #' @note When \code{method = "KR"}, obtaining p-values is known to crash due too #' insufficient memory or other computational limitations (especially with #' complex random effects structures). In these cases, the other methods #' should be used. The RAM demand is a problem especially on 32 bit Windows #' which only supports up to 2 or 3GB RAM (see #' \href{https://CRAN.R-project.org/bin/windows/base/rw-FAQ.html}{R Windows #' FAQ}). Then it is probably a good idea to use methods "S", "LRT", or "PB". #' #' \code{"mixed"} will throw a message if numerical variables are not centered #' on 0, as main effects (of other variables then the numeric one) can be hard #' to interpret if numerical variables appear in interactions. See Dalal & #' Zickar (2012). #' #' Per default \code{mixed} uses \code{\link[lmerTest]{lmer}}, this can be #' changed to \code{\link[lme4]{lmer}} by calling: #' \code{afex_options(lmer_function = "lme4")} #' #' Formulas longer than 500 characters will most likely fail due to the use of #' \code{\link{deparse}}. #' #' Please report bugs or unexpected behavior by opening a guthub issue: #' \url{https://github.com/singmann/afex/issues} #' #' @author Henrik Singmann with contributions from #' \href{http://stackoverflow.com/q/11335923/289572}{Ben Bolker and Joshua #' Wiley}. #' #' @seealso \code{\link{aov_ez}} and \code{\link{aov_car}} for convenience #' functions to analyze experimental deisgns with classical ANOVA or ANCOVA #' wrapping \code{\link[car]{Anova}}. #' #' see the following for the data sets from Maxwell and Delaney (2004) used #' and more examples: \code{\link{md_15.1}}, \code{\link{md_16.1}}, and #' \code{\link{md_16.4}}. #' #' @references Baayen, R. H. (2008). \emph{Analyzing linguistic data: a #' practical introduction to statistics using R}. Cambridge, UK; New York: #' Cambridge University Press. #' #' Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects #' modeling with crossed random effects for subjects and items. \emph{Journal #' of Memory and Language}, 59(4), 390-412. doi:10.1016/j.jml.2007.12.005 #' #' Baayen, R. H., & Milin, P. (2010). Analyzing Reaction Times. #' \emph{International Journal of Psychological Research}, 3(2), 12-28. #' #' Barr, D. J. (2013). Random effects structure for testing interactions in #' linear mixed-effects models. \emph{Frontiers in Quantitative Psychology and #' Measurement}, 328. doi:10.3389/fpsyg.2013.00328 #' #' Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects #' structure for confirmatory hypothesis testing: Keep it maximal. #' \emph{Journal of Memory and Language}, 68(3), 255-278. #' doi:10.1016/j.jml.2012.11.001 #' #' Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015). #' \emph{Parsimonious Mixed Models}. arXiv:1506.04967 [stat]. Retrieved from #' \url{http://arxiv.org/abs/1506.04967} #' #' Dalal, D. K., & Zickar, M. J. (2012). Some Common Myths About Centering #' Predictor Variables in Moderated Multiple Regression and Polynomial #' Regression. \emph{Organizational Research Methods}, 15(3), 339-362. #' doi:10.1177/1094428111430540 #' #' Judd, C. M., Westfall, J., & Kenny, D. A. (2012). Treating stimuli as a #' random factor in social psychology: A new and comprehensive solution to a #' pervasive but largely ignored problem. \emph{Journal of Personality and #' Social Psychology}, 103(1), 54-69. doi:10.1037/a0028347 #' #' Luke, S. (2017). Evaluating significance in linear mixed-effects models in #' R. \emph{Behavior Research Methods}. #' \url{https://doi.org/10.3758/s13428-016-0809-y} #' #' Maxwell, S. E., & Delaney, H. D. (2004). \emph{Designing experiments and #' analyzing data: a model-comparisons perspective.} Mahwah, N.J.: Lawrence #' Erlbaum Associates. #' #' ## @import pbkrtest #' @importFrom lme4 glmer nobars getME isREML #' @importFrom parallel clusterCall clusterExport clusterEvalQ clusterApplyLB #' @importFrom stats logLik terms as.formula contrasts<- model.matrix model.frame anova #' @importFrom methods is #' @encoding UTF-8 #' #' @example examples/examples.mixed.R #' #' @export mixed <- function(formula, data, type = afex_options("type"), method = afex_options("method_mixed"), per_parameter = NULL, args_test = list(), test_intercept = FALSE, check_contrasts = afex_options("check_contrasts"), expand_re = FALSE, all_fit = FALSE, set_data_arg = afex_options("set_data_arg"), progress = TRUE, cl = NULL, return = "mixed", sig_symbols = afex_options("sig_symbols"), ...) { dots <- list(...) data <- as.data.frame(data) # adding droplevels() here seems to lead to problems # with factors that have contrasts associated with it. ### deprercate old argument names: if("per.parameter" %in% names(dots)) { warn_deprecated_arg("per.parameter", "per_parameter") per_parameter <- dots$per.parameter } if("args.test" %in% names(dots)) { warn_deprecated_arg("args.test", "args_test") args_test <- dots$args.test } if("test.intercept" %in% names(dots)) { warn_deprecated_arg("test.intercept", "test_intercept") test_intercept <- dots$test.intercept } if("check.contrasts" %in% names(dots)) { warn_deprecated_arg("check.contrasts", "check_contrasts") check_contrasts <- dots$check.contrasts } if("set.data.arg" %in% names(dots)) { warn_deprecated_arg("set.data.arg", "set_data_arg") set_data_arg <- dots$set.data.arg } if("sig.symbols" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("sig.symbols", "sig_symbols") sig_symbols <- dots$sig.symbols } ## real function begins: vars.to.check <- all.vars(formula) if (check_contrasts) { #browser() resetted <- NULL for (i in vars.to.check) { if (is.character(data[,i])) { data[,i] <- factor(data[,i]) } if (is.factor(data[,i])) { if (is.null(attr(data[,i], "contrasts")) & (options("contrasts")[[1]][1] != "contr.sum")) { contrasts(data[,i]) <- "contr.sum" resetted <- c(resetted, i) } else if (!is.null(attr(data[,i], "contrasts")) && attr(data[,i], "contrasts") != "contr.sum") { contrasts(data[,i]) <- "contr.sum" resetted <- c(resetted, i) } } } if (!is.null(resetted)) message(paste0("Contrasts set to contr.sum for the following variables: ", paste0(resetted, collapse=", "))) } method <- match.arg(method, c("KR", "S", "PB", "LRT", "nested-KR", "F"), several.ok=FALSE) #################### ### Part I: prepare fitting (i.e., obtain model info, check model, ...) #################### mc <- match.call() formula.f <- as.formula(formula) if (!inherits(formula, "formula")) message("Formula (the first argument) converted to formula.") dv <- as.character(formula.f)[[2]] all.terms <- attr(terms(formula.f), "term.labels") effect.order <- attr(terms(formula.f), "order") effect.order <- effect.order[!grepl("\\|", all.terms)] max.effect.order <- max(effect.order) random <- paste0(paste0("(", all.terms[grepl("\\|", all.terms)], ")"), collapse = " + ") rh2 <- nobars(formula.f) rh2[[2]] <- NULL m.matrix <- model.matrix(rh2, data = data) fixed.effects <- attr(terms(rh2, data = data), "term.labels") mapping <- attr(m.matrix, "assign") fixed.vars <- all.vars(rh2) # check for missing values in variables used: if (nrow(m.matrix) != nrow(data)) { data <- model.frame( as.formula(paste0(vars.to.check[1], "~", paste0(vars.to.check[-1], collapse = "+"))), data = data) m.matrix <- model.matrix(rh2, data = data) warning(paste0("Due to missing values, reduced number of observations to ", nrow(data))) if(set_data_arg) { warning("Due to missing values, set_data_arg set to FALSE.") set_data_arg <- FALSE } } # check if numerical variables are centered c.ns <- fixed.vars[vapply(data[, fixed.vars, drop = FALSE], is.numeric, TRUE)] if (length(c.ns) > 0) { non.null <- c.ns[!abs(vapply(data[, c.ns, drop = FALSE], mean, 0)) < .Machine$double.eps ^ 0.5] if (length(non.null) > 0) message(paste0("Numerical variables NOT centered on 0: ", paste0(non.null, collapse = ", "), "\nIf in interactions, interpretation of lower order", " (e.g., main) effects difficult.")) } if (expand_re) { expand_re_out <- expand_re_fun(all.terms = all.terms, data = data) data <- expand_re_out$data random <- expand_re_out$random } if (return == "data") return(data) #################### ### Part II: obtain the lmer fits #################### ## Part IIa: prepare formulas mf <- mc[!names(mc) %in% c("type", "method", "args.test", "args_test", "progress", "check.contrasts", "check_contrasts", "per.parameter", "per_parameter", "cl", "test.intercept", "test_intercept","expand_re", "return", "all_fit", "sig_symbols", "sig.symbols", "set_data_arg")] mf[["formula"]] <- as.formula(paste0(dv,deparse(rh2, width.cutoff = 500L),"+",random)) if ("family" %in% names(mf)) { mf[[1]] <- as.name("glmer") use_reml <- FALSE } else { if (afex_options("lmer_function") == "lmerTest") mf[[1]] <- quote(lmerTest::lmer) else if (afex_options("lmer_function") == "lme4") { if (!(return %in% c("merMod")) && method %in% c("KR", "S")) stop('afex_options("lmer_function") needs to be "lmerTest" for method="', method, '"', call. = FALSE) mf[[1]] <- quote(lme4::lmer) } else stop("value of afex_options('lmer_function') not supported.") use_reml <- TRUE } mf[["data"]] <- as.name("data") if ((method[1] %in% c("PB", "LRT")) & !("family" %in% names(mf))) { if ((!"REML" %in% names(mf)) || mf[["REML"]]) { message("REML argument to lmer() set to FALSE for method = 'PB' or 'LRT'") mf[["REML"]] <- FALSE use_reml <- FALSE } } if (return == "merMod") { out <- eval(mf) if(set_data_arg) out@call[["data"]] <- mc[["data"]] return(out) } if ("family" %in% names(mf)) { if (!(method[1] %in% c("LRT", "PB"))) stop("GLMMs can only be estimated with 'LRT' or 'PB'.") } ## do not calculate nested models for these methods: if (method[1] %in% c("KR", "S")) { if (progress) cat("Fitting one lmer() model. ") full_model <- eval(mf) if (all_fit) { all_fits <- suppressWarnings(all_fit(full_model, data = data, verbose = FALSE)) all_fits <- c(default = full_model, all_fits) tmp_ll <- vapply(all_fits, function(x) tryCatch(logLik(x), error = function(e) NA), 0) full_model <- all_fits[[which.max(tmp_ll)]] full_model@optinfo$logLik_other <- tmp_ll } fits <- NULL tests <- NULL anova_tab_addition <- NULL if (progress) cat("[DONE]\nCalculating p-values. ") if (method[1] == "KR") { #lmerTest_method <- if(method[1] == "KR") "Kenward-Roger" else "Satterthwaite" if (test_intercept) { anova_out <- car::Anova(full_model, type = type, test.statistic = "F") anova_table <- as.data.frame(anova_out) anova_table <- anova_table[, c("Df", "Df.res", "F", "Pr(>F)")] colnames(anova_table) <- c("num Df", "den Df", "F", "Pr(>F)") } else { anova_out <- lmerTest_anova(full_model, ddf = "Kenward-Roger", type = type) anova_table <- as.data.frame(anova_out) get <- c("NumDF", "DenDF", "F.value", "F value", "Pr(>F)") anova_table <- anova_table[, match(get, colnames(anova_table), nomatch = 0L)] colnames(anova_table) <- c("num Df", "den Df", "F", "Pr(>F)") } } else if (method[1] == "S") { if (test_intercept) warning("Cannot test intercept with Satterthwaite approximation.") anova_out <- lmerTest_anova(full_model, ddf = "Satterthwaite", type = type) anova_table <- as.data.frame(anova_out) if (!("Pr(>F)" %in% colnames(anova_table))) { colnames(anova_table)[c(1,4)] <- c("NumDF", "F.value") anova_table$DenDF <- NA_real_ anova_table$`Pr(>F)` <- NA_real_ } get <- c("NumDF", "DenDF", "F.value", "F value", "Pr(>F)") anova_table <- anova_table[, match(get, colnames(anova_table), nomatch = 0L)] colnames(anova_table) <- c("num Df", "den Df", "F", "Pr(>F)") } if (progress) cat("[DONE]\n") if(set_data_arg) full_model@call[["data"]] <- mc[["data"]] } else { ## do calculate nested models for the methods below ## prepare (g)lmer formulas: if (type == 3 | type == "III") { if (attr(terms(rh2, data = data), "intercept") == 1) fixed.effects <- c("(Intercept)", fixed.effects) # The next part alters the mapping of parameters to effects/variables if # per_parameter is not NULL (this does the complete magic). if (!is.null(per_parameter)) { fixed.to.change <- c() for (parameter in per_parameter) { fixed.to.change <- c(fixed.to.change, grep(parameter, fixed.effects)) } fixed.to.change <- fixed.effects[sort(unique(fixed.to.change))] if ("(Intercept)" %in% fixed.to.change) fixed.to.change <- fixed.to.change[-1] fixed.all <- dimnames(m.matrix)[[2]] #tf2 <- fixed.to.change[2] for (tf2 in fixed.to.change) { tf <- which(fixed.effects == tf2) fixed.lower <- fixed.effects[seq_len(tf-1)] fixed.upper <- if (tf < length(fixed.effects)) fixed.effects[(tf+1):length(fixed.effects)] else NULL fixed.effects <- c(fixed.lower, fixed.all[which(mapping == (tf-1))], fixed.upper) map.to.replace <- which(mapping == (tf-1)) map.lower <- mapping[seq_len(map.to.replace[1]-1)] map.upper <- if (max(map.to.replace) < length(mapping)) mapping[(map.to.replace[length(map.to.replace)]+1): length(mapping)] else NULL mapping <- c(map.lower, seq_along(map.to.replace) + map.lower[length(map.lower)], map.upper + length(map.to.replace)-1) } } # make formulas formulas <- vector("list", length(fixed.effects) + 1) formulas[[1]] <- mf[["formula"]] for (i in seq_along(fixed.effects)) { tmp.columns <- paste0(deparse(-which(mapping == (i-1))), collapse = "") formulas[[i+1]] <- as.formula(paste0(dv, "~ 0 + m.matrix[,", tmp.columns, "] +", random)) } names(formulas) <- c("full_model", fixed.effects) if (!test_intercept && fixed.effects[1] == "(Intercept)") { fixed.effects <- fixed.effects[-1] formulas[["(Intercept)"]] <- NULL } } else if (type == 2 | type == "II") { if (!is.null(per_parameter)) stop("per_parameter argument only implemented for Type 3 tests.") full_model.formulas <- vector("list", max.effect.order) submodel.formulas <- vector("list", length(fixed.effects)) full_model.formulas[[length(full_model.formulas)]] <- mf[["formula"]] for (c in seq_len(max.effect.order)) { if (c == max.effect.order) next tmp.columns <- paste0(deparse(-which(mapping %in% which(effect.order > c))), collapse = "") full_model.formulas[[c]] <- as.formula(paste0(dv, "~ 0 + m.matrix[,", tmp.columns, "] +", random)) } for (c in seq_along(fixed.effects)) { order.c <- effect.order[c] tmp.columns <- paste0(deparse(-which(mapping == (c) | mapping %in% if (order.c == max.effect.order) -1 else which(effect.order > order.c))), collapse = "") submodel.formulas[[c]] <- as.formula( paste0(dv, "~ 0 + m.matrix[,", tmp.columns, "] +", random)) } formulas <- c(full_model.formulas, submodel.formulas) } else stop('Only type 3 and type 2 tests implemented.') ## Part IIb: fit models # single core if (is.null(cl)) { if (progress) cat(paste0("Fitting ", length(formulas), " (g)lmer() models:\n[")) fits <- vector("list", length(formulas)) if (all_fit) all_fits <- vector("list", length(formulas)) for (i in seq_along(formulas)) { mf[["formula"]] <- formulas[[i]] fits[[i]] <- eval(mf) if (all_fit) { all_fits[[i]] <- suppressWarnings( all_fit(fits[[i]], data = data, verbose = FALSE)) all_fits[[i]] <- c(default = fits[[i]], all_fits[[i]]) tmp_ll <- vapply(all_fits[[i]], function(x) tryCatch(logLik(x), error = function(e) NA), 0) fits[[i]] <- all_fits[[i]][[which.max(tmp_ll)]] fits[[i]]@optinfo$logLik_other <- tmp_ll } if (progress) cat(".") } if (progress) cat("]\n") } else { # multicore eval.cl <- function(formula, m.call, progress, all_fit, data) { m.call[[2]] <- formula res <- eval(m.call) if (all_fit) { all_fits <- suppressWarnings(all_fit(res, data = data, verbose = FALSE)) all_fits <- c(default = res, all_fits) tmp_ll <- vapply(all_fits, function(x) tryCatch(logLik(x), error = function(e) NA), 0) res <- all_fits[[which.max(tmp_ll)]] res@optinfo$logLik_other <- tmp_ll } if (progress) cat(".") return(res) } if (progress) cat(paste0("Fitting ", length(formulas), " (g)lmer() models.\n")) junk <- clusterCall(cl = cl, "require", package = "afex", character.only = TRUE) if (check_contrasts) { curr.contrasts <- getOption("contrasts") clusterExport(cl = cl, "curr.contrasts", envir = sys.nframe()) junk <- clusterEvalQ(cl = cl, options(contrasts=curr.contrasts)) } if (progress) junk <- clusterEvalQ(cl = cl, cat("[")) fits <- clusterApplyLB(cl = cl, x = formulas, eval.cl, m.call = mf, progress = progress, all_fit=all_fit, data = data) if (progress) junk <- clusterEvalQ(cl = cl, cat("]")) } #################### ### Part IIb: likelihood checks and refitting (refitting is DISABLED for the time being!) #################### check_likelihood <- function(fits) { if (type == 3 | type == "III") { logLik_full <- as.numeric(logLik(fits[[1]])) logLik_restricted <- as.numeric(vapply(fits[2:length(fits)], logLik, 0)) if(any(logLik_restricted > logLik_full)) return(fixed.effects[logLik_restricted > logLik_full]) } else if (type == 2 | type == "II") { logLik_full <- as.numeric(vapply(fits[1:max.effect.order],logLik, 0)) logLik_restricted <- as.numeric(vapply(fits[(max.effect.order+1):length(fits)], logLik, 0)) warn_logLik <- c() for (c in seq_along(fixed.effects)) { order.c <- effect.order[c] if(logLik_restricted[[c]] > logLik_full[[order.c]]) warn_logLik <- c(warn_logLik, fixed.effects[c]) } if(length(warn_logLik)>0) return(warn_logLik) } return(TRUE) } # check for smaller likelihood of nested model and refit if test fails: if (FALSE) { if(!isTRUE(check_likelihood(fits))) { if (progress) cat("refitting...") refits <- lapply(fits, all_fit, verbose=FALSE, data = data) browser() str(fits[[1]], 2) fits[[1]]@call sapply(refits, function(x) sapply(x, function(y) tryCatch(as.numeric(logLik(y)), error = function(e) as.numeric(NA)))) fits <- lapply(refits, function(x) { tmp_llk <- vapply(x, function(y) tryCatch(logLik(y), error = function(e) as.numeric(NA)), 0) x[[which.min(tmp_llk)]] }) } } # check again and warn if(!isREML(fits[[1]]) & !isTRUE(check_likelihood(fits))) { warning(paste( "Following nested model(s) provide better fit than full model:", paste(check_likelihood(fits), collapse = ", "), "\n Results cannot be trusted.", "Try all_fit=TRUE or reduce random effect structure!")) } if(set_data_arg){ for (i in seq_along(fits)) { fits[[i]]@call[["data"]] <- mc[["data"]] } } ## prepare for p-values: if (type == 3 | type == "III") { full_model <- fits[[1]] fits <- fits[-1] } else if (type == 2 | type == "II") { full_model <- fits[1:max.effect.order] fits <- fits[(max.effect.order+1):length(fits)] } names(fits) <- fixed.effects #################### ### Part III: obtain p-values #################### ## obtain p-values: #browser() if (method[1] == "nested-KR") { if (progress) cat(paste0("Obtaining ", length(fixed.effects), " p-values:\n[")) tests <- vector("list", length(fixed.effects)) for (c in seq_along(fixed.effects)) { if (type == 3 | type == "III") tests[[c]] <- pbkrtest::KRmodcomp(full_model, fits[[c]]) else if (type == 2 | type == "II") { order.c <- effect.order[c] tests[[c]] <- pbkrtest::KRmodcomp(full_model[[order.c]], fits[[c]]) } if (progress) cat(".") } if (progress) cat("]\n") names(tests) <- fixed.effects anova_table <- data.frame( t(vapply(tests, function(x) unlist(x[["test"]][1,]), unlist(tests[[1]][["test"]][1,])))) rownames(anova_table) <- fixed.effects colnames(anova_table) <- c("F", "num Df", "den Df", "F.scaling", "Pr(>F)") anova_table <- anova_table[, c("num Df", "den Df", "F.scaling", "F", "Pr(>F)")] anova_tab_addition <- NULL } else if (method[1] == "PB") { if (progress) cat(paste0("Obtaining ", length(fixed.effects), " p-values:\n[")) tests <- vector("list", length(fixed.effects)) for (c in seq_along(fixed.effects)) { if (type == 3 | type == "III") tests[[c]] <- do.call(pbkrtest::PBmodcomp, args = c(largeModel = full_model, smallModel = fits[[c]], args_test)) else if (type == 2 | type == "II") { order.c <- effect.order[c] tests[[c]] <- do.call(pbkrtest::PBmodcomp, args = c(largeModel = full_model[[order.c]], smallModel = fits[[c]], args_test)) } if (progress) cat(".") } if (progress) cat("]\n") names(tests) <- fixed.effects anova_table <- data.frame(t(vapply(tests, function(x) unlist(x[["test"]][2,]), unlist(tests[[1]][["test"]][2,])))) anova_table <- anova_table[,-2] LRT <- vapply(tests, function(x) unlist(x[["test"]][1,]), unlist(tests[[1]][["test"]][1,])) row.names(LRT) <- paste0(row.names(LRT), ".LRT") anova_table <- cbind(anova_table, t(LRT)) rownames(anova_table) <- fixed.effects anova_table <- anova_table[, c("stat", "df.LRT", "p.value.LRT", "p.value")] colnames(anova_table) <- c("Chisq", "Chi Df", "Pr(>Chisq)", "Pr(>PB)") anova_tab_addition <- NULL } else if (method[1] == "LRT") { tests <- vector("list", length(fixed.effects)) for (c in seq_along(fixed.effects)) { if (type == 3 | type == "III") tests[[c]] <- anova(full_model, fits[[c]]) else if (type == 2 | type == "II") { order.c <- effect.order[c] tmpModel <- full_model[[order.c]] tests[[c]] <- anova(tmpModel, fits[[c]]) } } names(tests) <- fixed.effects df.large <- vapply(tests, function(x) x[["Df"]][2], 0) df.small <- vapply(tests, function(x) x[["Df"]][1], 0) chisq <- vapply(tests, function(x) x[["Chisq"]][2], 0) df <- vapply(tests, function(x) x[["Chi Df"]][2], 0) p.value <- vapply(tests, function(x) x[["Pr(>Chisq)"]][2], 0) anova_table <- data.frame(Df = df.small, Chisq = chisq, "Chi Df" = df, "Pr(>Chisq)"=p.value, stringsAsFactors = FALSE, check.names = FALSE) rownames(anova_table) <- fixed.effects if (type == 3 | type == "III") anova_tab_addition <- paste0("Df full model: ", df.large[1]) else anova_tab_addition <- paste0("Df full model(s): ", df.large) } else stop('Only methods "KR", "PB", "LRT", or "nested-KR" currently implemented.') } #################### ### Part IV: prepare output #################### class(anova_table) <- c("anova", "data.frame") attr(anova_table, "heading") <- c( paste0("Mixed Model Anova Table (Type ", type , " tests, ", method, "-method)\n"), paste0("Model: ", deparse(formula.f)), paste0("Data: " ,mc[["data"]]), anova_tab_addition ) attr(anova_table, "sig_symbols") <- sig_symbols list.out <- list( anova_table = anova_table, full_model = full_model, restricted_models = fits, tests = tests, data = data, call = mc) #, type = type, method = method[[1]] class(list.out) <- "mixed" attr(list.out, "type") <- type attr(list.out, "method") <- method if (all_fit) { attr(list.out, "all_fit_selected") <- rapply(c(full_model = list.out$full_model, list.out$restricted_models), function(x) x@optinfo$optimizer, how = "unlist") attr(list.out, "all_fit_logLik") <- as.data.frame( rapply(c(full_model = list.out$full_model, list.out$restricted_models), function(x) x@optinfo$logLik_other, how = "replace")) } list.out } ## expand random effects sructure expand_re_fun <- function(all.terms, data) { random_parts <- paste0(all.terms[grepl("\\|", all.terms)]) which_random_double_bars <- grepl("\\|\\|", random_parts) random_units <- sub("^.+\\|\\s+", "", random_parts) tmp_random <- lapply(sub("\\|.+$", "", random_parts), function(x) as.formula(paste0("~", x))) tmp_model.matrix <- vector("list", length(random_parts)) re_contains_intercept <- rep(FALSE, length(random_parts)) new_random <- vector("character", length(random_parts)) for (i in seq_along(random_parts)) { tmp_model.matrix[[i]] <- model.matrix(tmp_random[[i]], data = data) if (ncol(tmp_model.matrix[[i]]) == 0) stop("Invalid random effects term, e.g., (0|id)") if (colnames(tmp_model.matrix[[i]])[1] == "(Intercept)") { tmp_model.matrix[[i]] <- tmp_model.matrix[[i]][,-1, drop = FALSE] re_contains_intercept[i] <- TRUE } if (ncol(tmp_model.matrix[[i]]) > 0) { colnames(tmp_model.matrix[[i]]) <- paste0("re", i, ".", gsub(":", "_by_", colnames(tmp_model.matrix[[i]]))) colnames(tmp_model.matrix[[i]]) <- make.names(colnames(tmp_model.matrix[[i]])) new_random[i] <- paste0("(", as.numeric(re_contains_intercept[i]), "+", paste0(colnames(tmp_model.matrix[[i]]), collapse = "+"), if (which_random_double_bars[i]) "||" else "|", random_units[i], ")") } else { new_random[i] <- paste0("(", as.numeric(re_contains_intercept[i]), if (which_random_double_bars[i]) "||" else "|", random_units[i], ")") } } data <- cbind(data, as.data.frame(do.call(cbind, tmp_model.matrix))) random <- paste0(new_random, collapse = "+") return(list(data = data, random = random)) } get_mixed_warnings <- function(x) { full_model_name <- names(x)[[2]] ntry <- function(x) tryCatch(x, error = function(e) NULL) if (is.list(x$full)) { warnings1 <- c(full = lapply(x[[2]], function(y) y@optinfo$warnings), lapply(x[[3]], function(y) y@optinfo$warnings)) warnings2 <- c(full = lapply(x[[2]], function(y) ntry(y@optinfo$conv$lme4$messages)), lapply(x[[3]], function(y) ntry(y@optinfo$conv$lme4$messages))) } else { warnings1 <- c(full = list(x[[full_model_name]]@optinfo$warnings), lapply(x[[3]], function(y) y@optinfo$warnings)) warnings2 <- c(full = list(ntry(x[[full_model_name]]@optinfo$conv$lme4$messages)), lapply(x[[3]], function(y) ntry(y@optinfo$conv$lme4$messages))) } warnings <- mapply(function(x, y) c(unlist(x), y), warnings1, warnings2, SIMPLIFY=FALSE) warn <- vapply(warnings, function(y) !length(y)==0, NA) for (i in names(warn)[warn]) warning("lme4 reported (at least) the following warnings for '", i, "':\n * ", paste(warnings[[i]], collapse = "\n * "), call. = FALSE) } check_likelihood <- function(object) { full_model_name <- names(object)[[2]] restricted_models_name <- names(object)[[3]] if (is.null(attr(object, "type"))) { attr(object, "type") <- object$type } if (attr(object, "type") == 3 | attr(object, "type") == "III") { logLik_full <- as.numeric(logLik(object[[full_model_name]])) logLik_restricted <- as.numeric(vapply(object[[restricted_models_name]], logLik, 0)) if(any(logLik_restricted > logLik_full)) return(rownames(object$anova_table)[logLik_restricted > logLik_full]) } else if (attr(object, "type") == 2 | attr(object, "type") == "II") { NULL } return(TRUE) } #' @rdname mixed #' @export lmer_alt <- function(formula, data, check_contrasts = FALSE, ...) { mc <- match.call() #assign(all.vars(mc[["data"]]), data) mc[[1]] <- as.name("mixed") mc[["return"]] <- "merMod" mc[["expand_re"]] <- TRUE mc[["progress"]] <- FALSE mc[["check_contrasts"]] <- check_contrasts #browser() eval(mc) } #' @method print mixed #' @export print.mixed <- function(x, ...) { full_model_name <- names(x)[[2]] try(if(!isREML(x[[full_model_name]]) && !isTRUE(check_likelihood(x))) warning(paste("Following nested model(s) provide better fit than full model:", paste(check_likelihood(x), collapse = ", "), "\n Results cannot be trusted. Try all_fit=TRUE!"), call. = FALSE), silent = TRUE) get_mixed_warnings(x) tmp <- nice.mixed(x, ...) print(tmp) invisible(tmp) } #anova.mixed <- #' @method summary mixed #' @export summary.mixed <- function(object, ...) { if ("full_model" %in% names(object)) summary(object = if (length(object[["full_model"]]) == 1) object[["full_model"]] else object[["full_model"]][[length(object[["full_model"]])]], ...) else if("full.model" %in% names(object)) summary(object = if (length(object[["full.model"]]) == 1) object[["full.model"]] else object[["full.model"]][[length(object[["full.model"]])]], ...) } #' @method anova mixed #' @export anova.mixed <- function(object, ..., sig_symbols = attr(object$anova_table, "sig_symbols"), refit = FALSE) { mCall <- match.call(expand.dots = TRUE) full_model_name <- names(object)[[2]] dots <- list(...) modp <- (as.logical(vapply(dots, is, NA, "merMod")) | as.logical(vapply(dots, is, NA, "lm")) | as.logical(vapply(dots, is, NA, "mixed")) ) if (any(modp)) { model.names <- c(deparse(mCall[["object"]]), vapply(which(modp), function(x) deparse(mCall[[x+2]]), "")) for (i in which(as.logical(vapply(dots, is, NA, "mixed")))) dots[[i]] <- dots[[i]][[full_model_name]] anova_table <- do.call(anova, args = c(object = object[[full_model_name]], dots, model.names = list(model.names), refit = refit)) } else { try(if(!isREML(object[[full_model_name]]) && !isTRUE(check_likelihood(object))) warning( paste("Following nested model(s) provide better fit than full model:", paste(check_likelihood(object), collapse = ", "), "\n Results cannot be trusted. Try all_fit=TRUE!"), call. = FALSE), silent=TRUE) get_mixed_warnings(object) anova_table <- object$anova_table } attr(anova_table, "sig_symbols") <- if (!is.null(sig_symbols)) sig_symbols else afex_options("sig_symbols") anova_table } ## support for emmeans for mixed objects: ## @importFrom emmeans recover_data emm_basis ## @method recover_data mixed ## @export recover_data.mixed <- function(object, ...) { full_model_name <- names(object)[[2]] if (inherits(object[[full_model_name]], "merMod") | is_lmerTest_class(object[[full_model_name]])) { obj_use <- object[[full_model_name]] } else if (inherits(object[[full_model_name]][[1]], "merMod") | is_lmerTest_class(object[[full_model_name]][[1]])) { message("emmeans are based on full model which includes all effects.") obj_use <- object[[full_model_name]][[length(object[[full_model_name]])]] } else { stop("Cannot find 'merMod' object in ", full_model_name, " slot.") } if (is_lmerTest_class(obj_use)) { class(obj_use) <- "lmerMod" } emmeans::recover_data(obj_use, ...) } ## @method lsm_basis mixed ## @export emm_basis.mixed <- function(object, trms, xlev, grid, ...) { full_model_name <- names(object)[[2]] if (inherits(object[[full_model_name]], "merMod") | is_lmerTest_class(object[[full_model_name]])) { obj_use <- object[[full_model_name]] } else if (inherits(object[[full_model_name]][[1]], "merMod") | is_lmerTest_class(object[[full_model_name]][[1]])) { obj_use <- object[[full_model_name]][[length(object[[full_model_name]])]] } else { stop("Cannot find 'merMod' object in ", full_model_name, " slot.") } if (is_lmerTest_class(obj_use)) { class(obj_use) <- "lmerMod" } emmeans::emm_basis(obj_use, trms, xlev, grid, ...) } afex/R/md_16.1-data.R0000644000176200001440000000350613351525342013504 0ustar liggesusers#' Data 16.1 / 10.9 from Maxwell & Delaney #' #' Hypothetical Reaction Time Data for 2 x 3 Perceptual Experiment: Example data for chapter 12 of Maaxwell and Delaney (2004, Table 12.1, p. 574) in long format. Has two within.subjects factors: angle and noise. #' #' Description from pp. 829: #' #' As brief background, the goal of the study here is to examine the extent to which female and male clinical psychology graduate student trainees may assign different severity ratings to clients at initial intake. Three female and 3 male graduate students are randomly selected to participate and each is randomly assigned four clients with whom to do an intake interview, after which each clinical trainee assigns a severity rating to each client, producing the data shown in Table 16.1. #' #' Note that I changed the labeling of the id slightly, so that they are now labeled from 1 to 6. Furthermore, I changed the contrasts of sex to \code{contr.treatment} to replicate the exact results of Table 16.3 (p. 837). #' #' @docType data #' @keywords dataset #' @name md_16.1 #' @usage md_16.1 #' @format A data.frame with 24 rows and 3 variables. #' @source Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates. p. 574 #' #' @examples #' ### replicate results from Table 16.3 (Maxwell & Delaney, 2004, p. 837) #' data(md_16.1) #' #' # original results need treatment contrasts: #' (mixed1_orig <- mixed(severity ~ sex + (1|id), md_16.1, check.contrasts=FALSE)) #' summary(mixed1_orig$full.model) #' #' # p-values stay the same with afex default contrasts (contr.sum), #' # but estimates and t-values for the fixed effects parameters change. #' (mixed1 <- mixed(severity ~ sex + (1|id), md_16.1)) #' summary(mixed1$full.model) #' #' @encoding UTF-8 #' NULL afex/R/nice.R0000644000176200001440000004030513432553127012446 0ustar liggesusers#' Make nice ANOVA table for printing. #' #' This generic function produces a nice ANOVA table for printing for objects of #' class. \code{nice_anova} takes an object from \code{\link[car]{Anova}} #' possible created by the convenience functions \code{\link{aov_ez}} or #' \code{\link{aov_car}}. When within-subject factors are present, either #' sphericity corrected or uncorrected degrees of freedom can be reported. #' #' #' @param object,x An object of class \code{"afex_aov"} (see #' \code{\link{aov_car}}) or of class \code{"mixed"} (see \code{\link{mixed}}) #' as returned from the \pkg{afex} functions. Alternatively, an object of #' class \code{"Anova.mlm"} or \code{"anova"} as returned from #' \code{\link[car]{Anova}}. #' @param es Effect Size to be reported. The default is given by #' \code{afex_options("es_aov")}, which is initially set to \code{"ges"} #' (i.e., reporting generalized eta-squared, see details). Also supported is #' partial eta-squared (\code{"pes"}) or \code{"none"}. #' @param observed character vector referring to the observed (i.e., non #' manipulated) variables/effects in the design. Important for calculation of #' generalized eta-squared (ignored if \code{es} is not \code{"ges"}), see #' details. #' @param correction Character. Which sphericity correction of the degrees of #' freedom should be reported for the within-subject factors. The default is #' given by \code{afex_options("correction_aov")}, which is initially set to #' \code{"GG"} corresponding to the Greenhouse-Geisser correction. Possible #' values are \code{"GG"}, \code{"HF"} (i.e., Hyunh-Feldt correction), and #' \code{"none"} (i.e., no correction). #' @param p_adjust_method \code{character} indicating if p-values for individual #' effects should be adjusted for multiple comparisons (see #' \link[stats]{p.adjust} and details). The default \code{NULL} corresponds to #' no adjustment. #' @param sig_symbols Character. What should be the symbols designating #' significance? When entering an vector with \code{length(sig.symbol) < 4} #' only those elements of the default (\code{c(" +", " *", " **", " ***")}) #' will be replaced. \code{sig_symbols = ""} will display the stars but not #' the \code{+}, \code{sig_symbols = rep("", 4)} will display no symbols. The #' default is given by \code{afex_options("sig_symbols")}. #' @param MSE logical. Should the column containing the Mean Sqaured Error (MSE) #' be displayed? Default is \code{TRUE}. #' @param intercept logical. Should intercept (if present) be included in the #' ANOVA table? Default is \code{FALSE} which hides the intercept. #' @param sig.symbols deprecated argument, only for backwards compatibility, use #' \code{"sig_symbols"} instead. #' @param ... currently ignored. #' #' @return A \code{data.frame} of class \code{nice_table} with the ANOVA table #' consisting of characters. The columns that are always present are: #' \code{Effect}, \code{df} (degrees of freedom), \code{F}, and \code{p}. #' #' \code{ges} contains the generalized eta-squared effect size measure #' (Bakeman, 2005), \code{pes} contains partial eta-squared (if requested). #' #' @details The returned \code{data.frame} is print-ready when adding to a #' document with proper methods. Either directly via \pkg{knitr} or similar #' approaches such as via package \pkg{xtable} (nowadays \pkg{knitr} is #' probably the best approach, see \href{http://yihui.name/knitr/}{here}). #' \pkg{xtable} converts a \code{data.frame} into LaTeX code with many #' possible options (e.g., allowing for \code{"longtable"} or #' \code{"sidewaystable"}), see \code{\link[xtable]{xtable}} and #' \code{\link[xtable]{print.xtable}}. See Examples. #' #' Conversion functions to other formats (such as HTML, ODF, or Word) can be #' found at the #' \href{https://CRAN.R-project.org/view=ReproducibleResearch}{Reproducible #' Research Task View}. #' #' The default reports generalized eta squared (Olejnik & Algina, 2003), the #' "recommended effect size for repeated measured designs" (Bakeman, 2005). #' Note that it is important that all measured variables (as opposed to #' experimentally manipulated variables), such as e.g., age, gender, weight, #' ..., must be declared via \code{observed} to obtain the correct effect size #' estimate. Partial eta squared (\code{"pes"}) does not require this. #' #' Exploratory ANOVA, for which no detailed hypotheses have been specified a #' priori, harbor a multiple comparison problem (Cramer et al., 2015). To #' avoid an inflation of familywise Type I error rate, results need to be #' corrected for multiple comparisons using \code{p_adjust_method}. #' \code{p_adjust_method} defaults to the method specified in the call to #' \code{\link{aov_car}} in \code{anova_table}. If no method was specified and #' \code{p_adjust_method = NULL} p-values are not adjusted. #' #' @seealso \code{\link{aov_ez}} and \code{\link{aov_car}} are the convenience #' functions to create the object appropriate for \code{nice_anova}. #' #' @author The code for calculating generalized eta-squared was written by Mike #' Lawrence.\cr Everything else was written by Henrik Singmann. #' #' @references Bakeman, R. (2005). Recommended effect size statistics for #' repeated measures designs. \emph{Behavior Research Methods}, 37(3), #' 379-384. doi:10.3758/BF03192707 #' #' Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., #' Wetzels, R., Grasman, R. P. P. P., ... Wagenmakers, E.-J. (2015). Hidden #' multiplicity in exploratory multiway ANOVA: Prevalence and remedies. #' \emph{Psychonomic Bulletin & Review}, 1-8. #' doi:\href{http://doi.org/10.3758/s13423-015-0913-5}{10.3758/s13423-015-0913-5} #' #' #' Olejnik, S., & Algina, J. (2003). Generalized Eta and Omega Squared #' Statistics: Measures of Effect Size for Some Common Research Designs. #' \emph{Psychological Methods}, 8(4), 434-447. doi:10.1037/1082-989X.8.4.434 #' #' @name nice #' @importFrom stats anova #' @encoding UTF-8 #' #' @example examples/examples.nice.R #' #' @export nice nice <- function(object, ...) UseMethod("nice", object) #' @rdname nice #' @method nice afex_aov #' @export nice.afex_aov <- function(object, es = attr(object$anova_table, "es"), observed = attr(object$anova_table, "observed"), correction = attr(object$anova_table, "correction"), MSE = NULL, intercept = NULL, p_adjust_method = attr(object$anova_table, "p_adjust_method"), sig_symbols = attr(object$anova_table, "sig_symbols"), ...) { # if(is.null(es)) { # Defaults to afex_options("es") because of default set in anova.afex_aov # es <- c("pes", "ges")[c("pes", "ges") %in% colnames(object$anova_table)] # } dots <- list(...) if(is.null(MSE)) { # Defaults to TRUE because of default set in anova.afex_aov MSE <- "MSE" %in% colnames(object$anova_table) } if(is.null(intercept)) { # Defaults to FALSE because of default set in anova.afex_aov intercept <- "(Intercept)" %in% rownames(object$anova_table) } if("sig.symbols" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("sig.symbols", "sig_symbols") sig_symbols <- dots$sig.symbols } if("p.adjust.method" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("p.adjust.method", "p_adjust_method") p_adjust_method <- dots$p.adjust.method } anova_table <- as.data.frame(anova(object, es = es, observed = observed, correction = correction, MSE = MSE, intercept = intercept, p_adjust_method = p_adjust_method)) nice.anova(anova_table, MSE = MSE, intercept = intercept, sig_symbols = sig_symbols) } #' @rdname nice #' @method nice anova #' @export nice.anova <- function(object, MSE = NULL, intercept = NULL, sig_symbols = attr(object, "sig_symbols"), sig.symbols, ...) { dots <- list(...) if(is.null(MSE)) { # Defaults to TRUE because of default set in anova.afex_aov MSE <- "MSE" %in% colnames(object) } if(is.null(intercept)) { # Defaults to FALSE because of default set in anova.afex_aov intercept <- "(Intercept)" %in% rownames(object) } if("sig.symbols" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("sig.symbols", "sig_symbols") sig_symbols <- dots$sig.symbols } if(is.null(sig_symbols)) { sig_symbols <- afex_options("sig_symbols") } # internal functions: is.wholenumber <- function(x, tol = .Machine$double.eps^0.5) abs(x - round(x)) < tol make.fs <- function(anova, symbols) { ifelse(anova[["Pr(>F)"]] < 0.001, paste0(formatC( anova[["F"]], digits = 2, format = "f"), symbols[4]), ifelse(anova[["Pr(>F)"]] < 0.01, paste0(formatC( anova[["F"]], digits = 2, format = "f"), symbols[3]), ifelse(anova[["Pr(>F)"]] < 0.05, paste0(formatC( anova[["F"]], digits = 2, format = "f"), symbols[2]), ifelse(anova[["Pr(>F)"]] < 0.1, paste0(formatC( anova[["F"]], digits = 2, format = "f"), symbols[1]), formatC(anova[["F"]], digits = 2, format = "f"))))) } anova_table <- object anova_table[,"df"] <- paste(ifelse(is.wholenumber(anova_table[,"num Df"]), anova_table[,"num Df"], formatC(anova_table[,"num Df"], digits = 2, format = "f")), ifelse(is.wholenumber(anova_table[,"den Df"]), anova_table[,"den Df"], formatC(anova_table[,"den Df"], digits = 2, format = "f")), sep = ", ") symbols.use <- c(" +", " *", " **", " ***") symbols.use[seq_along(sig_symbols)] <- sig_symbols df.out <- data.frame(Effect = row.names(anova_table), df = anova_table[,"df"], stringsAsFactors = FALSE) if (MSE) df.out <- cbind(df.out, data.frame(MSE = formatC(anova_table[,"MSE"], digits = 2, format = "f"), stringsAsFactors = FALSE)) df.out <- cbind(df.out, data.frame(F = make.fs(anova_table, symbols.use), stringsAsFactors = FALSE)) if (!is.null(anova_table$ges)) df.out$ges <- round_ps(anova_table$ges) if (!is.null(anova_table$pes)) df.out$pes <- round_ps(anova_table$pes) df.out$p.value <- round_ps(anova_table[,"Pr(>F)"]) if (!intercept) if (df.out[1,1] == "(Intercept)") { df.out <- df.out[-1,, drop = FALSE] } rownames(df.out) <- NULL attr(df.out, "heading") <- attr(object, "heading") attr(df.out, "p_adjust_method") <- attr(object, "p_adjust_method") attr(df.out, "correction") <- attr(object, "correction") attr(df.out, "observed") <- attr(object, "observed") attr(df.out, "es") <- attr(object, "es") attr(df.out, "sig_symbols") <- symbols.use class(df.out) <- c("nice_table", class(df.out)) df.out } make.stat <- function(anova, stat, symbols) { out <- ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.001, paste0(formatC(anova[[stat]], digits = 2, format = "f"), symbols[4]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.01, paste0(formatC(anova[[stat]], digits = 2, format = "f"), symbols[3]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.05, paste0(formatC(anova[[stat]], digits = 2, format = "f"), symbols[2]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.1, paste0(formatC(anova[[stat]], digits = 2, format = "f"), symbols[1]), formatC(anova[[stat]], digits = 2, format = "f"))))) out[is.na(anova[[paste0("Pr(>", stat,")")]])] <- formatC( anova[[stat]][is.na(anova[[paste0("Pr(>", stat,")")]])], digits = 2, format = "f") out } is.wholenumber <- function(x, tol = .Machine$double.eps^0.5) abs(x - round(x)) < tol #' @rdname nice #' @method nice mixed #' @export nice.mixed <- function(object, sig_symbols = attr(object$anova_table, "sig_symbols"), ...) { anova_table <- object$anova_table dots <- list(...) if("sig.symbols" %in% names(dots)) { #(!missing(sig.symbols)) { warn_deprecated_arg("sig.symbols", "sig_symbols") sig_symbols <- dots$sig.symbols } if(is.null("sig_symbols")) sig_symbols <- afex_options("sig_symbols") symbols.use <- c(" +", " *", " **", " ***") symbols.use[seq_along(sig_symbols)] <- sig_symbols if (is.null(attr(object, "method"))) { df.out <- object[[1]] warning("mixed object was created with old version of afex, table not nicely formatted.") } else if (attr(object, "method") %in% c("KR", "S", "nested-KR") ) { anova_table[,"df"] <- paste(ifelse(is.wholenumber(anova_table[,"num Df"]), round(anova_table[,"num Df"]), formatC(anova_table[,"num Df"], digits = 2, format = "f")), ifelse(is.wholenumber(anova_table[,"den Df"]), round(anova_table[,"den Df"]), formatC(anova_table[,"den Df"], digits = 2, format = "f")), sep = ", ") if ("F.scaling" %in% anova_table) { df.out <- data.frame( Effect = row.names(anova_table), df = anova_table[,"df"], "F.scaling" = formatC(anova_table[,"F.scaling"], digits = 2, format = "f"), stringsAsFactors = FALSE, check.names = FALSE) } else { df.out <- data.frame( Effect = row.names(anova_table), df = anova_table[,"df"], stringsAsFactors = FALSE, check.names = FALSE) } df.out <- cbind(df.out, data.frame( F = make.stat(anova_table, stat = "F", symbols.use), stringsAsFactors = FALSE)) df.out$p.value <- round_ps(anova_table[,"Pr(>F)"]) } else if (attr(object, "method") == "PB") { anova_table[,"Pr(>Chisq)"] <- anova_table[,"Pr(>PB)"] df.out <- data.frame(Effect = row.names(anova_table), df = anova_table[,"Chi Df"], Chisq = make.stat(anova_table, stat = "Chisq", symbols.use), p.value = round_ps(anova_table[,"Pr(>Chisq)"]), stringsAsFactors = FALSE, check.names = FALSE) } else if (attr(object, "method") == "LRT") { 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Mixed Model Reanalysis of RT data

Henrik Singmann

2020-01-15

Overview

This documents reanalysis response time data from an Experiment performed by Freeman, Heathcote, Chalmers, and Hockley (2010) using the mixed model functionality of afex implemented in function mixed followed by post-hoc tests using package emmeans (Lenth, 2017). After a brief description of the data set and research question, the code and results are presented.

Description of Experiment and Data

The data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The 300 items in each stimulus condition were selected to form a balanced \(2 \times 2\) design with factors neighborhood density (low versus high) and frequency (low versus high). The task was a between subjects factor: 25 participants worked on the lexical decision task and 20 participants on the naming task. After excluding erroneous responses each participants responded to between 135 and 150 words and between 124 and 150 nonwords. We analyzed log RTs which showed an approximately normal picture.

Data and R Preperation

We start with loading some packages we will need throughout this example. For data manipulation we will be using the dplyr and tidyr packages from the tidyverse. A thorough introduction to these packages is beyond this example, but well worth it, and can be found in ‘R for Data Science’ by Wickham and Grolemund. For plotting we will be diverging from the tidyverse and use lattice instead. At some later point in time I will change this to ggplot2 plots.

After loading the packages, we will load the data (which comes with afex), remove the errors, and take a look at the variables in the data.

library("afex") # needed for mixed() and attaches lme4 automatically.
library("emmeans") # emmeans is needed for follow-up tests (and not anymore loaded automatically).
library("multcomp") # for advanced control for multiple testing/Type 1 errors.
library("dplyr") # for working with data frames
library("tidyr") # for transforming data frames from wide to long and the other way round.
library("lattice") # for plots
library("latticeExtra") # for combining lattice plots, etc.
lattice.options(default.theme = standard.theme(color = FALSE)) # black and white
lattice.options(default.args = list(as.table = TRUE)) # better ordering

data("fhch2010") # load 
fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors
str(fhch2010) # structure of the data
## 'data.frame':    13222 obs. of  10 variables:
##  $ id       : Factor w/ 45 levels "N1","N12","N13",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ task     : Factor w/ 2 levels "naming","lexdec": 1 1 1 1 1 1 1 1 1 1 ...
##  $ stimulus : Factor w/ 2 levels "word","nonword": 1 1 1 2 2 1 2 2 1 2 ...
##  $ density  : Factor w/ 2 levels "low","high": 2 1 1 2 1 2 1 1 1 1 ...
##  $ frequency: Factor w/ 2 levels "low","high": 1 2 2 2 2 2 1 2 1 2 ...
##  $ length   : Factor w/ 3 levels "4","5","6": 3 3 2 2 1 1 3 2 1 3 ...
##  $ item     : Factor w/ 600 levels "abide","acts",..: 363 121 202 525 580 135 42 368 227 141 ...
##  $ rt       : num  1.091 0.876 0.71 1.21 0.843 ...
##  $ log_rt   : num  0.0871 -0.1324 -0.3425 0.1906 -0.1708 ...
##  $ correct  : logi  TRUE TRUE TRUE TRUE TRUE TRUE ...

To make sure our expectations about the data match the data we use some dplyr magic to confirm the number of participants per condition and items per participant.

## are all participants in only one task?
fhch2010 %>% group_by(id) %>%
  summarise(task = n_distinct(task)) %>%
  as.data.frame() %>% 
  {.$task == 1} %>%
  all()
## [1] TRUE
## participants per condition:
fhch2010 %>% group_by(id) %>%
  summarise(task = first(task)) %>%
  ungroup() %>%
  group_by(task) %>%
  summarise(n = n())
## # A tibble: 2 x 2
##   task       n
##   <fct>  <int>
## 1 naming    20
## 2 lexdec    25
## number of different items per participant:
fhch2010 %>% group_by(id, stimulus) %>%
  summarise(items = n_distinct(item)) %>%
  ungroup() %>%
  group_by(stimulus) %>%
  summarise(min = min(items), 
            max = max(items), 
            mean = mean(items))
## # A tibble: 2 x 4
##   stimulus   min   max  mean
##   <fct>    <int> <int> <dbl>
## 1 word       139   150  147.
## 2 nonword    134   150  146.

Before running the analysis we should make sure that our dependent variable looks roughly normal. To compare rt with log_rt within the same graph using lattice we first need to transform the data from the wide format (where both rt types occupy one column each) into the long format (in which the two rt types are combined into a single column with an additional indicator column). To do so we use tidyr::gather. Then we simply call the histogram function on the new data.frame and make a few adjustments to the defaults to obtain a nice looking output. The plot shows that log_rt looks clearly more normal than rt, although not perfectly so. An interesting exercise could be to rerun the analysis below using a transformation that provides an even better ‘normalization’.

fhch_long <- fhch %>% gather("rt_type", "rt", rt, log_rt)
histogram(~rt|rt_type, fhch_long, breaks = "Scott", type = "density",
          scale = list(x = list(relation = "free")))

Descriptive Analysis

The main factors in the experiment were the between-subjects factor task (naming vs. lexdec), and the within-subjects factors stimulus (word vs. nonword), density (low vs. high), and frequency (low vs. high). Before running an analysis it is a good idea to visually inspect the data to gather some expectations regarding the results. Should the statistical results dramatically disagree with the expectations this suggests some type of error along the way (e.g., model misspecification) or at least encourages a thorough check to make sure everything is correct. We first begin by plotting the data aggregated by-participant.

In each plot we plot the raw data in the background. To make the individual data points visible we add some jitter on the x-axis and choose pch and alpha values such that we see where more data points are (i.e., where plot overlaps it is darker). Then we add the mean as a x in a circle. Both of this is done in the same call to xyplot using a custom panel function. Finally, we combine this plot with a simple boxplot using bwplot.

agg_p <- fhch %>% group_by(id, task, stimulus, density, frequency) %>%
  summarise(mean = mean(log_rt)) %>%
  ungroup()

xyplot(mean ~ density:frequency|task+stimulus, agg_p, jitter.x = TRUE, pch = 20, alpha = 0.5, 
       panel = function(x, y, ...) {
         panel.xyplot(x, y, ...)
         tmp <- aggregate(y, by = list(x), mean)
         panel.points(tmp$x, tmp$y, pch = 13, cex =1.5)
       }) + 
bwplot(mean ~ density:frequency|task+stimulus, agg_p, pch="|", do.out = FALSE)

Now we plot the same data but aggregated across items:

agg_i <- fhch %>% group_by(item, task, stimulus, density, frequency) %>%
  summarise(mean = mean(log_rt)) %>%
  ungroup()

xyplot(mean ~ density:frequency|task+stimulus, agg_i, jitter.x = TRUE, pch = 20, alpha = 0.2, 
       panel = function(x, y, ...) {
         panel.xyplot(x, y, ...)
         tmp <- aggregate(y, by = list(x), mean)
         panel.points(tmp$x, tmp$y, pch = 13, cex =1.5)
       }) + 
bwplot(mean ~ density:frequency|task+stimulus, agg_i, pch="|", do.out = FALSE)

These two plots show a very similar pattern and suggest several things:

  • Responses to nonwords appear slower than responses to words, at least for the naming task.
  • lexdec responses appear to be slower than naming responses, particularly in the word condition.
  • In the nonword and naming condition we see a clear effect of frequency with slower responses to high than low frequency words.
  • In the word conditions the frequency pattern appears to be in the opposite direction to the pattern described in the previous point: faster responses to low frequency than to high frequency words.
  • density appears to have no effect, perhaps with the exception of the nonword lexdec condition.

Model Setup

To set up a mixed model it is important to identify which factors vary within which grouping factor generating random variability (i.e., grouping factors are sources of stochastic variability). The two grouping factors are participants (id) and items (item). The within-participant factors are stimulus, density, and frequency. The within-item factor is task. The ‘maximal model’ (Barr, Levy, Scheepers, and Tily, 2013) therefore is the model with by-participant random slopes for stimulus, density, and frequency and their interactions and by-item random slopes for task.

Occasionally, the maximal model does not converge successfully. In this case a good first approach for dealing with this problem is to remove the corelations among the random terms. In our example, there are two sets of correlations, one for each random effect grouping variable. Consequently, we can build four model that have the maximal structure in terms of random-slopes and only differ in which correlations among random terms are calculated:

  1. With all correlations.
  2. No correlation among by-item random effects (i.e., no correlation between random intercept and task random slope).
  3. No correlation among by-participant random effect terms (i.e., no correlation among random slopes themselves and between the random slopes and the random intercept).
  4. No correlation among either random grouping factor.

The next decision to be made is which method to use for obtaining \(p\)-values. The default method is KR (=Kenward-Roger) which provides the best control against anti-conservative results. However, KR needs quite a lot of RAM, especially with complicated random effect structures and large data sets. As in this case we have both, relatively large data (i.e., many levels on each random effect, especially the item random effect) and a complicated random effect structure, it seems a reasonable decision to choose another method. The second ‘best’ method (in terms of controlling for Type I errors) is the ‘Satterthwaite’ approximation, method='S'. It provides a similar control of Type I errors as the Kenward-Roger approximation and needs less RAM, however one downside is that it simply fails in some cases.

Results

Satterthwaite Results

The following code fits the four models using the Satterthwaite method. To suppress random effects we use the || notation. Note that it is necessary to set expand_re=TRUE when suppressing random effects among variables that are entered as factors and not as numerical variables (as done here). Also note that mixed automatically uses appropriate contrast codings if factors are included in interactions (contr.sum) in contrast to the R default (which is contr.treatment). To make sure the estimation does not end prematurely we set the allowed number of function evaluations to a very high value (using lmerControl).

m1s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+
               (task|item), fhch, method = "S", 
             control = lmerControl(optCtrl = list(maxfun = 1e6)))
m2s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+
               (task||item), fhch, method = "S", 
             control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)
m3s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+
               (task|item), fhch, method = "S", 
             control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)
m4s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+
               (task||item), fhch, method = "S", 
             control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)

As the estimation of these model may take some time, afex inlcudes the estimated models which can be loaded with the following code. Note that when using the print or anova method for mixed objects, the warnings emitted during estimation of the model by lmer will be printed again. So there is no downside of loading the already estimated models. We then inspect the four results.

load(system.file("extdata/", "freeman_models.rda", package = "afex"))
m1s
## Warning: lme4 reported (at least) the following warnings for 'full':
##   * unable to evaluate scaled gradient
##   * Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: log_rt ~ task * stimulus * density * frequency + (stimulus * 
## Model:     density * frequency | id) + (task | item)
## Data: fhch
##                             Effect    df      F p.value
## 1                             task 1, NA 128.72    <NA>
## 2                         stimulus 1, NA 117.02    <NA>
## 3                          density 1, NA   1.20    <NA>
## 4                        frequency 1, NA   1.30    <NA>
## 5                    task:stimulus 1, NA  63.74    <NA>
## 6                     task:density 1, NA  10.59    <NA>
## 7                 stimulus:density 1, NA   0.39    <NA>
## 8                   task:frequency 1, NA  55.81    <NA>
## 9               stimulus:frequency 1, NA  85.68    <NA>
## 10               density:frequency 1, NA   0.03    <NA>
## 11           task:stimulus:density 1, NA  12.87    <NA>
## 12         task:stimulus:frequency 1, NA 119.08    <NA>
## 13          task:density:frequency 1, NA   5.22    <NA>
## 14      stimulus:density:frequency 1, NA   2.45    <NA>
## 15 task:stimulus:density:frequency 1, NA  10.16    <NA>
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
m2s
## Warning: lme4 reported (at least) the following warnings for 'full':
##   * unable to evaluate scaled gradient
##   * Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: log_rt ~ task * stimulus * density * frequency + (stimulus * 
## Model:     density * frequency | id) + (task || item)
## Data: fhch
##                             Effect        df          F p.value
## 1                             task  1, 43.54  13.69 ***   .0006
## 2                         stimulus  1, 51.06 150.61 ***  <.0001
## 3                          density 1, 192.25       0.31     .58
## 4                        frequency  1, 72.78       0.52     .47
## 5                    task:stimulus  1, 52.03  71.20 ***  <.0001
## 6                     task:density 1, 201.56  15.92 ***  <.0001
## 7                 stimulus:density 1, 287.88       1.06     .30
## 8                   task:frequency  1, 76.76  80.05 ***  <.0001
## 9               stimulus:frequency 1, 177.48  55.45 ***  <.0001
## 10               density:frequency 1, 235.01       0.12     .73
## 11           task:stimulus:density 1, 300.16  14.21 ***   .0002
## 12         task:stimulus:frequency 1, 190.61 109.33 ***  <.0001
## 13          task:density:frequency 1, 248.09     5.46 *     .02
## 14      stimulus:density:frequency 1, 104.15     3.72 +     .06
## 15 task:stimulus:density:frequency 1, 111.32   10.07 **    .002
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
m3s
## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: log_rt ~ task * stimulus * density * frequency + (stimulus * 
## Model:     density * frequency || id) + (task | item)
## Data: fhch
##                             Effect        df          F p.value
## 1                             task  1, 43.52  13.68 ***   .0006
## 2                         stimulus  1, 50.57 151.33 ***  <.0001
## 3                          density 1, 584.49       0.36     .55
## 4                        frequency  1, 70.26       0.56     .46
## 5                    task:stimulus  1, 51.50  71.29 ***  <.0001
## 6                     task:density 1, 578.65  17.89 ***  <.0001
## 7                 stimulus:density 1, 584.50       1.19     .28
## 8                   task:frequency  1, 74.11  82.66 ***  <.0001
## 9               stimulus:frequency 1, 584.68  63.34 ***  <.0001
## 10               density:frequency 1, 584.54       0.11     .74
## 11           task:stimulus:density 1, 578.66  14.86 ***   .0001
## 12         task:stimulus:frequency 1, 578.82 124.10 ***  <.0001
## 13          task:density:frequency 1, 578.69     5.92 *     .02
## 14      stimulus:density:frequency  1, 88.40     4.16 *     .04
## 15 task:stimulus:density:frequency  1, 94.42   10.60 **    .002
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
m4s
## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: log_rt ~ task * stimulus * density * frequency + (stimulus * 
## Model:     density * frequency || id) + (task || item)
## Data: fhch
##                             Effect        df          F p.value
## 1                             task  1, 43.54  13.67 ***   .0006
## 2                         stimulus  1, 51.05 150.79 ***  <.0001
## 3                          density 1, 587.35       0.35     .55
## 4                        frequency  1, 71.90       0.53     .47
## 5                    task:stimulus  1, 52.02  71.50 ***  <.0001
## 6                     task:density 1, 582.30  17.50 ***  <.0001
## 7                 stimulus:density 1, 587.35       1.13     .29
## 8                   task:frequency  1, 75.90  81.49 ***  <.0001
## 9               stimulus:frequency 1, 587.51  62.27 ***  <.0001
## 10               density:frequency 1, 587.39       0.11     .74
## 11           task:stimulus:density 1, 582.31  14.61 ***   .0001
## 12         task:stimulus:frequency 1, 582.45 121.11 ***  <.0001
## 13          task:density:frequency 1, 582.34     5.84 *     .02
## 14      stimulus:density:frequency  1, 90.80     3.90 +     .05
## 15 task:stimulus:density:frequency  1, 97.08   10.52 **    .002
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Before looking at the results we can see that for models 1 and 2, lmer emmited a warning that the model failed to converge. These warnings do not necessarily mean that the results cannot be used. As we will see below, model 2 (m2s) produces essentially the same results as models 3 and 4 suggesting that this warning is indeed a false positive. However, the results also show that estimating the Satterthwaite approximation failed for m1s, we have no denominator degrees of freedom and no \(p\)-values. If this happens, we can only try another method or a reduced model.

Models 2 to 4 produce results and the results are extremely similar across models. A total of 9 or 10 effects reached significance. We found main effects for task and stimulus, two-way interactions of task:stimulus, task:density, task:frequency, and stimulus:frequency, three-way interactions of task:stimulus:density, task:stimulus:frequency, and task:density:frequency, a marginal three-way interaction (for two of three models) of stimulus:density:frequency, and the four-way interaction of task:stimulus:density:frequency. Additionally, all \(F\) and \(p\) values are very similar to each other across the three models.

The only difference in terms of significant versus non-significant effects between the three models is the three-way interaction of stimulus:density:frequency which is only significant for model 3 with \(F(1, 88.40) = 4.16\), \(p = .04\), and only reaches marginal significance for the other two models with \(p > .05\) and a very similar \(F\)-value.

LRT Results

It is instructive to compare those results with results obtained using the comparatively ‘worst’ method for obtaining \(p\)-value simplmeneted in afex, likelihood ratio tests. Likelihood ratio-tests should in principle deliver reasonable results for large data sets such as the current one, so we should expect not too many deviations. We again fit all four models, this time using method='LRT'.

m1lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+
                 (task|item), fhch, method = "LRT", 
               control = lmerControl(optCtrl = list(maxfun = 1e6)))
m2lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+
                 (task||item), fhch, method = "LRT", 
               control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)
m3lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+
                 (task|item), fhch, method = "LRT", 
               control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)
m4lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+
                 (task||item), fhch, method = "LRT", 
               control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE)

Because the resulting mixed objects are of considerable size, we do not include the full objects, but only the resulting ANOVA tables and data.frames (nice_lrt is a list containing the result from calling nice on the objects, anova_lrt contains the result from calling anova).

Before considering the results, we again first consider the warnings emitted when fitting the models. Because methods 'LRT' and 'PB' fit one full_model and one restricted_model for each effect (i.e., term), there can be more warnings than for methods 'KR' and 'S' which only fit one model (the full_model). And this is exactly what happens. For m1lrt there are 11 convergence warnings, almost one per fitted model. However, none of those immediately invalidates the results. This is different for models 2 and 3 for both of which warnings indicate that nested model(s) provide better fit than full model. What this warning means is that the full_model does not provide a better fit than at least one of the restricted_model, which is mathematically impossible as the restricted_models are nested within the full model (i.e., they result from setting one or several parameters equal to 0, so the full_model can always provide an at least as good account as the restricted_models). Model 4 finally shows no warnings.

The following code produces a single output comparing models 1 and 4 next to each other. The results show basically the same pattern as obtained with the Satterthwaite approximation. Even the \(p\)-values are extremely similar to the \(p\)-values of the Satterthwaite models. The only ‘difference’ is that the stimulus:density:frequency three-way interaction is significant in each case now, although only barely so.

res_lrt <- cbind(nice_lrt[[1]], "  " = " ", 
                 nice_lrt[[4]][,-(1:2)])
colnames(res_lrt)[c(3,4,6,7)] <- paste0(
  rep(c("m1_", "m4_"), each =2), colnames(res_lrt)[c(3,4)])
res_lrt
##                             Effect df  m1_Chisq m1_p.value     m4_Chisq m4_p.value
## 1                             task  1 12.18 ***      .0005    12.43 ***      .0004
## 2                         stimulus  1 70.00 ***     <.0001    70.03 ***     <.0001
## 3                          density  1      0.01        .91         0.35        .55
## 4                        frequency  1      0.57        .45         0.54        .46
## 5                    task:stimulus  1 45.06 ***     <.0001    45.68 ***     <.0001
## 6                     task:density  1 15.50 ***     <.0001    17.43 ***     <.0001
## 7                 stimulus:density  1      0.82        .36         1.14        .29
## 8                   task:frequency  1 52.87 ***     <.0001    53.51 ***     <.0001
## 9               stimulus:frequency  1 45.44 ***     <.0001    50.45 ***     <.0001
## 10               density:frequency  1      0.11        .73         0.12        .73
## 11           task:stimulus:density  1 14.15 ***      .0002    14.59 ***      .0001
## 12         task:stimulus:frequency  1 73.40 ***     <.0001    77.83 ***     <.0001
## 13          task:density:frequency  1    5.59 *        .02       5.88 *        .02
## 14      stimulus:density:frequency  1    4.00 *        .05       3.92 *        .05
## 15 task:stimulus:density:frequency  1   9.91 **       .002     10.24 **       .001

We can also compare this with the results from model 3. Although the full_model cannot be the maximum-likelihood estimate (as it provides a worse than the density:frequency model), the difference seems to be minimal as it also shows exactly the same pattern as the other models.

nice_lrt[[2]]
## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: log_rt ~ task * stimulus * density * frequency + (stimulus * 
## Model:     density * frequency | id) + (task || item)
## Data: fhch
## Df full model: 55
##                             Effect df     Chisq p.value
## 1                             task  1 12.15 ***   .0005
## 2                         stimulus  1 70.00 ***  <.0001
## 3                          density  1      0.32     .57
## 4                        frequency  1      0.24     .63
## 5                    task:stimulus  1 45.55 ***  <.0001
## 6                     task:density  1 15.27 ***  <.0001
## 7                 stimulus:density  1      0.78     .38
## 8                   task:frequency  1 52.71 ***  <.0001
## 9               stimulus:frequency  1 45.54 ***  <.0001
## 10               density:frequency  1      0.00    >.99
## 11           task:stimulus:density  1 14.33 ***   .0002
## 12         task:stimulus:frequency  1 72.79 ***  <.0001
## 13          task:density:frequency  1    5.28 *     .02
## 14      stimulus:density:frequency  1    3.45 +     .06
## 15 task:stimulus:density:frequency  1   9.57 **    .002
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Summary of Results

Fortunately, the results from all models that actually produced results and converged without a critical warning (e.g., one critical warning is that a restricted_model provides a better fit than the full_model) agreed very strongly providing a high degree of confidence in the results. This might not be too surprising given the comparatively large number of total data points and the fact that each random effect grouping factor has a considerable number of levels (way above 20 for both participants and items). This also suggests that the convergence warnings are likely false positives; the models seem to have converged successfully to the maximum likelihood estimate, or at least to a value very near the maximum likelihood estimate. How further reducing the random effects structure (e.g., removing the random slopes for the highest interaction) affects the results is left as an exercise for the reader.

In terms of the significant findings, there are many that seem to be in line with the descriptive results described above. For example, the highly significant effect of task:stimulus:frequency with \(F(1, 190.61) = 109.33\), \(p < .0001\) (values from m2s), appears to be in line with the observation that the frequency effect appears to change its sign depending on the task:stimulus cell (with nonword and naming showing the opposite patterns than the other three conditions). Consequently, we start by investigating this interaction further below.

Follow-Up Analyses

Before investigating the significant interaction in detail it is a good idea to remind oneself what a significant interaction represents on a conceptual level; that one or multiple of the variables in the interaction moderate (i.e., affect) the effect of the other variable or variables. Consequently, there are several ways to investigate a significant interaction. Each of the involved variables can be seen as the moderating variables and each of the variables can be seen as the effect of interest. Which one of those possible interpretations is of interest in a given situation highly depends on the actual data and research question and multiple views can be ‘correct’ in a given situation.

In addition to this conceptual issue, there are also multiple technical ways to investigate a significant interaction. One approach not followed here is to split the data according to the moderating variables and compute the statistical model again for the splitted data sets with the effect variable(s) as remaining fixed effect. This approach, also called simple effects analysis, is, for example, recommended by Maxwell and Delaney (2004) as it does not assume variance homogeneity and is faithful to the data at each level. The approach taken here is to simply perform the test on the fitted full model. This approach assumes variance homogeneity (i.e., that the variances in all groups are homogeneous) and has the added benefit that it is computationally relatively simple. In addition, it can all be achieved using the framework provided by emmeans (Lenth, 2017).

task:stimulus:frequency Interaction

Our interest in the beginning is on the effect of frequency by task:stimulus combination. So let us first look at the estimated marginal means os this effect. In emmeans parlance these estimated means are called ‘least-square means’ because of historical reasons, but because of the lack of least-square estimation in mixed models we prefer the term estimated marginal means, or EMMs for short. Those can be obtained in the following way. To prevent emmeans from calculating the df for the EMMs (which can be quite costly), we use asymptotic dfs (i.e., \(z\) values and tests). emmeans requires to first specify the variable(s) one wants to treat as the effect variable(s) (here frequency) and then allows to specify condition variables.

emm_options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger'
emm_i1 <- emmeans(m2s, "frequency", by = c("stimulus", "task"))
## NOTE: Results may be misleading due to involvement in interactions
emm_i1
## stimulus = word, task = naming:
##  frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low       -0.32326 0.0415 Inf   -0.4047   -0.2418
##  high      -0.38193 0.0457 Inf   -0.4715   -0.2923
## 
## stimulus = nonword, task = naming:
##  frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low       -0.14314 0.0458 Inf   -0.2330   -0.0533
##  high       0.06363 0.0497 Inf   -0.0337    0.1610
## 
## stimulus = word, task = lexdec:
##  frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low        0.02323 0.0373 Inf   -0.0499    0.0964
##  high      -0.03996 0.0410 Inf   -0.1203    0.0404
## 
## stimulus = nonword, task = lexdec:
##  frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low        0.10406 0.0412 Inf    0.0234    0.1847
##  high      -0.00646 0.0445 Inf   -0.0937    0.0808
## 
## Results are averaged over the levels of: density 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95

The returned values are in line with our observation that the nonword and naming condition diverges from the other three. But is there actual evidence that the effect flips? We can test this using additional emmeans functionality. Specifically, we first use the pairs function which provides us with a pairwise test of the effect of frequency in each task:stimulus combination. Then we need to combine the four tests within one object to obtain a familywise error rate correction which we do via update(..., by = NULL) (i.e., we revert the effect of the by statement from the earlier emmeans call) and finally we select the holm method for controlling for family wise error rate (the Holm method is uniformly more powerful than the Bonferroni).

update(pairs(emm_i1), by = NULL, adjust = "holm")
##  contrast   stimulus task   estimate     SE  df z.ratio p.value
##  low - high word     naming   0.0587 0.0162 Inf   3.620 0.0003 
##  low - high nonword  naming  -0.2068 0.0177 Inf -11.703 <.0001 
##  low - high word     lexdec   0.0632 0.0152 Inf   4.165 0.0001 
##  low - high nonword  lexdec   0.1105 0.0164 Inf   6.719 <.0001 
## 
## Results are averaged over the levels of: density 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: holm method for 4 tests

We could also use a slightly more powerful method than the Holm method, method free from package multcomp, which takes the correlation of the model parameters into account (note that due a bug in the current emmenas version this is currently deactivated):

summary(as.glht(update(pairs(emm_i1), by = NULL)), test = adjusted("free"))

We see that the results are exactly as expected. In the nonword and naming condition we have a clear negative effect of frequency while in the other three conditions it is clearly positive. We could now also use the EMMs and retransform them onto the response scale (i.e., RTs) which we could use for plotting. Note that the \(p\)-values in this ouput are for the \(z\) test of whether or not a value is significantly above 0 on the log_rt-scale (i.e., above 1 second on the response scale). That seems not the most interesting test, but the output is interesting because of the EMMs and standard errors that could be used for printing.

emm_i1b <- summary(contrast(emm_i1, by = NULL))
emm_i1b[,c("estimate", "SE")] <- exp(emm_i1b[,c("estimate", "SE")])
emm_i1b
##  contrast                   estimate   SE  df z.ratio p.value
##  low,word,naming effect        0.790 1.03 Inf -8.076  <.0001 
##  high,word,naming effect       0.745 1.03 Inf -9.019  <.0001 
##  low,nonword,naming effect     0.946 1.03 Inf -1.695  0.1029 
##  high,nonword,naming effect    1.164 1.04 Inf  4.305  <.0001 
##  low,word,lexdec effect        1.118 1.03 Inf  3.796  0.0002 
##  high,word,lexdec effect       1.049 1.03 Inf  1.498  0.1341 
##  low,nonword,lexdec effect     1.212 1.03 Inf  5.991  <.0001 
##  high,nonword,lexdec effect    1.085 1.03 Inf  2.384  0.0228 
## 
## Results are averaged over the levels of: density 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: fdr method for 8 tests

task:stimulus:density:frequency Interaction

As the last example, let us take a look at the significant four-way interaction of task:stimulus:density:frequency, \(F(1, 111.32) = 10.07\), \(p = .002\). Here we might be interested in a slightly more difficult question namely whether the density:frequency interaction varies across task:stimulus conditions. If we again look at the figures above, it appears that there is a difference between low:low and high:low in the nonword and lexdec condition, but not in the other conditions. We again first begin by obtaining the EMMs. However, the actual values are not interesting at the moment, we are basically only interested in the interaction for each task:stimulus condition. Therefore, we use the EMMs to create two consecutive contrasts, the first one for density and then for frequency using the fist contrast. Then we run a joint test conditional on the task:stimulus conditions.

emm_i2 <- emmeans(m2s, c("density", "frequency"), by = c("stimulus", "task"))
con1 <- contrast(emm_i2, "trt.vs.ctrl1", by = c("frequency", "stimulus", "task")) # density
con2 <- contrast(con1, "trt.vs.ctrl1", by = c("contrast", "stimulus", "task")) 
test(con2, joint = TRUE, by = c("stimulus", "task"))
##  stimulus task   df1 df2 F.ratio p.value
##  word     naming   1 Inf   0.105 0.7464 
##  nonword  naming   1 Inf   2.537 0.1112 
##  word     lexdec   1 Inf   1.790 0.1809 
##  nonword  lexdec   1 Inf  16.198 0.0001

This test indeed shows that the density:frequency interaction is only significant in the nonword and lexdec condition. Next, let’s see if we can unpack this interaction in a meaningful manner. For this we compare low:low and high:low in each of the four groups. And just for the sake of making the example more complex, we also compare low:high and high:high. This can simply be done by specifying a list of custom contrasts on the EMMs (or reference grid in emmeans parlance) which can be passed again to the contrast function. The contrasts are a list where each element should sum to one (i.e., be a proper contrast) and be of length equal to the number of EMMs (although we have 16 EMMs in total, we only need to specify it for a length of four due to conditiong by c("stimulus", "task")). To control for the family wise error rate across all tests, we again use update(..., by = NULL) on the result this time again specifying by = NULL to revert the effect of conditiong. Note that although we entered the variables into emmeans in the same order as into our plot call above, the order of the four EMMs differs.

emm_i2
## stimulus = word, task = naming:
##  density frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low     low       -0.31384 0.0448 Inf   -0.4016  -0.22606
##  high    low       -0.33268 0.0408 Inf   -0.4127  -0.25269
##  low     high      -0.37741 0.0466 Inf   -0.4688  -0.28601
##  high    high      -0.38645 0.0472 Inf   -0.4790  -0.29390
## 
## stimulus = nonword, task = naming:
##  density frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low     low       -0.10399 0.0500 Inf   -0.2019  -0.00606
##  high    low       -0.18230 0.0442 Inf   -0.2688  -0.09575
##  low     high       0.07823 0.0520 Inf   -0.0237   0.18019
##  high    high       0.04902 0.0495 Inf   -0.0479   0.14599
## 
## stimulus = word, task = lexdec:
##  density frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low     low        0.03714 0.0404 Inf   -0.0420   0.11624
##  high    low        0.00932 0.0368 Inf   -0.0628   0.08144
##  low     high      -0.04513 0.0419 Inf   -0.1273   0.03705
##  high    high      -0.03479 0.0424 Inf   -0.1180   0.04837
## 
## stimulus = nonword, task = lexdec:
##  density frequency   emmean     SE  df asymp.LCL asymp.UCL
##  low     low        0.04480 0.0449 Inf   -0.0432   0.13282
##  high    low        0.16331 0.0399 Inf    0.0852   0.24144
##  low     high      -0.00728 0.0467 Inf   -0.0988   0.08425
##  high    high      -0.00563 0.0445 Inf   -0.0928   0.08151
## 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95
# desired contrats:
des_c <- list(
  ll_hl = c(1, -1, 0, 0),
  lh_hh = c(0, 0, 1, -1)
  )
update(contrast(emm_i2, des_c), by = NULL, adjust = "holm")
##  contrast stimulus task   estimate     SE  df z.ratio p.value
##  ll_hl    word     naming  0.01883 0.0210 Inf  0.898  1.0000 
##  lh_hh    word     naming  0.00904 0.0212 Inf  0.427  1.0000 
##  ll_hl    nonword  naming  0.07831 0.0220 Inf  3.554  0.0027 
##  lh_hh    nonword  naming  0.02921 0.0211 Inf  1.385  0.9763 
##  ll_hl    word     lexdec  0.02782 0.0199 Inf  1.396  0.9763 
##  lh_hh    word     lexdec -0.01034 0.0199 Inf -0.520  1.0000 
##  ll_hl    nonword  lexdec -0.11852 0.0209 Inf -5.670  <.0001 
##  lh_hh    nonword  lexdec -0.00164 0.0198 Inf -0.083  1.0000 
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: holm method for 8 tests

In contrast to our expectation, the results show two significant effects and not only one. In line with our expectations, in the nonword and lexdec condition the EMM of low:high is smaller than the EMM for high:high, \(z = -6.30\), \(p < .0001\). However, in the nonword and naming condition we found the opposite pattern; the EMM of low:high is larger than the EMM for high:high, \(z = 3.65\), \(p = .002\). For all other effects \(|z| < 1.3\), \(p > .99\). In addition, there is no difference between low:high and high:high in any condition.

References

  • Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255-278. https://doi.org/10.1016/j.jml.2012.11.001
  • Bretz, F., Hothorn, T., & Westfall, P. H. (2011). Multiple comparisons using R. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp
  • Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. Journal of Memory and Language, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004
  • Lenth, R. (2017). emmeans: Estimated Marginal Means, aka Least-Squares Means. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans
  • Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: a model-comparisons perspective. Mahwah, N.J.: Lawrence Erlbaum Associates.
afex/inst/doc/afex_mixed_example.R0000644000176200001440000002106313607676760016712 0ustar liggesusers## ----set-options, echo=FALSE, cache=FALSE----------------------------------------------- options(width = 90) knitr::opts_chunk$set(dpi=72) ## ----message=FALSE, warning=FALSE------------------------------------------------------- library("afex") # needed for mixed() and attaches lme4 automatically. library("emmeans") # emmeans is needed for follow-up tests (and not anymore loaded automatically). library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("dplyr") # for working with data frames library("tidyr") # for transforming data frames from wide to long and the other way round. library("lattice") # for plots library("latticeExtra") # for combining lattice plots, etc. lattice.options(default.theme = standard.theme(color = FALSE)) # black and white lattice.options(default.args = list(as.table = TRUE)) # better ordering data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors str(fhch2010) # structure of the data ## --------------------------------------------------------------------------------------- ## are all participants in only one task? fhch2010 %>% group_by(id) %>% summarise(task = n_distinct(task)) %>% as.data.frame() %>% {.$task == 1} %>% all() ## participants per condition: fhch2010 %>% group_by(id) %>% summarise(task = first(task)) %>% ungroup() %>% group_by(task) %>% summarise(n = n()) ## number of different items per participant: fhch2010 %>% group_by(id, stimulus) %>% summarise(items = n_distinct(item)) %>% ungroup() %>% group_by(stimulus) %>% summarise(min = min(items), max = max(items), mean = mean(items)) ## ---- fig.width=7, fig.height=4--------------------------------------------------------- fhch_long <- fhch %>% gather("rt_type", "rt", rt, log_rt) histogram(~rt|rt_type, fhch_long, breaks = "Scott", type = "density", scale = list(x = list(relation = "free"))) ## ---- fig.width=7, fig.height=6--------------------------------------------------------- agg_p <- fhch %>% group_by(id, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_p, jitter.x = TRUE, pch = 20, alpha = 0.5, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_p, pch="|", do.out = FALSE) ## ---- fig.width=7, fig.height=6--------------------------------------------------------- agg_i <- fhch %>% group_by(item, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_i, jitter.x = TRUE, pch = 20, alpha = 0.2, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_i, pch="|", do.out = FALSE) ## ---- eval = FALSE---------------------------------------------------------------------- # # m1s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ # (task|item), fhch, method = "S", # control = lmerControl(optCtrl = list(maxfun = 1e6))) # m2s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ # (task||item), fhch, method = "S", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) # m3s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ # (task|item), fhch, method = "S", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) # m4s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ # (task||item), fhch, method = "S", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ## --------------------------------------------------------------------------------------- load(system.file("extdata/", "freeman_models.rda", package = "afex")) m1s m2s m3s m4s ## ---- eval = FALSE---------------------------------------------------------------------- # m1lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ # (task|item), fhch, method = "LRT", # control = lmerControl(optCtrl = list(maxfun = 1e6))) # m2lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ # (task||item), fhch, method = "LRT", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) # m3lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ # (task|item), fhch, method = "LRT", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) # m4lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ # (task||item), fhch, method = "LRT", # control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ## --------------------------------------------------------------------------------------- res_lrt <- cbind(nice_lrt[[1]], " " = " ", nice_lrt[[4]][,-(1:2)]) colnames(res_lrt)[c(3,4,6,7)] <- paste0( rep(c("m1_", "m4_"), each =2), colnames(res_lrt)[c(3,4)]) res_lrt ## --------------------------------------------------------------------------------------- nice_lrt[[2]] ## --------------------------------------------------------------------------------------- emm_options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- emmeans(m2s, "frequency", by = c("stimulus", "task")) emm_i1 ## --------------------------------------------------------------------------------------- update(pairs(emm_i1), by = NULL, adjust = "holm") ## ---- eval=FALSE------------------------------------------------------------------------ # summary(as.glht(update(pairs(emm_i1), by = NULL)), test = adjusted("free")) ## --------------------------------------------------------------------------------------- emm_i1b <- summary(contrast(emm_i1, by = NULL)) emm_i1b[,c("estimate", "SE")] <- exp(emm_i1b[,c("estimate", "SE")]) emm_i1b ## --------------------------------------------------------------------------------------- emm_i2 <- emmeans(m2s, c("density", "frequency"), by = c("stimulus", "task")) con1 <- contrast(emm_i2, "trt.vs.ctrl1", by = c("frequency", "stimulus", "task")) # density con2 <- contrast(con1, "trt.vs.ctrl1", by = c("contrast", "stimulus", "task")) test(con2, joint = TRUE, by = c("stimulus", "task")) ## --------------------------------------------------------------------------------------- emm_i2 # desired contrats: des_c <- list( ll_hl = c(1, -1, 0, 0), lh_hh = c(0, 0, 1, -1) ) update(contrast(emm_i2, des_c), by = NULL, adjust = "holm") ## ---- echo=FALSE, eval = FALSE---------------------------------------------------------- # ### OLD STUFF BELOW. PLEASE IGNORE. # load("freeman_models.rda") # load("../freeman_models_all.rda") # m1lrt$restricted_models <- list(NULL) # m2lrt$restricted_models <- list(NULL) # m3lrt$restricted_models <- list(NULL) # m4lrt$restricted_models <- list(NULL) # # save(m1lrt, file = "freeman_models1.rda", compress = "xz") # save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models.rda", compress = "xz") # # anovas_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), anova) # nice_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), nice) # # res_lrt <- cbind(nice_lrt[[1]], " " = " ", # nice_lrt[[2]][,-(1:2)], " " = " ", # nice_lrt[[3]][,-(1:2)], " " = " ", # nice_lrt[[4]][,-(1:2)]) # colnames(res_lrt)[c(3,4,6,7, 9,10, 12,13)] <- paste0( # rep(c("m1_", "m2_", "m3_","m4_"), each =2), colnames(res_lrt)[c(3,4)]) # # ## warnings: # m1s # fails and 1 warning # m2s # 1 warning # m3s # 0 warnings # m4s # 0 warnings # # m1lrt # 11 warnings # m2lrt # 1 nested model(s) provide better, 7 other warnings # m3lrt # 7 nested models provide better fit, 9 other warnings # m4lrt # 0 warnings # # cbind(nice_lrt[[1]]$Effect, do.call("cbind", lapply(nice_lrt, function(x) x[,3:4]))) # # save(m1s, m2s, m3s, m4s, anovas_lrt, nice_lrt,file = "freeman_models.rda", compress = "xz") # save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models2.rda", compress = "bzip2") # tools::resaveRdaFiles("freeman_models1.rda") # afex/inst/doc/introduction-mixed-models.pdf.asis0000644000176200001440000000027713351525342021467 0ustar liggesusers%\VignetteIndexEntry{An Introduction to Mixed Models for Experimental Psychology} %\VignetteEngine{R.rsp::asis} %\VignetteKeyword{PDF} %\VignetteKeyword{vignette} %\VignetteKeyword{package} afex/inst/doc/afex_plot_introduction.Rmd0000644000176200001440000006345713607676143020201 0ustar liggesusers--- title: "afex_plot: Publication Ready Plots for Experimental Designs" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{afex_plot: Publication Ready Plots for Experimental Designs} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` `afex_plot()` visualizes results from factorial experiments combining estimated marginal means and uncertainties associated with the estimated means in the foreground with a depiction of the raw data in the background. Currently, `afex_plots()` supports the following models: - ANOVAs estimated with `aov_car()`, `aov_ez()`, or `aov_4()` (i.e., objects of class `"afex_aov"`) - Linear mixed models estimated with `mixed()` (i.e., objects of class `"mixed"`) - Linear mixed models estimated with `lme4::lmer` (i.e., objects of class `"merMod"`) This document provides an overview of the plots possible with `afex_plot()`. It does so mostly using the `afex_plot()` examples, see `?afex_plot`. We begin by loading `afex` and [`ggplot2`](https://ggplot2.tidyverse.org/) which is the package `afex_plot()` uses for plotting. Loading `ggplot2` explicitly is not strictly necessary, but makes the following code nicer. Otherwise, we would need to prepend each call to a function from `ggplot2` needed for customization with `ggplot2::` (as is done in the examples in `?afex_plot`). We also load the [`cowplot`](https://cran.r-project.org/package=cowplot) package ([introduction](https://cran.r-project.org/package=cowplot/vignettes/introduction.html)) which makes combining plots (with functions `plot_grid()` and `legend()`) very easy. However, loading `cowplot` sets a different theme for `ggplot2` plots than the default grey one. Although I am not a big fan of the default theme with its grey background, we reset the theme globally using `theme_set(theme_grey())` to start with the default behavior if `cowplot` it not attached. Note that `cowplot` also has the cool `draw_plot()` function which allows embedding plots within other plots. We furthermore will need the following packages, however, we will not attach them directly, but only call a few selected functions using the `package::function` notation. - [`jtools`](https://cran.r-project.org/package=jtools) for `theme_apa()` - [`ggpubr`](https://cran.r-project.org/package=jtools) for `theme_pubr()` - [`ggbeeswarm`](https://cran.r-project.org/package=ggbeeswarm) for producing bee swarm plots with `geom_beeswarm` - [`ggpol`](https://cran.r-project.org/package=ggpol) for producing combined box plots and jitter plots using `geom_boxjitter()` ```{r message=FALSE, warning=FALSE} library("afex") library("ggplot2") library("cowplot") theme_set(theme_grey()) ``` # Two-Way Within-Subjects ANOVA We begin with a two-way within-subjects ANOVA using synthetic data from Maxwell and Delaney (2004, p. 547). The data are hypothetical reaction times from a 2 x 3 Perceptual Experiment with factors `angle` with 3 levels and factor `noise` with 2 levels (see `?md_12.1` for a longer description). We first load the data and then fit the corresponding ANOVA. ```{r} data(md_12.1) (aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"))) ``` The ANOVA shows that both, the two main effect as well as the interaction, are significant. We therefore inspect the pattern underlying the interaction. There exist two different ways of plotting a 2-way interaction. Either of the two variables can be depicted on the x-axis. And before having looked at both cases, it is often not clear which visualization of the interaction is more instructive. Consequently, we plot both next to each other. For this we simply need to exchange which variable is the `x` factor and which is the `trace` factor. We then use `plot_grid()` to plot them next to each other. ## Basic Plot ```{r fig.width=9, fig.height=4} p_an <- afex_plot(aw, x = "angle", trace = "noise") p_na <- afex_plot(aw, x = "noise", trace = "angle") plot_grid(p_an, p_na) ## try adding: labels = "AUTO" ``` Before we can even take a look at the plot, we notice that creating the plots has produced two warnings. These warnings complain that the plots depict within-subject factors, but do not use within-subject error bars. However, the warnings also tell us the solution (i.e., adding `error = "within"`), which we will do in the following. The help page `?afex_plot` contains more information on which type of error bars are appropriate in which situation and how to interpret different type of error bars. For ANOVAs, `afex_plot()` will emit warnings if it thinks the error bars are not appropriate for the chosen factors. Comparing both plots, my impression is that the plot with `angle` on the `x`-axis tells the clearer story. We can see that when `noise` is `absent` there is hardly any effect of the increase of `angle`. However, if `noise` is `present` an increasing `angle` clearly leads to increased RTs. We therefore use this plot in the following. ## Exploring Graphical Options and Themes We now produce a new variant of the left plot using more appropriate error bars and change several other graphical details which make the plot publication ready. We use the `factor_levels` argument to `afex_plot()` for renaming the factor levels (for technical reasons the ANOVA functions in `afex` transform all factor levels to proper `R` variable names using `make.names()` which changed the labels from e.g., `4` to `X4`) and the `legend_title` argument for changing the title of the legend. We also change the labels on the `x` and `y` axis. ```{r} p_an <- afex_plot(aw, x = "angle", trace = "noise", error = "within", factor_levels = list(angle = c("0°", "4°", "8°"), noise = c("Absent", "Present")), legend_title = "Noise") + labs(y = "RTs (in ms)", x = "Angle (in degrees)") ``` As the additional output shows, changing the factor levels via `factor_levels` emits a `message` detailing old and new factor levels in the form `old -> new`. This message can be suppressed by wrapping the `afex_plot()` call into a `suppressMessages()` call or via `RMarkdown` settings. Note that we could have also used the `factor_levels` argument for changing the order of the factor levels by passing a named character vector (e.g., `factor_levels = list(angle = c(X8 = "8°", X4 = "4°", X0 = "0°"))`). This would change the order either on the x-axis or in the legend. As said above, I am not a big fan of the default grey theme of `ggplot2` plots. Consequently, we compare a number of different themes for this plot in the following. For all but `ggpubr::theme_pubr()`, we also move the legend to the bottom as this better allows the plot to cover only a single column in a two-column layout. `ggpubr::theme_pubr()` automatically plots the legend on top. ```{r fig.width=8.5, fig.height=6, dpi = 150} plot_grid( p_an + theme_bw() + theme(legend.position="bottom"), p_an + theme_light() + theme(legend.position="bottom"), p_an + theme_minimal() + theme(legend.position="bottom"), p_an + jtools::theme_apa() + theme(legend.position="bottom"), p_an + ggpubr::theme_pubr(), p_an + theme_cowplot() + theme(legend.position="bottom"), labels = "AUTO" ) ``` The first row, panels A to C, shows themes coming with `ggplot2` and the second row, panels D to F, shows themes from additional packages. In my opinion all of these plots are an improvement above the default grey theme. For the themes coming with `ggplot2`, I really like that those shown here have a reference grid in the background. This often makes it easier to judge the actual values the shown data points have. I know that many people find this distracting, so many of the contributed themes do not have this grid. One thing I really like about the last two themes is that they per default use larger font sizes for the axes labels. One way to achieve something similar for most themes is to change `base_size`. One general criticism I have with the current plots is that they show too many values on the y-axis. In the following I plot one more variant of this plot in which we change this to three values on the y-axis. We also increase the axes labels and remove the vertical grid lines. ```{r fig.width=3.5, fig.height=3, dpi = 150, out.width='50%'} p_an + scale_y_continuous(breaks=seq(400, 900, length.out = 3)) + theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank()) ``` We can also set this theme for the reminder of the `R` session with `theme_set()`. ```{r} theme_set(theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank())) ``` ## Saving Plots and Plot Sizes To get our plot into a publication, we need to export it as a graphics file. I would generally advise against exporting plots via the `RStudio` interface as this is not reproducible. Instead I would use some of the following functions which save the document in the current working directory. Note that following [Elsevier guidelines](https://www.elsevier.com/authors/author-schemas/artwork-and-media-instructions/artwork-sizing), a single column figure should have a width of 9 cm (~ 3 inch) and a two column figure should have a width of 19 cm (~ 7.5 inch). For Word or similar documents I would export the plot as a `png` (never `jpg`): ```{r, eval=FALSE} ggsave("my_plot.png", device = "png", width = 9, height = 8, units = "cm", dpi = 600) ## the higher the dpi, the better the resolution ``` For `LaTeX` I would export as `pdf`: ```{r, eval=FALSE} ggsave("my_plot.pdf", device = "pdf", width = 9, height = 8, units = "cm") ``` ## Data in the Background `afex_plot()` per default plots the raw data in the background. It does so using an [alpha blending](https://en.wikipedia.org/wiki/Alpha_compositing#Alpha_blending) of `0.5`. Thus, overlapping points appear darker. Examples of this can be seen in the previous graphs where some data points in the background appear clearly darker than others. The darker points indicate values for which several data points lie exactly on top of each other. `afex_plot()` provides the possibility to change or alter the graphical primitive, called `geom` in `ggplot2` parlance, used for plotting the points in the background. This offers a vast array of options for handling overlapping points or, more generally, how to display the raw data in the background. I show some of these examples in the following. The first two variants display only points, whereas the remaining ones use different visualizations of the raw data. Note that depending on the specific variant we change a few further plot options to obtain a visually pleasing result. For example, the `dodge` argument controls the spread of points belonging to different levels of the `trace` factor at each x-axis position. 1. Add jitter on the y-axis to points which avoids perfect overlap. 2. Display points using a bee swarm plot, which displaces overlapping points on the x-axis: `ggbeeswarm::geom_beeswarm` 3. Size of points show number of data points at a given y-axis position: `geom_count`. For this geom, adding a call to `scale_size_area()` can sometimes be beneficial. 3. Violin plot: `geom_violin` 4. Box plot: `geom_boxplot`. Note that for this plot we have added `linetype = 1` to `data_arg`, which avoids that the outline of the box plots is affected by the linetype mapping (this is in contrast with the violin plot). 5. Combine box plot with jittered points: `ggpol::geom_boxjitter` ```{r fig.width=8.5, fig.height=12, dpi = 150} p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 10, dodge.width = 0.3 ## needs to be same as dodge ), color = "darkgrey")) p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8, color = "darkgrey")) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = geom_count) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3, linetype = 1)) p6 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0)) plot_grid(p1, p2, p3, p4, p5, p6, ncol = 2, labels = 1:6) ``` ## Adding Color to Plots So far, all plots were shown in black and white only. However, it is easy to include color. We do so for plots 2 to 5 from above. To achieve this, we have to change the value of the `mapping` argument. ```{r fig.width=8.5, fig.height=8, dpi = 150} p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, mapping = c("shape", "color"), data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8)) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("linetype", "shape", "fill"), data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("shape", "fill"), data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), line_arg = list(linetype = 0), error_arg = list(size = 1.5, width = 0)) plot_grid(p2, p3, p4, p5, ncol = 2, labels = 2:5) ``` ## Plotting Order and Error Bars For graphical element in the foreground, `afex_plot` first plots all graphical elements belonging to the same factor level before plotting graphical elements belonging to different factor levels. This provides a consistent graphical impression for each factor level that is particularly relevant in case color is mapped. In case we have overlapping lines and error bars or use thick lines, we sometimes do not want that the error bars also receives different line types. In this case, we can simply pass `linetype = 1` to `error_arg` to overwrite the corresponding mapping. This is shown in the right plot. ```{r fig.width=8.5, fig.height=4, dpi = 150} p1 <- afex_plot(aw, x = "noise", trace = "angle", mapping = "color", error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2)) p2 <- afex_plot(aw, x = "noise", trace = "angle", mapping = c("color", "shape", "linetype"), error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2, width = 0, linetype = 1)) plot_grid(p1, p2, ncol = 2) ``` ## One-way Plots Without Trace Factor If `afex_plot` is called without a trace factor, a one-way plot is created. We can customize this plot in very much the same way. Per default a one-way plot contains a legend if `mapping` is not empty (i.e., `""`). We show this legend for the left plot, but suppress it for the right one. ```{r fig.width=7, fig.height=3.5, message=FALSE} po1 <- afex_plot(aw, x = "angle", mapping = "color", error = "within", data_arg = list(), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) po2 <- afex_plot(aw, x = "angle", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") plot_grid(po1, po2) ``` One-way plots can also be split across different panels by specifying a `panel` factor: ```{r fig.width=7, fig.height=3.5, message=FALSE} afex_plot(aw, x = "angle", panel = "noise", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") ``` Sometimes we still want to add a line connecting the estimated marginal means. As `afex_plot` returns a `ggplot2` object, we can do this easily by adding a `geom_line()` object to the call. As we want to add a line through all of the shown points in the foreground, we need to add the corresponding groups aesthetics to this call: `geom_line(aes(group = 1))`. We can add further arguments to this call, as shown in the left panel below. ```{r fig.width=7, fig.height=3.5, message=FALSE} plot_grid( po1 + geom_line(aes(group = 1), color = "darkgrey", size = 1.5), po2 + geom_line(aes(group = 1)) ) ``` # 3-Way Mixed Model ## Data and Model ```{r, eval=FALSE, echo=FALSE, results='hide'} data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### following model should take less than a minute to fit: mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ (task||item), fhch, method = "S", expand_re = TRUE) save(mrt, file = "../inst/extdata/freeman_reduced_model.rda", compress = "xz") ``` To exemplify the support for linear mixed models, we will use the data from Freeman and colleagues also discussed in the [mixed model vignette](https://cran.r-project.org/package=afex/vignettes/afex_mixed_example.html). These data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The dependent variable we are interested in is `log` RTs. Here, we are only looking at a reduced design with factors `task` (between participants, but within items), `stimulus`, and `frequency` (within participants, but between items), for a total of almost 13,000 observations. We fit the model with crossed-random effects for participants (`id`) and `item`s with maximal random-slopes. To reduce computation time we suppress the correlations among random-effects parameters. ```{r, eval=FALSE} data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors ### following model should take less than a minute to fit: mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ (task||item), fhch, method = "S", expand_re = TRUE) ``` Instead of fitting the model, you can also load the fitted model. We also disable calculation of degrees of freedom for `emmeans` as this speeds up computation and/or avoids messages we are currently not interested in. ```{r} load(system.file("extdata/", "freeman_reduced_model.rda", package = "afex")) emmeans::emm_options(lmer.df = "asymptotic") ``` The ANOVA table of the mixed model indicates that the three-way interaction is significant on which we focus in the following. ```{r} mrt ``` ## Which Data to Plot in the Background For mixed models, one important decision is the random-effects grouping factor(s) based on which the raw data plotted in the background is aggregated. This decision is necessary, because without such a factor, there would only be one observation for each cell of the design (unless the full design is considered). In the default setting, with `id` missing, the combination of all random-effects grouping factor is used. ```{r fig.width=7, fig.height=3.5} afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task") ``` In the present case, a message informs us that the data is aggregated over both random-effects grouping factors. However, this leads to way too many data points in the background. Let us compare this plot with plots in which we use each of the two random-effects grouping factors in turn. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item"), labels = c("ID", "Item") ) ``` The by-id plot looks usable. However, the by-item plot has still way too many data-points to be informative. Some other ways of displaying the raw data, such as violin plots or box plots, seems preferable for it. ## Ways of Plotting Data in the Background We compare violin plots or box plots for the by-item data in the next plot. For the box plot, we increase the width of the error bars and use a consistent line type to distinguish them more easily from the graphical elements of the box plot. We could probably further improve these plots by, for example, adding colors or using some of the other customizations discussed above for the ANOVA example. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_violin, data_arg = list(width = 0.5)), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_boxplot, data_arg = list(width = 0.5), error_arg = list(size = 1.5, width = 0, linetype = 1)) ) ``` ## Error Bars for Mixed Models The default error bars for `afex_plot()` are based on the statistical model (i.e., the mixed model in the present case). These error bars can only be used to judge whether or not two means differ from each other, if the corresponding factor (or factors) are independent samples factors (i.e., not repeated-measures factors for any of the random-effects grouping factors). Of course, in addition to this the requirement of approximately equal sample size and variance also needs to hold. In the present case, all of the factors are repeated-measures factors with respect to one of the random-effects grouping factors. Consequently, the default error bars cannot be used for "inference by eye" for any of the factors. This is also easy to see when looking at all pairwise comparisons between means for each of the panels/tasks. This shows that for the `naming` task all comparisons are significant. In visual contrast with that, the two error bars for the `low` versus `high` `word`s are overlapping very strongly. ```{r} pairs(emmeans::emmeans(mrt, c("stimulus", "frequency"), by = "task")) ``` An alternative in the present situation would be using within-subjects error bars and aggregating the data by-id (i.e., `error = "within"`), as done in the left panel below. This is somewhat appropriate here as the factors within each panel are all within-subject factors. In contrast, using by-item within-subjects error bars, as done in the right panel below, seems not appropriate as the only within-item factor, `task`, is spread across panels. Unfortunately, it is not immediately clear if these error bars allow one to correctly detect, which means do not differ from each other. ```{r fig.width=7, fig.height=3.5} plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id", error = "within"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, error = "within", data_geom = geom_violin, data_arg = list(width = 0.5)) ) ``` In sum, using error bars for performing "inference by eye" - that is, using overlap or non-overlap of error bars to judge which means differ or do not differ from each other - is highly problematic for mixed models, due to the potentially complex dependency structures between the means. It would be best to avoid comparisons between means altogether. Instead, it is perhaps a good idea to plot the model-based error bars (which is the default) and use them for their intended purpose; judging which values of the estimated means are likely given what we have learned from the model (however, note that one cannot interpret a 95% confidence interval as having a 95% probability of containing the population mean). The help page `?afex_plot` contains further information and references on how to interpret confidence intervals and other error bars. # References * Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. _Journal of Memory and Language_, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004 * Maxwell, S. E., & Delaney, H. D. (2004). _Designing Experiments and Analyzing Data: A Model-Comparisons Perspective._ Mahwah, N.J.: Lawrence Erlbaum Associates. afex/inst/doc/afex_plot_introduction.html0000644000176200001440000462302313607677004020413 0ustar liggesusers afex_plot: Publication Ready Plots for Experimental Designs

afex_plot: Publication Ready Plots for Experimental Designs

Henrik Singmann

2020-01-15

afex_plot() visualizes results from factorial experiments combining estimated marginal means and uncertainties associated with the estimated means in the foreground with a depiction of the raw data in the background. Currently, afex_plots() supports the following models:

  • ANOVAs estimated with aov_car(), aov_ez(), or aov_4() (i.e., objects of class "afex_aov")
  • Linear mixed models estimated with mixed() (i.e., objects of class "mixed")
  • Linear mixed models estimated with lme4::lmer (i.e., objects of class "merMod")

This document provides an overview of the plots possible with afex_plot(). It does so mostly using the afex_plot() examples, see ?afex_plot. We begin by loading afex and ggplot2 which is the package afex_plot() uses for plotting. Loading ggplot2 explicitly is not strictly necessary, but makes the following code nicer. Otherwise, we would need to prepend each call to a function from ggplot2 needed for customization with ggplot2:: (as is done in the examples in ?afex_plot).

We also load the cowplot package (introduction) which makes combining plots (with functions plot_grid() and legend()) very easy. However, loading cowplot sets a different theme for ggplot2 plots than the default grey one. Although I am not a big fan of the default theme with its grey background, we reset the theme globally using theme_set(theme_grey()) to start with the default behavior if cowplot it not attached. Note that cowplot also has the cool draw_plot() function which allows embedding plots within other plots.

We furthermore will need the following packages, however, we will not attach them directly, but only call a few selected functions using the package::function notation.

  • jtools for theme_apa()
  • ggpubr for theme_pubr()
  • ggbeeswarm for producing bee swarm plots with geom_beeswarm
  • ggpol for producing combined box plots and jitter plots using geom_boxjitter()
library("afex")     
library("ggplot2")  
library("cowplot")
theme_set(theme_grey())

Two-Way Within-Subjects ANOVA

We begin with a two-way within-subjects ANOVA using synthetic data from Maxwell and Delaney (2004, p. 547). The data are hypothetical reaction times from a 2 x 3 Perceptual Experiment with factors angle with 3 levels and factor noise with 2 levels (see ?md_12.1 for a longer description). We first load the data and then fit the corresponding ANOVA.

data(md_12.1)
(aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise")))
## Anova Table (Type 3 tests)
## 
## Response: rt
##        Effect          df     MSE         F ges p.value
## 1       angle 1.92, 17.31 3702.02 40.72 *** .39  <.0001
## 2       noise        1, 9 8460.00 33.77 *** .39   .0003
## 3 angle:noise 1.81, 16.27 1283.22 45.31 *** .19  <.0001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG

The ANOVA shows that both, the two main effect as well as the interaction, are significant. We therefore inspect the pattern underlying the interaction. There exist two different ways of plotting a 2-way interaction. Either of the two variables can be depicted on the x-axis. And before having looked at both cases, it is often not clear which visualization of the interaction is more instructive. Consequently, we plot both next to each other. For this we simply need to exchange which variable is the x factor and which is the trace factor. We then use plot_grid() to plot them next to each other.

Basic Plot

p_an <- afex_plot(aw, x = "angle", trace = "noise") 
## Warning: Panel(s) show within-subjects factors, but not within-subjects error bars.
## For within-subjects error bars use: error = "within"
p_na <- afex_plot(aw, x = "noise", trace = "angle")
## Warning: Panel(s) show within-subjects factors, but not within-subjects error bars.
## For within-subjects error bars use: error = "within"
plot_grid(p_an, p_na)  ## try adding: labels = "AUTO"

Before we can even take a look at the plot, we notice that creating the plots has produced two warnings. These warnings complain that the plots depict within-subject factors, but do not use within-subject error bars. However, the warnings also tell us the solution (i.e., adding error = "within"), which we will do in the following. The help page ?afex_plot contains more information on which type of error bars are appropriate in which situation and how to interpret different type of error bars. For ANOVAs, afex_plot() will emit warnings if it thinks the error bars are not appropriate for the chosen factors.

Comparing both plots, my impression is that the plot with angle on the x-axis tells the clearer story. We can see that when noise is absent there is hardly any effect of the increase of angle. However, if noise is present an increasing angle clearly leads to increased RTs. We therefore use this plot in the following.

Exploring Graphical Options and Themes

We now produce a new variant of the left plot using more appropriate error bars and change several other graphical details which make the plot publication ready. We use the factor_levels argument to afex_plot() for renaming the factor levels (for technical reasons the ANOVA functions in afex transform all factor levels to proper R variable names using make.names() which changed the labels from e.g., 4 to X4) and the legend_title argument for changing the title of the legend. We also change the labels on the x and y axis.

p_an <- afex_plot(aw, x = "angle", trace = "noise", error = "within",
                  factor_levels = list(angle = c("0°", "4°", "8°"),
                                    noise = c("Absent", "Present")), 
                  legend_title = "Noise") +
  labs(y = "RTs (in ms)", x = "Angle (in degrees)")
## Renaming/reordering factor levels of 'angle':
##   X0 -> 0°
##   X4 -> 4°
##   X8 -> 8°
## Renaming/reordering factor levels of 'noise':
##   absent -> Absent
##   present -> Present

As the additional output shows, changing the factor levels via factor_levels emits a message detailing old and new factor levels in the form old -> new. This message can be suppressed by wrapping the afex_plot() call into a suppressMessages() call or via RMarkdown settings. Note that we could have also used the factor_levels argument for changing the order of the factor levels by passing a named character vector (e.g., factor_levels = list(angle = c(X8 = "8°", X4 = "4°", X0 = "0°"))). This would change the order either on the x-axis or in the legend.

As said above, I am not a big fan of the default grey theme of ggplot2 plots. Consequently, we compare a number of different themes for this plot in the following. For all but ggpubr::theme_pubr(), we also move the legend to the bottom as this better allows the plot to cover only a single column in a two-column layout. ggpubr::theme_pubr() automatically plots the legend on top.

plot_grid(
  p_an + theme_bw() + theme(legend.position="bottom"),
  p_an + theme_light() + theme(legend.position="bottom"),
  p_an + theme_minimal() + theme(legend.position="bottom"),
  p_an + jtools::theme_apa() + theme(legend.position="bottom"),
  p_an + ggpubr::theme_pubr(),
  p_an + theme_cowplot() + theme(legend.position="bottom"),
  labels = "AUTO"
)  

The first row, panels A to C, shows themes coming with ggplot2 and the second row, panels D to F, shows themes from additional packages. In my opinion all of these plots are an improvement above the default grey theme. For the themes coming with ggplot2, I really like that those shown here have a reference grid in the background. This often makes it easier to judge the actual values the shown data points have. I know that many people find this distracting, so many of the contributed themes do not have this grid. One thing I really like about the last two themes is that they per default use larger font sizes for the axes labels. One way to achieve something similar for most themes is to change base_size.

One general criticism I have with the current plots is that they show too many values on the y-axis. In the following I plot one more variant of this plot in which we change this to three values on the y-axis. We also increase the axes labels and remove the vertical grid lines.

p_an + 
  scale_y_continuous(breaks=seq(400, 900, length.out = 3)) +
  theme_bw(base_size = 15) + 
  theme(legend.position="bottom", 
        panel.grid.major.x = element_blank())

We can also set this theme for the reminder of the R session with theme_set().

theme_set(theme_bw(base_size = 15) + 
            theme(legend.position="bottom", 
                  panel.grid.major.x = element_blank()))

Saving Plots and Plot Sizes

To get our plot into a publication, we need to export it as a graphics file. I would generally advise against exporting plots via the RStudio interface as this is not reproducible. Instead I would use some of the following functions which save the document in the current working directory. Note that following Elsevier guidelines, a single column figure should have a width of 9 cm (~ 3 inch) and a two column figure should have a width of 19 cm (~ 7.5 inch).

For Word or similar documents I would export the plot as a png (never jpg):

ggsave("my_plot.png", device = "png", 
       width = 9, height = 8, units = "cm", 
       dpi = 600) ## the higher the dpi, the better the resolution

For LaTeX I would export as pdf:

ggsave("my_plot.pdf", device = "pdf", 
       width = 9, height = 8, units = "cm") 

Data in the Background

afex_plot() per default plots the raw data in the background. It does so using an alpha blending of 0.5. Thus, overlapping points appear darker. Examples of this can be seen in the previous graphs where some data points in the background appear clearly darker than others. The darker points indicate values for which several data points lie exactly on top of each other.

afex_plot() provides the possibility to change or alter the graphical primitive, called geom in ggplot2 parlance, used for plotting the points in the background. This offers a vast array of options for handling overlapping points or, more generally, how to display the raw data in the background. I show some of these examples in the following.

The first two variants display only points, whereas the remaining ones use different visualizations of the raw data. Note that depending on the specific variant we change a few further plot options to obtain a visually pleasing result. For example, the dodge argument controls the spread of points belonging to different levels of the trace factor at each x-axis position.

  1. Add jitter on the y-axis to points which avoids perfect overlap.
  2. Display points using a bee swarm plot, which displaces overlapping points on the x-axis: ggbeeswarm::geom_beeswarm
  3. Size of points show number of data points at a given y-axis position: geom_count. For this geom, adding a call to scale_size_area() can sometimes be beneficial.
  4. Violin plot: geom_violin
  5. Box plot: geom_boxplot. Note that for this plot we have added linetype = 1 to data_arg, which avoids that the outline of the box plots is affected by the linetype mapping (this is in contrast with the violin plot).
  6. Combine box plot with jittered points: ggpol::geom_boxjitter
p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3,
                data_arg = list(
                  position = 
                    ggplot2::position_jitterdodge(
                      jitter.width = 0, 
                      jitter.height = 10, 
                      dodge.width = 0.3  ## needs to be same as dodge
                    ),
                  color = "darkgrey"))
p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5,
                data_geom = ggbeeswarm::geom_beeswarm,
                data_arg = list(
                  dodge.width = 0.5,  ## needs to be same as dodge
                  cex = 0.8,
                  color = "darkgrey"))
p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5,
                data_geom = geom_count)
p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", 
                data_geom = ggplot2::geom_violin, 
                data_arg = list(width = 0.5))
p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", 
                data_geom = ggplot2::geom_boxplot, 
                data_arg = list(width = 0.3, linetype = 1))
p6 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, 
                data_geom = ggpol::geom_boxjitter, 
                data_arg = list(
                  width = 0.5, 
                  jitter.width = 0,
                  jitter.height = 10,
                  outlier.intersect = TRUE),
                point_arg = list(size = 2.5), 
                error_arg = list(size = 1.5, width = 0))
plot_grid(p1, p2, p3, p4, p5, p6, ncol = 2, labels = 1:6)  

Adding Color to Plots

So far, all plots were shown in black and white only. However, it is easy to include color. We do so for plots 2 to 5 from above. To achieve this, we have to change the value of the mapping argument.

p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5,
                mapping = c("shape", "color"),
                data_geom = ggbeeswarm::geom_beeswarm,
                data_arg = list(
                  dodge.width = 0.5,  ## needs to be same as dodge
                  cex = 0.8))
p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", 
                mapping = c("linetype", "shape", "fill"),
                data_geom = ggplot2::geom_violin, 
                data_arg = list(width = 0.5))
p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", 
                mapping = c("shape", "fill"),
                data_geom = ggplot2::geom_boxplot, 
                data_arg = list(width = 0.3))
p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7,
                mapping = c("shape", "fill"),
                data_geom = ggpol::geom_boxjitter, 
                data_arg = list(
                  width = 0.5, 
                  jitter.width = 0,
                  jitter.height = 10,
                  outlier.intersect = TRUE),
                point_arg = list(size = 2.5), 
                line_arg = list(linetype = 0),
                error_arg = list(size = 1.5, width = 0))
plot_grid(p2, p3, p4, p5, ncol = 2, labels = 2:5) 

Plotting Order and Error Bars

For graphical element in the foreground, afex_plot first plots all graphical elements belonging to the same factor level before plotting graphical elements belonging to different factor levels. This provides a consistent graphical impression for each factor level that is particularly relevant in case color is mapped.

In case we have overlapping lines and error bars or use thick lines, we sometimes do not want that the error bars also receives different line types. In this case, we can simply pass linetype = 1 to error_arg to overwrite the corresponding mapping. This is shown in the right plot.

p1 <- afex_plot(aw, x = "noise", trace = "angle", mapping = "color", 
                error = "within", 
                point_arg = list(size = 5), line_arg = list(size = 2),
                error_arg = list(size = 2))
p2 <- afex_plot(aw, x = "noise", trace = "angle", 
                mapping = c("color", "shape", "linetype"), 
                error = "within", 
                point_arg = list(size = 5), line_arg = list(size = 2),
                error_arg = list(size = 2, width = 0, linetype = 1))
plot_grid(p1, p2, ncol = 2)

One-way Plots Without Trace Factor

If afex_plot is called without a trace factor, a one-way plot is created. We can customize this plot in very much the same way. Per default a one-way plot contains a legend if mapping is not empty (i.e., ""). We show this legend for the left plot, but suppress it for the right one.

po1 <- afex_plot(aw, x = "angle", mapping = "color", error = "within", 
                 data_arg = list(),
                 point_arg = list(size = 2.5), 
                 error_arg = list(size = 1.5, width = 0.05)) 
po2 <- afex_plot(aw, x = "angle", error = "within", 
                 data_geom = ggpol::geom_boxjitter, 
                 mapping = "fill", data_alpha = 0.7, 
                 data_arg = list(
                   width = 0.6, 
                   jitter.width = 0.05,
                   jitter.height = 10,
                   outlier.intersect = TRUE
                 ),
                 point_arg = list(size = 2.5), 
                 error_arg = list(size = 1.5, width = 0.05)) +
  theme(legend.position="none")
plot_grid(po1, po2) 

One-way plots can also be split across different panels by specifying a panel factor:

afex_plot(aw, x = "angle", panel = "noise", error = "within",
          data_geom = ggpol::geom_boxjitter,
          mapping = "fill", data_alpha = 0.7,
          data_arg = list(
            width = 0.6,
            jitter.width = 0.05,
            jitter.height = 10,
            outlier.intersect = TRUE
          ),
          point_arg = list(size = 2.5),
          error_arg = list(size = 1.5, width = 0.05)) +
  theme(legend.position="none")

Sometimes we still want to add a line connecting the estimated marginal means. As afex_plot returns a ggplot2 object, we can do this easily by adding a geom_line() object to the call. As we want to add a line through all of the shown points in the foreground, we need to add the corresponding groups aesthetics to this call: geom_line(aes(group = 1)). We can add further arguments to this call, as shown in the left panel below.

plot_grid(
  po1 + geom_line(aes(group = 1), color = "darkgrey", size = 1.5), 
  po2 + geom_line(aes(group = 1))
) 

3-Way Mixed Model

Data and Model

To exemplify the support for linear mixed models, we will use the data from Freeman and colleagues also discussed in the mixed model vignette. These data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The dependent variable we are interested in is log RTs. Here, we are only looking at a reduced design with factors task (between participants, but within items), stimulus, and frequency (within participants, but between items), for a total of almost 13,000 observations. We fit the model with crossed-random effects for participants (id) and items with maximal random-slopes. To reduce computation time we suppress the correlations among random-effects parameters.

data("fhch2010") # load 
fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors
### following model should take less than a minute to fit:
mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+
               (task||item), fhch, method = "S", expand_re = TRUE)

Instead of fitting the model, you can also load the fitted model. We also disable calculation of degrees of freedom for emmeans as this speeds up computation and/or avoids messages we are currently not interested in.

load(system.file("extdata/", "freeman_reduced_model.rda", package = "afex"))
emmeans::emm_options(lmer.df = "asymptotic")

The ANOVA table of the mixed model indicates that the three-way interaction is significant on which we focus in the following.

mrt
## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: log_rt ~ task * stimulus * frequency + (stimulus * frequency || 
## Model:     id) + (task || item)
## Data: fhch
##                    Effect        df          F p.value
## 1                    task  1, 43.63  13.60 ***   .0006
## 2                stimulus  1, 51.14 150.25 ***  <.0001
## 3               frequency  1, 72.39       0.48     .49
## 4           task:stimulus  1, 53.69  70.64 ***  <.0001
## 5          task:frequency  1, 82.70  77.58 ***  <.0001
## 6      stimulus:frequency 1, 591.09  62.53 ***  <.0001
## 7 task:stimulus:frequency 1, 583.64 112.01 ***  <.0001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Which Data to Plot in the Background

For mixed models, one important decision is the random-effects grouping factor(s) based on which the raw data plotted in the background is aggregated. This decision is necessary, because without such a factor, there would only be one observation for each cell of the design (unless the full design is considered). In the default setting, with id missing, the combination of all random-effects grouping factor is used.

afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task") 
## Aggregating data over: item, id

In the present case, a message informs us that the data is aggregated over both random-effects grouping factors. However, this leads to way too many data points in the background. Let us compare this plot with plots in which we use each of the two random-effects grouping factors in turn.

plot_grid( 
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "id"), 
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "item"), 
  labels = c("ID", "Item") 
)

The by-id plot looks usable. However, the by-item plot has still way too many data-points to be informative. Some other ways of displaying the raw data, such as violin plots or box plots, seems preferable for it.

Ways of Plotting Data in the Background

We compare violin plots or box plots for the by-item data in the next plot. For the box plot, we increase the width of the error bars and use a consistent line type to distinguish them more easily from the graphical elements of the box plot. We could probably further improve these plots by, for example, adding colors or using some of the other customizations discussed above for the ANOVA example.

plot_grid( 
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "item", dodge = 0.8,
            data_geom = geom_violin, 
            data_arg = list(width = 0.5)), 
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "item", dodge = 0.8,
            data_geom = geom_boxplot, 
            data_arg = list(width = 0.5),
            error_arg = list(size = 1.5, width = 0, linetype = 1))
)

Error Bars for Mixed Models

The default error bars for afex_plot() are based on the statistical model (i.e., the mixed model in the present case). These error bars can only be used to judge whether or not two means differ from each other, if the corresponding factor (or factors) are independent samples factors (i.e., not repeated-measures factors for any of the random-effects grouping factors). Of course, in addition to this the requirement of approximately equal sample size and variance also needs to hold. In the present case, all of the factors are repeated-measures factors with respect to one of the random-effects grouping factors. Consequently, the default error bars cannot be used for “inference by eye” for any of the factors.

This is also easy to see when looking at all pairwise comparisons between means for each of the panels/tasks. This shows that for the naming task all comparisons are significant. In visual contrast with that, the two error bars for the low versus high words are overlapping very strongly.

pairs(emmeans::emmeans(mrt, c("stimulus", "frequency"), by = "task"))
## task = naming:
##  contrast                   estimate     SE  df z.ratio p.value
##  word,low - nonword,low      -0.1799 0.0247 Inf  -7.276 <.0001 
##  word,low - word,high         0.0586 0.0167 Inf   3.515 0.0025 
##  word,low - nonword,high     -0.3867 0.0260 Inf -14.877 <.0001 
##  nonword,low - word,high      0.2385 0.0260 Inf   9.181 <.0001 
##  nonword,low - nonword,high  -0.2069 0.0167 Inf -12.364 <.0001 
##  word,high - nonword,high    -0.4454 0.0247 Inf -18.009 <.0001 
## 
## task = lexdec:
##  contrast                   estimate     SE  df z.ratio p.value
##  word low - nonword low      -0.0793 0.0227 Inf  -3.496 0.0027 
##  word low - word high         0.0634 0.0156 Inf   4.053 0.0003 
##  word low - nonword high      0.0299 0.0237 Inf   1.260 0.5887 
##  nonword low - word high      0.1426 0.0237 Inf   6.013 <.0001 
##  nonword low - nonword high   0.1091 0.0157 Inf   6.955 <.0001 
##  word high - nonword high    -0.0335 0.0225 Inf  -1.485 0.4464 
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 4 estimates

An alternative in the present situation would be using within-subjects error bars and aggregating the data by-id (i.e., error = "within"), as done in the left panel below. This is somewhat appropriate here as the factors within each panel are all within-subject factors. In contrast, using by-item within-subjects error bars, as done in the right panel below, seems not appropriate as the only within-item factor, task, is spread across panels. Unfortunately, it is not immediately clear if these error bars allow one to correctly detect, which means do not differ from each other.

plot_grid( 
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "id", error = "within"),
  afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", 
            id = "item", dodge = 0.8, error = "within",
            data_geom = geom_violin, 
            data_arg = list(width = 0.5))
)

In sum, using error bars for performing “inference by eye” - that is, using overlap or non-overlap of error bars to judge which means differ or do not differ from each other - is highly problematic for mixed models, due to the potentially complex dependency structures between the means. It would be best to avoid comparisons between means altogether. Instead, it is perhaps a good idea to plot the model-based error bars (which is the default) and use them for their intended purpose; judging which values of the estimated means are likely given what we have learned from the model (however, note that one cannot interpret a 95% confidence interval as having a 95% probability of containing the population mean).

The help page ?afex_plot contains further information and references on how to interpret confidence intervals and other error bars.

References

  • Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. Journal of Memory and Language, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004
  • Maxwell, S. E., & Delaney, H. D. (2004). Designing Experiments and Analyzing Data: A Model-Comparisons Perspective. Mahwah, N.J.: Lawrence Erlbaum Associates.
afex/inst/doc/afex_plot_supported_models.Rmd0000644000176200001440000004274713531256341021035 0ustar liggesusers--- title: "afex_plot: Supported Models" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{afex_plot: Supported Models} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) knitr::knit_hooks$set(document = function(x){ gsub("```\n*```r*\n*", "", x) }) ``` # Introduction `afex_plot()` visualizes results from factorial experiments and, more generally, data set with interactions of categorical/factor variables. It does so by combining estimated marginal means and uncertainties associated with these means in the foreground with a depiction of the raw data in the background. If models include continuous covariates, other approaches are recommended (e.g., such as implemented in package [`effects`](https://cran.r-project.org/package=effects) or by using the possibility of `afex_plot` [to return the data and build the plot on ones own](https://github.com/singmann/afex/issues/65)). This document provides an overview of the different models supported by `afex_plot()` in addition to the `afex` objects (i.e., `afex_aov` and `mixed`). In general, these are models which are supported by the [`emmeans`](https://cran.r-project.org/package=emmeans) package as the `afex_plot.default()` method uses `emmeans` to get the estimated marginal means. `afex_plot.default()` then guesses whether there are repeated measures or all samples are independent. Based on this guess (which can be changed via the `id` argument) data in the background is plotted. Calculation of error bars can also be based on this guess (but the default is to plot the model based error bars obtained from `emmeans`). For a generally introduction to the functionality of `afex_plot` see: [`afex_plot`: Publication Ready Plots for Experimental Designs](afex_plot_introduction.html) Throughout the document, we will need `afex` as well as `ggplot2`. In addition, we load [`cowplot`](https://cran.r-project.org/package=cowplot) for function `plot_grid()` (which allows to easily combine multiple `ggplot2` plots). In addition, we will set a somewhat nicer `ggplot2` theme. ```{r message=FALSE, warning=FALSE} library("afex") library("ggplot2") library("cowplot") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) ``` Importantly, we also set the contrasts for the current `R` session to sum-to-zero contrasts. For models that include interactions with categorical variables this generally produces estimates that are easier to interpret. ```{r} set_sum_contrasts() ``` Please note, the best way to export a figure is via `ggsave()` or a similar function call. For Word and similar document formats, `png` is a good file type, for `LaTeX` and similar document formats, `pdf` is a good file type. # Base R stats models: lm, glm `afex_plot()` generally supports models implemeneted via the `stats` package. Here I show the main model functions that work with independent samples. These models can be passed to `afex_plot` without specifying additional arguments. Most importantly, `lm` models work directly. For those we use the `warpbreaks` data. ```{r} warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks) ``` Note that `afex_plot` produces several messages that are shown here as comments below the corresponding calls. Important is maybe that `afex_plot` assumes all observations (i.e., rows) are independent. This is of course the case here. In addition, for the first plot we are informed that the presence of an interaction may lead to a misleading impression if only a lower-order effect (here a main effect) is shown. This message is produced by `emmeans` and passed through. ```{r fig.width=7, fig.height=3} p1 <- afex_plot(warp.lm, "tension") p2 <- afex_plot(warp.lm, "tension", "wool") plot_grid(p1, p2) ``` `glm` models also work without further setting. Here we first use a poisson GLM for which we need to generate the data. ```{r} ins <- data.frame( n = c(500, 1200, 100, 400, 500, 300), size = factor(rep(1:3,2), labels = c("S","M","L")), age = factor(rep(1:2, each = 3)), claims = c(42, 37, 1, 101, 73, 14)) ``` We can then fit the data and pass the model object as is. ```{r fig.width=3, fig.height=3} ins.glm <- glm(claims ~ size + age + offset(log(n)), data = ins, family = "poisson") afex_plot(ins.glm, "size", "age") ``` `afex_plot` also works with binomial GLMs for which we also first need to generate some data which we will then fit. ```{r} ## binomial glm adapted from ?predict.glm ldose <- factor(rep(0:5, 2)) numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16) sex <- factor(rep(c("M", "F"), c(6, 6))) SF <- numdead/20 ## dv should be a vector, no matrix budworm.lg <- glm(SF ~ sex*ldose, family = binomial, weights = rep(20, length(numdead))) ``` For this model, we will produce three plots we can then compare. The first only shows the main effect of one variable (`ldose`). The other show the interaction of the two variables. Because for binomial GLMs we then only have one data point (with several observations), the individual data points and mean cannot be distinguished. This is made clear in the ther two (panels B and C). ```{r fig.width=8, fig.height=3} a <- afex_plot(budworm.lg, "ldose") b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! c <- afex_plot(budworm.lg, "ldose", "sex", data_arg = list(size = 4, color = "red")) plot_grid(a, b, c, labels = "AUTO", nrow = 1) ``` # nlme mixed model Hot to use `afex_plot` for mixed models fitted with `afex::mixed` (or [`lme4`](https://cran.r-project.org/package=lme4) directly) is shown in the [other vignette](afex_plot_introduction.html). However, we can also use `afex_plot` for mixed models fitted with the older `nlme` package. For this, however we need to pass the data used for fitting via the `data` argument. We can change on which of the two nested factors the individual data points in the background are based via the `id` argument. This is shown below. ```{r fig.width=8, fig.height=6} ## nlme mixed model data(Oats, package = "nlme") Oats$nitro <- factor(Oats$nitro) oats.1 <- nlme::lme(yield ~ nitro * Variety, random = ~ 1 | Block / Variety, data = Oats) plot_grid( afex_plot(oats.1, "nitro", "Variety", data = Oats), # A afex_plot(oats.1, "nitro", "Variety", data = Oats), # B afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block"), # C afex_plot(oats.1, "nitro", data = Oats), # D afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")), # E afex_plot(oats.1, "nitro", data = Oats, id = "Block"), # F labels = "AUTO" ) ``` # glmmTMB Support for [`glmmTMB`](https://cran.r-project.org/package=glmmTMB) is also provided. Here we use an example data set for which we model zero-inflation as well as overdispersion. The latter is achieved with a variant of the negative binomial distribution. ```{r, eval=FALSE} library("glmmTMB") tmb <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) ``` ```{r, eval=FALSE, include=FALSE} library("glmmTMB") set_sum_contrasts() tmb <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) save(tmb, file = "inst/extdata/tmb_example_fit.rda", compress = "xz") ``` ```{r, echo=FALSE, include=FALSE} library("glmmTMB") data(Salamanders, package = "glmmTMB") load(system.file("extdata/", "tmb_example_fit.rda", package = "afex")) ``` `afex_plot` does not automatically detect the random-effect for `site`. This means that per default all `r nrow(Salamanders)` data points are shown. When plotting only one variable, in which the default `data_geom` is `ggbeeswarm::geom_beeswarm`, this can lead to rather ugly plots due to the zero inflation. This is shon in panel A below. In panel B, we address this by changing the geom to a violin plot. In panel C, we address this by aggregating the data within site, but still use the beeswarm plot. Note that for panel C it is necessary to pass the data via the `data` argument as otherwise `site` cannot be found for aggregation. ```{r fig.width=8, fig.height=3} plot_grid( afex_plot(tmb, "spp"), afex_plot(tmb, "spp", data_geom = geom_violin), afex_plot(tmb, "spp", id = "site", data = Salamanders), labels = "AUTO", nrow = 1 ) ``` When plotting both variables, the problem is somewhat hidden, because instead of beeswarm plots, semi-transparency (i.e., `alpha` < 1) is used to show overlapping points. In panel B we again make this clearer but this time by adding jitter (on both the y- and x-axis) and increasing the degree of semi-transparancy (i.e., decreasing alpha). ```{r fig.width=8.5, fig.height=3.5} a <- afex_plot(tmb, "spp", "mined") b <- afex_plot(tmb, "spp", "mined", data_alpha = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0.2, jitter.height = 0.5, dodge.width = 0.5 ## needs to be same as dodge ), color = "darkgrey")) plot_grid(a, b, labels = "AUTO") ``` For the final plot we also plot the interaction, but this time aggregate the individual-data within site. This allows us again to use a beeswarm plot (after decreasing the width of the "bees") and produces a relatively clear result. ```{r fig.width=5.5, fig.height=3.5} afex_plot(tmb, "spp", "mined", id = "site", data = Salamanders, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list(dodge.width = 0.5, cex = 0.4, color = "darkgrey") ) ``` # rstanarm `afex_plot()` also supports Bayesian models that are also supported via `emmeans`. For example, we can easily fit a binomial model with [`rstanarm`](https://cran.r-project.org/package=rstanarm). ```{r, eval=FALSE} library("rstanarm") ## requires resetting the ggplot2 theme theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) example_model <- stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) ``` We can directly pass this model to `afex_plot`. However, we also see quite some zeros leading to a not super nice plot. It looks a bit better using a violin plot for the raw data. ```{r, eval=FALSE} b1 <- afex_plot(example_model, "period") ## dv column detected: prob ## No id column passed. Assuming all rows are independent samples. b2 <- afex_plot(example_model, "period", data_geom = geom_violin) ## dv column detected: prob ## No id column passed. Assuming all rows are independent samples. plot_grid(b1, b2, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} load(system.file("extdata/", "plots_rstanarm.rda", package = "afex")) plot_grid(b1, b2, labels = "AUTO") ``` We can also produce a plot based on the individual Bernoulli observations in the data. For this, we first need to expand the data such that we have one row per observation. With this, we can then fit the essentially same model as above. ```{r, eval=FALSE} cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$herd[i], period = cbpp$period[i], incidence = rep(0, cbpp$size[i]) ) cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 } cbpp_l <- do.call("rbind", cbpp_l) cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) example_model2 <- stan_glmer(incidence ~ period + (1|herd), data = cbpp_l, family = binomial, chains = 2, cores = 1, seed = 12345, iter = 500) ``` Again, this model can be directly passed to `afex_plot`. However, here we see even more 0 as the data is not yet aggregated. Consequently, we need to pass `id = "herd"` to aggregate the individual observations within each herd. ```{r, eval=FALSE} b3 <- afex_plot(example_model2, "period") ## dv column detected: incidence ## No id column passed. Assuming all rows are independent samples. b4 <- afex_plot(example_model2, "period", id = "herd") ## dv column detected: incidence plot_grid(b3, b4, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} plot_grid(b3, b4, labels = "AUTO") ``` We can of course also fit a model assuming a normal distribution using `rstanarm`. For example using the `Machines` data. ```{r, eval=FALSE} data("Machines", package = "MEMSS") mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) ``` As before, we can pass this model directly to `afex_plot` (see panel A). However, the data is again not aggregated within the grouping variable `Worker`. If we want to aggregate the individual data points for the grouping factor, we need to pass both the name of the grouping variable (`Worker`) and the data used for fitting. ```{r, eval=FALSE} b5 <- afex_plot(mm, "Machine") ## dv column detected: score ## No id column passed. Assuming all rows are independent samples. b6 <- afex_plot(mm, "Machine", id = "Worker") ## dv column detected: score plot_grid(b5, b6, labels = "AUTO") ``` ```{r fig.width=7, fig.height=3, echo=FALSE} plot_grid(b5, b6, labels = "AUTO") ``` ```{r, eval=FALSE, include=FALSE} library("rstanarm") ## requires resetting the ggplot2 theme library("ggplot2") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) set_sum_contrasts() cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) example_model <- stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) b1 <- afex_plot(example_model, "period") b2 <- afex_plot(example_model, "period", data_geom = geom_violin) cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$herd[i], period = cbpp$period[i], incidence = rep(0, cbpp$size[i]) ) cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 } cbpp_l <- do.call("rbind", cbpp_l) cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) example_model2 <- stan_glmer(incidence ~ period + (1|herd), data = cbpp_l, family = binomial, chains = 2, cores = 1, seed = 12345, iter = 500) b3 <- afex_plot(example_model2, "period") b4 <- afex_plot(example_model2, "period", id = "herd") data("Machines", package = "MEMSS") mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) b5 <- afex_plot(mm, "Machine") b6 <- afex_plot(mm, "Machine", id = "Worker", data = Machines) save(b1, b2, b3, b4, b5, b6, file = "../inst/extdata/plots_rstanarm.rda", compress = "xz", version = 2) ``` # brms We can also fit the `Machines` data using [`brms`](https://cran.r-project.org/package=brms). ```{r, eval=FALSE} library("brms") data("Machines", package = "MEMSS") mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) ``` However, to pass a `brms` object to `afex_plot` we need to pass both, the `data` used for fitting as well as the name of the dependent variable (here `score`) via the `dv` argument. We again build the plot such that the left panel shows the raw data without aggregation and the right panel shows the data aggregated within the grouping factor `Worker`. ```{r, eval=FALSE} bb1 <- afex_plot(mrt, "Machine", data = Machines, dv = "score") ## No id column passed. Assuming all rows are independent samples. bb2 <- afex_plot(mm, "Machine", id = "Worker", data = Machines, dv = "score") plot_grid(bb1, bb2) ``` ```{r fig.width=7, fig.height=3, echo=FALSE} load(system.file("extdata/", "plots_brms.rda", package = "afex")) plot_grid(bb1, bb2) ``` ```{r, eval=FALSE, include=FALSE} library("brms") data("Machines", package = "MEMSS") mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) bb1 <- afex_plot(mm2, "Machine", data = Machines, dv = "score") bb2 <- afex_plot(mm2, "Machine", id = "Worker", data = Machines, dv = "score") save(bb1, bb2, file = "../inst/extdata/plots_brms.rda", version = 2) ``` # Not Yet Supported: GLMMadaptive Some models are unfortunately not yet supported. For example, models fit with the new and pretty cool looking [`GLMMadaptive`](https://cran.r-project.org/package=GLMMadaptive) package using some of the special families do not seem to produce reasonable results. The following unfortunately does not produce a reasonable plot. ```{r fig.width=4, fig.height=3, eval = FALSE} library("GLMMadaptive") data(Salamanders, package = "glmmTMB") gm1 <- mixed_model(count~spp * mined, random = ~ 1 | site, data = Salamanders, family = zi.poisson(), zi_fixed = ~ mined) afex_plot(gm1, "spp", data = Salamanders) ``` afex/inst/doc/afex_plot_introduction.R0000644000176200001440000002474513607677003017651 0ustar liggesusers## ----set-options, echo=FALSE, cache=FALSE----------------------------------------------- options(width = 90) knitr::opts_chunk$set(dpi=72) ## ----message=FALSE, warning=FALSE------------------------------------------------------- library("afex") library("ggplot2") library("cowplot") theme_set(theme_grey()) ## --------------------------------------------------------------------------------------- data(md_12.1) (aw <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"))) ## ----fig.width=9, fig.height=4---------------------------------------------------------- p_an <- afex_plot(aw, x = "angle", trace = "noise") p_na <- afex_plot(aw, x = "noise", trace = "angle") plot_grid(p_an, p_na) ## try adding: labels = "AUTO" ## --------------------------------------------------------------------------------------- p_an <- afex_plot(aw, x = "angle", trace = "noise", error = "within", factor_levels = list(angle = c("0°", "4°", "8°"), noise = c("Absent", "Present")), legend_title = "Noise") + labs(y = "RTs (in ms)", x = "Angle (in degrees)") ## ----fig.width=8.5, fig.height=6, dpi = 150--------------------------------------------- plot_grid( p_an + theme_bw() + theme(legend.position="bottom"), p_an + theme_light() + theme(legend.position="bottom"), p_an + theme_minimal() + theme(legend.position="bottom"), p_an + jtools::theme_apa() + theme(legend.position="bottom"), p_an + ggpubr::theme_pubr(), p_an + theme_cowplot() + theme(legend.position="bottom"), labels = "AUTO" ) ## ----fig.width=3.5, fig.height=3, dpi = 150, out.width='50%'---------------------------- p_an + scale_y_continuous(breaks=seq(400, 900, length.out = 3)) + theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank()) ## --------------------------------------------------------------------------------------- theme_set(theme_bw(base_size = 15) + theme(legend.position="bottom", panel.grid.major.x = element_blank())) ## ---- eval=FALSE------------------------------------------------------------------------ # ggsave("my_plot.png", device = "png", # width = 9, height = 8, units = "cm", # dpi = 600) ## the higher the dpi, the better the resolution ## ---- eval=FALSE------------------------------------------------------------------------ # ggsave("my_plot.pdf", device = "pdf", # width = 9, height = 8, units = "cm") ## ----fig.width=8.5, fig.height=12, dpi = 150-------------------------------------------- p1 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0, jitter.height = 10, dodge.width = 0.3 ## needs to be same as dodge ), color = "darkgrey")) p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8, color = "darkgrey")) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, data_geom = geom_count) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3, linetype = 1)) p6 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0)) plot_grid(p1, p2, p3, p4, p5, p6, ncol = 2, labels = 1:6) ## ----fig.width=8.5, fig.height=8, dpi = 150--------------------------------------------- p2 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.5, mapping = c("shape", "color"), data_geom = ggbeeswarm::geom_beeswarm, data_arg = list( dodge.width = 0.5, ## needs to be same as dodge cex = 0.8)) p3 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("linetype", "shape", "fill"), data_geom = ggplot2::geom_violin, data_arg = list(width = 0.5)) p4 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", mapping = c("shape", "fill"), data_geom = ggplot2::geom_boxplot, data_arg = list(width = 0.3)) p5 <- afex_plot(aw, x = "noise", trace = "angle", error = "within", dodge = 0.7, mapping = c("shape", "fill"), data_geom = ggpol::geom_boxjitter, data_arg = list( width = 0.5, jitter.width = 0, jitter.height = 10, outlier.intersect = TRUE), point_arg = list(size = 2.5), line_arg = list(linetype = 0), error_arg = list(size = 1.5, width = 0)) plot_grid(p2, p3, p4, p5, ncol = 2, labels = 2:5) ## ----fig.width=8.5, fig.height=4, dpi = 150--------------------------------------------- p1 <- afex_plot(aw, x = "noise", trace = "angle", mapping = "color", error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2)) p2 <- afex_plot(aw, x = "noise", trace = "angle", mapping = c("color", "shape", "linetype"), error = "within", point_arg = list(size = 5), line_arg = list(size = 2), error_arg = list(size = 2, width = 0, linetype = 1)) plot_grid(p1, p2, ncol = 2) ## ----fig.width=7, fig.height=3.5, message=FALSE----------------------------------------- po1 <- afex_plot(aw, x = "angle", mapping = "color", error = "within", data_arg = list(), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) po2 <- afex_plot(aw, x = "angle", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") plot_grid(po1, po2) ## ----fig.width=7, fig.height=3.5, message=FALSE----------------------------------------- afex_plot(aw, x = "angle", panel = "noise", error = "within", data_geom = ggpol::geom_boxjitter, mapping = "fill", data_alpha = 0.7, data_arg = list( width = 0.6, jitter.width = 0.05, jitter.height = 10, outlier.intersect = TRUE ), point_arg = list(size = 2.5), error_arg = list(size = 1.5, width = 0.05)) + theme(legend.position="none") ## ----fig.width=7, fig.height=3.5, message=FALSE----------------------------------------- plot_grid( po1 + geom_line(aes(group = 1), color = "darkgrey", size = 1.5), po2 + geom_line(aes(group = 1)) ) ## ---- eval=FALSE, echo=FALSE, results='hide'-------------------------------------------- # data("fhch2010") # load # fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors # ### following model should take less than a minute to fit: # mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ # (task||item), fhch, method = "S", expand_re = TRUE) # save(mrt, file = "../inst/extdata/freeman_reduced_model.rda", compress = "xz") ## ---- eval=FALSE------------------------------------------------------------------------ # data("fhch2010") # load # fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors # ### following model should take less than a minute to fit: # mrt <- mixed(log_rt ~ task*stimulus*frequency + (stimulus*frequency||id)+ # (task||item), fhch, method = "S", expand_re = TRUE) ## --------------------------------------------------------------------------------------- load(system.file("extdata/", "freeman_reduced_model.rda", package = "afex")) emmeans::emm_options(lmer.df = "asymptotic") ## --------------------------------------------------------------------------------------- mrt ## ----fig.width=7, fig.height=3.5-------------------------------------------------------- afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task") ## ----fig.width=7, fig.height=3.5-------------------------------------------------------- plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item"), labels = c("ID", "Item") ) ## ----fig.width=7, fig.height=3.5-------------------------------------------------------- plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_violin, data_arg = list(width = 0.5)), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, data_geom = geom_boxplot, data_arg = list(width = 0.5), error_arg = list(size = 1.5, width = 0, linetype = 1)) ) ## --------------------------------------------------------------------------------------- pairs(emmeans::emmeans(mrt, c("stimulus", "frequency"), by = "task")) ## ----fig.width=7, fig.height=3.5-------------------------------------------------------- plot_grid( afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "id", error = "within"), afex_plot(mrt, x = "stimulus", trace = "frequency", panel = "task", id = "item", dodge = 0.8, error = "within", data_geom = geom_violin, data_arg = list(width = 0.5)) ) afex/inst/doc/afex_anova_example.R0000644000176200001440000001206413607676755016715 0ustar liggesusers## ----set-options, echo=FALSE, cache=FALSE----------------------------------------------- options(width = 90) knitr::opts_chunk$set(dpi=72) ## ----message=FALSE, warning=FALSE------------------------------------------------------- library("afex") # needed for ANOVA functions. library("emmeans") # emmeans must now be loaded explicitly for follow-up tests. library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("ggplot2") # for customizing plots. afex_options(emmeans_model = "multivariate") # use multivariate model for all follow-up tests. ## --------------------------------------------------------------------------------------- data(sk2011.1) str(sk2011.1) ## --------------------------------------------------------------------------------------- with(sk2011.1, table(inference, id, plausibility)) ## --------------------------------------------------------------------------------------- a1 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("inference", "plausibility")) a1 # the default print method prints a data.frame produced by nice ## ---- eval=FALSE------------------------------------------------------------------------ # aov_car(response ~ instruction + Error(id/inference*plausibility), sk2011.1) # aov_4(response ~ instruction + (inference*plausibility|id), sk2011.1) ## ---- results='asis'-------------------------------------------------------------------- knitr::kable(nice(a1)) ## ---- results='asis'-------------------------------------------------------------------- print(xtable::xtable(anova(a1), digits = c(rep(2, 5), 3, 4)), type = "html") ## --------------------------------------------------------------------------------------- m1 <- emmeans(a1, ~ inference) m1 ## --------------------------------------------------------------------------------------- pairs(m1) ## --------------------------------------------------------------------------------------- summary(as.glht(pairs(m1)), test=adjusted("free")) ## --------------------------------------------------------------------------------------- m2 <- emmeans(a1, "inference", by = "instruction") ## equal: emmeans(a1, ~ inference|instruction) m2 ## --------------------------------------------------------------------------------------- pairs(m2) ## --------------------------------------------------------------------------------------- m3 <- emmeans(a1, c("inference", "instruction")) ## equal: emmeans(a1, ~inference*instruction) m3 pairs(m3) ## --------------------------------------------------------------------------------------- c1 <- list( v_i.ded = c(0.5, 0.5, -0.5, -0.5, 0, 0, 0, 0), v_i.prob = c(0, 0, 0, 0, 0.5, 0.5, -0.5, -0.5) ) contrast(m3, c1, adjust = "holm") summary(as.glht(contrast(m3, c1)), test = adjusted("free")) ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility") ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "within") ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none") ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- p1 <- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none", mapping = c("color", "fill"), data_geom = geom_boxplot, data_arg = list(width = 0.4), point_arg = list(size = 1.5), line_arg = list(size = 1)) p1 ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- p1 + theme_light() ## --------------------------------------------------------------------------------------- theme_set(theme_light()) ## --------------------------------------------------------------------------------------- a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("validity", "plausibility", "what")) a2 ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- afex_plot(a2, x = c("plausibility", "validity"), trace = "instruction", panel = "what", error = "none") ## --------------------------------------------------------------------------------------- (m4 <- emmeans(a2, ~instruction+plausibility+validity|what)) c2 <- list( diff_1 = c(1, -1, 0, 0, 0, 0, 0, 0), diff_2 = c(0, 0, 1, -1, 0, 0, 0, 0), diff_3 = c(0, 0, 0, 0, 1, -1, 0, 0), diff_4 = c(0, 0, 0, 0, 0, 0, 1, -1), val_ded = c(0.5, 0, 0.5, 0, -0.5, 0, -0.5, 0), val_prob = c(0, 0.5, 0, 0.5, 0, -0.5, 0, -0.5), plau_ded = c(0.5, 0, -0.5, 0, -0.5, 0, 0.5, 0), plau_prob = c(0, 0.5, 0, -0.5, 0, 0.5, 0, -0.5) ) contrast(m4, c2, adjust = "holm") ## --------------------------------------------------------------------------------------- summary(as.glht(contrast(m4, c2)), test = adjusted("free")) afex/inst/doc/introduction-mixed-models.pdf0000644000176200001440000147705113607677016020554 0ustar liggesusers%PDF-1.5 % 375 0 obj << /Linearized 1 /L 425513 /H [ 2288 506 ] /O 379 /E 74590 /N 39 /T 422991 >> endobj 376 0 obj << /Type /XRef /Length 84 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Index [ 375 231 ] /Info 101 0 R /Root 377 0 R /Size 606 /Prev 422992 /ID [] >> stream xcbd`g`b``8 "9ٍ d D<o@lNI&vu10$5IƹQr+  q endstream endobj 377 0 obj << /Names 605 0 R /OpenAction 514 0 R /Outlines 485 0 R /PageMode /UseOutlines /Pages 484 0 R /Type /Catalog >> endobj 378 0 obj << /Filter /FlateDecode /S 416 /O 500 /Length 418 >> stream xc```b`:A lV eT Dt2*:4lZ!\|I1!z@ .+L2 HupDc0@& v E t$"^00Fx ;6uktDҪRWM^Ik{4ɝr %*Ic[hnH]FMzZyx~ii{$'ٕfp H&0hۙ yXIp扗Esl s(;E+w\ðrJs,[7lk vX}JI՞,&<4 00@,EӱYb 年_fDYEK**P%}eO8cޯ\9A⑱q s|c endstream endobj 379 0 obj << /Contents 380 0 R /MediaBox [ 0 0 595.276 841.89 ] /Parent 400 0 R /Resources 515 0 R /Type /Page >> endobj 380 0 obj << /Filter /FlateDecode /Length 758 >> stream xuTn0 }WiZv%lK74:AD"6?ɤ$K,SyxH܎7A)$tK' HH>zavJ (L5gQNO֚/aj"ʹ(r4+8"Mefn-ZQ)k+pW^Ѻnɥòj0y18_nWJV0ZDJh)qՈg73DlRFoߔz==a k_`F(u(' Ę>q)9w$]} #q`( Mᓐ a1 Msxw^/~ф lop! +ٶ=gGm))£֜BR)䡋y{~:l>uO;!0\-R[M a?Q,͔y?03RA,B#W3x~]WJbߖiK/v}0MIH;m 99FH0z5dT4U @ny-9K> stream xڴuT[>  lӰMw#-HwtK7H*%%<9 \35\^jru&Qs)P 7q`cgRZڙ8ؙYY9ŝ&.  ;@ `eCH9t1tL* :XZ;!. 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R~;Tn8A?YnR&rܾ?M[&@INk1Xs|Yq =>OpS@>| s*xXD#^n֮*lc>!7rdHCab=Ϛ9Mv "inP59_rȘ-;̞N'8Ŵw w3Vz_M`CNuRaHW[-%endstream endobj 101 0 obj << /Author () /CreationDate (D:20190503071507Z) /Creator (LaTeX with hyperref package) /Keywords () /ModDate (D:20190503071507Z) /PTEX.Fullbanner (This is pdfTeX, Version 3.14159265-2.6-1.40.17 \(TeX Live 2016/Debian\) kpathsea version 6.2.2) /Producer (pdfTeX-1.40.17) /Subject () /Title () /Trapped /False >> endobj 102 0 obj << /Type /XRef /Length 331 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Size 375 /ID [] >> stream xcb&FF8& DrHƍ ^ "9M # ̞fH IlNX|2X]0{1 ,Ν f V3loBH8"Xn_-B@? 0c%N 0d/#;/Xi=$3 ̬nfBPlM$JH`[ `Y`q-p0p@9#x$azI f^-$ .>)DXA*; l/8<`xد GQA2x7M$)$E endstream endobj startxref 216 %%EOF afex/inst/doc/afex_anova_example.Rmd0000644000176200001440000004161713531256332017221 0ustar liggesusers--- title: "ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` # Overview This documents reanalysis a dataset from an Experiment performed by Singmann and Klauer (2011) using the ANOVA functionality of __afex__ followed by post-hoc tests using package [__emmeans__](https://cran.r-project.org/package=emmeans) (Lenth, 2017). After a brief description of the dataset and research question, the code and results are presented. # Description of Experiment and Data Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this "inductive instruction" in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and plausibility of the problem (inferences which were consisted with the background knowledge versus problems that were inconsistent with the background knowledge). The critical comparison across the two conditions was among problems which were valid and implausible with problems that were invalid and plausible. For example, the next problem was invalid and plausible: > If a person is wet, then the person fell into a swimming pool. > A person fell into a swimming pool. > How valid is the conclusion/How likely is it that the person is wet? For those problems we predicted that under deductive instructions responses should be lower (as the conclusion does not necessarily follow from the premises) as under probabilistic instructions. For the valid but implausible problem, an example is presented next, we predicted the opposite pattern: > If a person is wet, then the person fell into a swimming pool. > A person is wet. > How valid is the conclusion/How likely is it that the person fell into a swimming pool? Our study also included valid and plausible and invalid and implausible problems. In contrast to the analysis reported in the manuscript, we initially do not separate the analysis into affirmation and denial problems, but first report an analysis on the full set of inferences, MP, MT, AC, and DA, where MP and MT are valid and AC and DA invalid. We report a reanalysis of our Experiment 1 only. Note that the factor `plausibility` is not present in the original manuscript, there it is a results of a combination of other factors. # Data and R Preperation We begin by loading the packages we will be using throughout. ```{r message=FALSE, warning=FALSE} library("afex") # needed for ANOVA functions. library("emmeans") # emmeans must now be loaded explicitly for follow-up tests. library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("ggplot2") # for customizing plots. afex_options(emmeans_model = "multivariate") # use multivariate model for all follow-up tests. ``` Note that for ANOVAs involving repeated-measures factors, follow-up tests based on the multivariate model are generally preferrably to univariate follow-up tests. Consequently, we set this option globally. Future versions of `afex` will likely use the multivariate model as the default. ```{r} data(sk2011.1) str(sk2011.1) ``` An important feature in the data is that each participant provided two responses for each cell of the design (the content is different for each of those, each participant saw all four contents). These two data points will be aggregated automatically by `afex`. ```{r} with(sk2011.1, table(inference, id, plausibility)) ``` # ANOVA To get the full ANOVA table for the model, we simply pass it to `aov_ez` using the design as described above. We save the returned object for further analysis. ```{r} a1 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("inference", "plausibility")) a1 # the default print method prints a data.frame produced by nice ``` The equivalent calls (i.e., producing exactly the same output) of the other two ANOVA functions `aov_car` or `aov4` is shown below. ```{r, eval=FALSE} aov_car(response ~ instruction + Error(id/inference*plausibility), sk2011.1) aov_4(response ~ instruction + (inference*plausibility|id), sk2011.1) ``` As mentioned before, the two responses per cell of the design and participants are aggregated for the analysis as indicated by the warning message. Furthermore, the degrees of freedom are Greenhouse-Geisser corrected per default for all effects involving `inference`, as `inference` is a within-subject factor with more than two levels (i.e., MP, MT, AC, & DA). In line with our expectations, the three-way interaction is significant. The object printed per default for `afex_aov` objects (produced by `nice`) can also be printed nicely using `knitr`: ```{r, results='asis', } knitr::kable(nice(a1)) ``` Alternatively, the `anova` method for `afex_aov` objects returns a `data.frame` of class `anova` that can be passed to, for example, `xtable` for nice formatting: ```{r, results='asis'} print(xtable::xtable(anova(a1), digits = c(rep(2, 5), 3, 4)), type = "html") ``` # Post-Hoc Contrasts and Plotting To further analyze the data we need to pass it to package `emmeans`, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on `emmeans` can be obtained in [its vignettes](https://cran.r-project.org/package=emmeans) and [faq](https://CRAN.R-project.org/package=emmeans/vignettes/FAQs.html). `emmeans` can work with `afex_aov` objects directly as __afex__ comes with the necessary methods for the generic functions defined in `emmeans`. When using the `multivariate` options as described above, `emmeans` uses the ANOVA model estimated via base R's `lm` method (which in the case of a multivariate response is an object of class `c("mlm", "lm")`). In the default setting (i.e., `emmeans_model = "univariate"`), `emmeans` uses the object created by base R's `aov` function, which for now is also part of an `afex_aov` object. ## Some First Contrasts ### Main Effects Only This object can now be passed to `emmeans`, for example to obtain the marginal means of the four inferences: ```{r} m1 <- emmeans(a1, ~ inference) m1 ``` This object can now also be used to compare whether or not there are differences between the levels of the factor: ```{r} pairs(m1) ``` To obtain more powerful p-value adjustments, we can furthermore pass it to `multcomp` (Bretz, Hothorn, & Westfall, 2011): ```{r} summary(as.glht(pairs(m1)), test=adjusted("free")) ``` ### A Simple interaction We could now also be interested in the marginal means of the inferences across the two instruction types. `emmeans` offers two ways to do so. The first splits the contrasts across levels of the factor using the `by` argument. ```{r} m2 <- emmeans(a1, "inference", by = "instruction") ## equal: emmeans(a1, ~ inference|instruction) m2 ``` Consequently, tests are also only performed within each level of the `by` factor: ```{r} pairs(m2) ``` The second version considers all factor levels together. Consequently, the number of pairwise comparisons is a lot larger: ```{r} m3 <- emmeans(a1, c("inference", "instruction")) ## equal: emmeans(a1, ~inference*instruction) m3 pairs(m3) ``` ### Running Custom Contrasts Objects returned from `emmeans` can also be used to test specific contrasts. For this, we can simply create a list, where each element corresponds to one contrasts. A contrast is defined as a vector of constants on the reference grid (i.e., the object returned from `emmeans`, here `m3`). For example, we might be interested in whether there is a difference between the valid and invalid inferences in each of the two conditions. ```{r} c1 <- list( v_i.ded = c(0.5, 0.5, -0.5, -0.5, 0, 0, 0, 0), v_i.prob = c(0, 0, 0, 0, 0.5, 0.5, -0.5, -0.5) ) contrast(m3, c1, adjust = "holm") summary(as.glht(contrast(m3, c1)), test = adjusted("free")) ``` The results can be interpreted as in line with expectations. Responses are larger for valid than invalid problems in the deductive, but not the probabilistic condition. ## Plotting Since version `0.22`, `afex` comes with its own plotting function based on `ggplot2`, `afex_plot`, which works directly with `afex_aov` objects. As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. As we saw above, this interaction was significant. Consequently, we are interested in plotting this interaction. ### Basic Plots For `afex_plot`, we need to specify the `x`-factor(s), which determine which factor-levels or combinations of factor-levels are plotted on the x-axis. We can also define `trace` factor(s), which determine which factor levels are connected by lines. Finally, we can also define `panel` factor(s), which determine if the plot is split into subplots. `afex_plot` then plots the estimated marginal means obtained from `emmeans`, confidence intervals, and the raw data in the background. Note that the raw data in the background is per default drawn using an alpha blending of .5 (i.e., 50% semi-transparency). Thus, in case of several points lying directly on top of each other, this point appears noticeably darker. ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility") ``` In the default settings, the error bars show 95%-confidence intervals based on the standard error of the underlying model (i.e., the `lm` model in the present case). In the present case, in which each subplot (defined by `x`- and `trace`-factor) shows a combination of a within-subjects factor (i.e., `inference`) and a between-subjects (i.e., `instruction`) factor, this is not optimal. The error bars only allow to assess differences regarding the between-subjects factor (i.e., across the lines), but not inferences regarding the within-subjects factor (i.e., within one line). This is also indicated by a warning. An alternative would be within-subject confidence intervals: ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "within") ``` However, those only allow inferences regarding the within-subject factors and not regarding the between-subjecta factor. So the same warning is emitted again. A further alternative is to suppress the error bars altogether. This is the approach used in our original paper and probably a good idea in general when figures show both between- and within-subjects factors within the same panel. The presence of the raw data in the background still provides a visual depiction of the variability of the data. ```{r fig.width=7.5, fig.height=4} afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none") ``` ### Customizing Plots `afex_plot` allows to customize the plot in a number of different ways. For example, we can easily change the aesthetic mapping associated with the `trace` factor. So instead of using lineytpe and shape of the symbols, we can use color. Furthermore, we can change the graphical element used for plotting the data points in the background. For example, instead of plotting the raw data, we can replace this with a boxplot. Finally, we can also make both the points showing the means and the lines connecting the means larger. ```{r fig.width=7.5, fig.height=4} p1 <- afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", error = "none", mapping = c("color", "fill"), data_geom = geom_boxplot, data_arg = list(width = 0.4), point_arg = list(size = 1.5), line_arg = list(size = 1)) p1 ``` Note that `afex_plot` returns a `ggplot2` plot object which can be used for further customization. For example, one can easily change the `theme` to something that does not have a grey background: ```{r fig.width=7.5, fig.height=4} p1 + theme_light() ``` We can also set the theme globally for the remainder of the `R` session. ```{r} theme_set(theme_light()) ``` The full set of customizations provided by `afex_plot` is beyond the scope of this vignette. The examples on the help page at `?afex_plot` provide a good overview. # Replicate Analysis from Singmann and Klauer (2011) However, the plots shown so far are not particularly helpful with respect to the research question. Next, we fit a new ANOVA model in which we separate the data in affirmation and denial inferences. This was also done in the original manuscript. We then lot the data a second time. ```{r} a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("validity", "plausibility", "what")) a2 ``` Then we plot the data from this ANOVA. Because each panel would again show a mixed-design, we suppress the error bars. ```{r fig.width=7.5, fig.height=4} afex_plot(a2, x = c("plausibility", "validity"), trace = "instruction", panel = "what", error = "none") ``` We see the critical and predicted cross-over interaction in the left of those two graphs. For implausible but valid problems deductive responses are larger than probabilistic responses. The opposite is true for plausible but invalid problems. We now tests these differences at each of the four x-axis ticks in each plot using custom contrasts (`diff_1` to `diff_4`). Furthermore, we test for a validity effect and plausibility effect in both conditions. ```{r} (m4 <- emmeans(a2, ~instruction+plausibility+validity|what)) c2 <- list( diff_1 = c(1, -1, 0, 0, 0, 0, 0, 0), diff_2 = c(0, 0, 1, -1, 0, 0, 0, 0), diff_3 = c(0, 0, 0, 0, 1, -1, 0, 0), diff_4 = c(0, 0, 0, 0, 0, 0, 1, -1), val_ded = c(0.5, 0, 0.5, 0, -0.5, 0, -0.5, 0), val_prob = c(0, 0.5, 0, 0.5, 0, -0.5, 0, -0.5), plau_ded = c(0.5, 0, -0.5, 0, -0.5, 0, 0.5, 0), plau_prob = c(0, 0.5, 0, -0.5, 0, 0.5, 0, -0.5) ) contrast(m4, c2, adjust = "holm") ``` We can also pass these tests to `multcomp` which gives us more powerful Type 1 error corrections. ```{r} summary(as.glht(contrast(m4, c2)), test = adjusted("free")) ``` Unfortunately, in the present case this function throws several warnings. Nevertheless, the p-values from both methods are very similar and agree on whether or not they are below or above .05. Because of the warnings it seems advisable to use the one provided by `emmeans` directly and not use the ones from `multcomp`. The pattern for the affirmation problems is in line with the expectations: We find the predicted differences between the instruction types for valid and implausible (`diff_2`) and invalid and plausible (`diff_3`) and the predicted non-differences for the other two problems (`diff_1` and `diff_4`). Furthermore, we find a validity effect in the deductive but not in the probabilistic condition. Likewise, we find a plausibility effect in the probabilistic but not in the deductive condition. # Some Cautionary Notes * Choosing the right correction for multiple testing can be difficult. In fact `multcomp` comes with an accompanying book (Bretz et al., 2011). If the degrees-of-freedom of all contrasts are identical using `multcomp`'s method `free` is more powerful than simply using the Bonferroni-Holm method. `free` is a generalization of the Bonferroni-Holm method that takes the correlations among the model parameters into account and uniformly more powerful. * For data sets with many within-subject factors, creating the `aov` object can take some time (i.e., compared to producing the ANOVA table which is usually very fast). Those objects are also comparatively large, often multiple MB. If speed is important and one is not interested in employing `emmeans` one can set `return = "nice"` in the call to the ANOVA function to only receive the ANOVA table (this can also be done globally: `afex_options(return_aov = "nice")`). # References * Bretz, F., Hothorn, T., & Westfall, P. H. (2011). _Multiple comparisons using R_. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp * Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. _Thinking & Reasoning_, 17(3), 247-281. doi: 10.1080/13546783.2011.572718 * Lenth, R. (2017). _emmeans: Estimated Marginal Means, aka Least-Squares Means_. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans afex/inst/doc/afex_plot_supported_models.html0000644000176200001440000126241513607677016021266 0ustar liggesusers afex_plot: Supported Models

afex_plot: Supported Models

Henrik Singmann

2020-01-15

Introduction

afex_plot() visualizes results from factorial experiments and, more generally, data set with interactions of categorical/factor variables. It does so by combining estimated marginal means and uncertainties associated with these means in the foreground with a depiction of the raw data in the background. If models include continuous covariates, other approaches are recommended (e.g., such as implemented in package effects or by using the possibility of afex_plot to return the data and build the plot on ones own).

This document provides an overview of the different models supported by afex_plot() in addition to the afex objects (i.e., afex_aov and mixed). In general, these are models which are supported by the emmeans package as the afex_plot.default() method uses emmeans to get the estimated marginal means. afex_plot.default() then guesses whether there are repeated measures or all samples are independent. Based on this guess (which can be changed via the id argument) data in the background is plotted. Calculation of error bars can also be based on this guess (but the default is to plot the model based error bars obtained from emmeans).

For a generally introduction to the functionality of afex_plot see: afex_plot: Publication Ready Plots for Experimental Designs

Throughout the document, we will need afex as well as ggplot2. In addition, we load cowplot for function plot_grid() (which allows to easily combine multiple ggplot2 plots). In addition, we will set a somewhat nicer ggplot2 theme.

library("afex")     
library("ggplot2")  
library("cowplot")
theme_set(theme_bw(base_size = 14) + 
            theme(legend.position="bottom", 
                  panel.grid.major.x = element_blank(),
                  panel.grid.minor.x = element_blank()))

Importantly, we also set the contrasts for the current R session to sum-to-zero contrasts. For models that include interactions with categorical variables this generally produces estimates that are easier to interpret.

set_sum_contrasts()
## setting contr.sum globally: options(contrasts=c('contr.sum', 'contr.poly'))

Please note, the best way to export a figure is via ggsave() or a similar function call. For Word and similar document formats, png is a good file type, for LaTeX and similar document formats, pdf is a good file type.

Base R stats models: lm, glm

afex_plot() generally supports models implemeneted via the stats package. Here I show the main model functions that work with independent samples. These models can be passed to afex_plot without specifying additional arguments.

Most importantly, lm models work directly. For those we use the warpbreaks data.

warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)

Note that afex_plot produces several messages that are shown here as comments below the corresponding calls. Important is maybe that afex_plot assumes all observations (i.e., rows) are independent. This is of course the case here. In addition, for the first plot we are informed that the presence of an interaction may lead to a misleading impression if only a lower-order effect (here a main effect) is shown. This message is produced by emmeans and passed through.

p1 <- afex_plot(warp.lm, "tension")
## dv column detected: breaks
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
p2 <- afex_plot(warp.lm, "tension", "wool")
## dv column detected: breaks
## No id column passed. Assuming all rows are independent samples.
plot_grid(p1, p2)

glm models also work without further setting. Here we first use a poisson GLM for which we need to generate the data.

ins <- data.frame(
    n = c(500, 1200, 100, 400, 500, 300),
    size = factor(rep(1:3,2), labels = c("S","M","L")),
    age = factor(rep(1:2, each = 3)),
    claims = c(42, 37, 1, 101, 73, 14))

We can then fit the data and pass the model object as is.

ins.glm <- glm(claims ~ size + age + offset(log(n)), 
               data = ins, family = "poisson")
afex_plot(ins.glm, "size", "age")
## dv column detected: claims
## No id column passed. Assuming all rows are independent samples.

afex_plot also works with binomial GLMs for which we also first need to generate some data which we will then fit.

## binomial glm adapted from ?predict.glm
ldose <- factor(rep(0:5, 2))
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- numdead/20  ## dv should be a vector, no matrix
budworm.lg <- glm(SF ~ sex*ldose, family = binomial, 
                  weights = rep(20, length(numdead)))

For this model, we will produce three plots we can then compare. The first only shows the main effect of one variable (ldose). The other show the interaction of the two variables. Because for binomial GLMs we then only have one data point (with several observations), the individual data points and mean cannot be distinguished. This is made clear in the ther two (panels B and C).

a <- afex_plot(budworm.lg, "ldose")
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean!
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
c <- afex_plot(budworm.lg, "ldose", "sex", 
          data_arg = list(size = 4, color = "red"))
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
plot_grid(a, b, c, labels = "AUTO", nrow = 1)

nlme mixed model

Hot to use afex_plot for mixed models fitted with afex::mixed (or lme4 directly) is shown in the other vignette. However, we can also use afex_plot for mixed models fitted with the older nlme package. For this, however we need to pass the data used for fitting via the data argument.

We can change on which of the two nested factors the individual data points in the background are based via the id argument. This is shown below.

## nlme mixed model
data(Oats, package = "nlme")
Oats$nitro <- factor(Oats$nitro)
oats.1 <- nlme::lme(yield ~ nitro * Variety, 
                    random = ~ 1 | Block / Variety,
                    data = Oats)
plot_grid(
  afex_plot(oats.1, "nitro", "Variety", data = Oats), # A
  afex_plot(oats.1, "nitro", "Variety", data = Oats), # B
  afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block"), # C
  afex_plot(oats.1, "nitro", data = Oats), # D
  afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")), # E
  afex_plot(oats.1, "nitro", data = Oats, id = "Block"), # F
  labels = "AUTO"
)
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## dv column detected: yield
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: yield
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: yield
## NOTE: Results may be misleading due to involvement in interactions

glmmTMB

Support for glmmTMB is also provided. Here we use an example data set for which we model zero-inflation as well as overdispersion. The latter is achieved with a variant of the negative binomial distribution.

library("glmmTMB")
tmb <- glmmTMB(count~spp * mined + (1|site), 
              ziformula = ~spp * mined, 
              family=nbinom2, Salamanders)

afex_plot does not automatically detect the random-effect for site. This means that per default all 644 data points are shown. When plotting only one variable, in which the default data_geom is ggbeeswarm::geom_beeswarm, this can lead to rather ugly plots due to the zero inflation. This is shon in panel A below. In panel B, we address this by changing the geom to a violin plot. In panel C, we address this by aggregating the data within site, but still use the beeswarm plot. Note that for panel C it is necessary to pass the data via the data argument as otherwise site cannot be found for aggregation.

plot_grid(
  afex_plot(tmb, "spp"),
  afex_plot(tmb, "spp", data_geom = geom_violin),
  afex_plot(tmb, "spp", id = "site", data = Salamanders), 
  labels = "AUTO", nrow = 1
)
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: count
## NOTE: Results may be misleading due to involvement in interactions

When plotting both variables, the problem is somewhat hidden, because instead of beeswarm plots, semi-transparency (i.e., alpha < 1) is used to show overlapping points. In panel B we again make this clearer but this time by adding jitter (on both the y- and x-axis) and increasing the degree of semi-transparancy (i.e., decreasing alpha).

a <- afex_plot(tmb, "spp", "mined")
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
b <- afex_plot(tmb, "spp", "mined", data_alpha = 0.3,
          data_arg = list(
            position = 
              ggplot2::position_jitterdodge(
                jitter.width = 0.2, 
                jitter.height = 0.5, 
                dodge.width = 0.5  ## needs to be same as dodge
                ),
            color = "darkgrey"))
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
plot_grid(a, b, labels = "AUTO")

For the final plot we also plot the interaction, but this time aggregate the individual-data within site. This allows us again to use a beeswarm plot (after decreasing the width of the “bees”) and produces a relatively clear result.

afex_plot(tmb, "spp", "mined", id = "site", data = Salamanders, 
          data_geom = ggbeeswarm::geom_beeswarm, 
          data_arg = list(dodge.width = 0.5, cex = 0.4,
                          color = "darkgrey")
          )
## dv column detected: count

rstanarm

afex_plot() also supports Bayesian models that are also supported via emmeans. For example, we can easily fit a binomial model with rstanarm.

library("rstanarm") ## requires resetting the ggplot2 theme
theme_set(theme_bw(base_size = 14) + 
            theme(legend.position="bottom", 
                  panel.grid.major.x = element_blank(),
                  panel.grid.minor.x = element_blank()))
cbpp <- lme4::cbpp 
cbpp$prob <- with(cbpp, incidence / size)
example_model <- stan_glmer(prob ~ period + (1|herd),
                            data = cbpp, family = binomial, weight = size,
                            chains = 2, cores = 1, seed = 12345, iter = 500)

We can directly pass this model to afex_plot. However, we also see quite some zeros leading to a not super nice plot. It looks a bit better using a violin plot for the raw data.

b1 <- afex_plot(example_model, "period")
## dv column detected: prob
## No id column passed. Assuming all rows are independent samples.
b2 <- afex_plot(example_model, "period", data_geom = geom_violin)
## dv column detected: prob
## No id column passed. Assuming all rows are independent samples.
plot_grid(b1, b2, labels = "AUTO")

We can also produce a plot based on the individual Bernoulli observations in the data. For this, we first need to expand the data such that we have one row per observation. With this, we can then fit the essentially same model as above.

cbpp_l <- vector("list", nrow(cbpp))
for (i in seq_along(cbpp_l)) {
  cbpp_l[[i]] <- data.frame(
    herd = cbpp$herd[i],
    period = cbpp$period[i],
    incidence = rep(0, cbpp$size[i])
  )
  cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1
}
cbpp_l <- do.call("rbind", cbpp_l)
cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd))
cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period))
example_model2 <- stan_glmer(incidence ~ period + (1|herd),
                             data = cbpp_l, family = binomial, 
                             chains = 2, cores = 1, seed = 12345, iter = 500)

Again, this model can be directly passed to afex_plot. However, here we see even more 0 as the data is not yet aggregated. Consequently, we need to pass id = "herd" to aggregate the individual observations within each herd.

b3 <- afex_plot(example_model2, "period")
## dv column detected: incidence
## No id column passed. Assuming all rows are independent samples.
b4 <- afex_plot(example_model2, "period", id = "herd")
## dv column detected: incidence
plot_grid(b3, b4, labels = "AUTO")
## Warning in f(...): The default behavior of beeswarm has changed in version 0.6.0. In
## versions <0.6.0, this plot would have been dodged on the y-axis. In versions >=0.6.0,
## grouponX=FALSE must be explicitly set to group on y-axis. Please set grouponX=TRUE/FALSE
## to avoid this warning and ensure proper axis choice.

We can of course also fit a model assuming a normal distribution using rstanarm. For example using the Machines data.

data("Machines", package = "MEMSS") 
mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines,
                chains = 2, cores = 1, seed = 12345, iter = 500)

As before, we can pass this model directly to afex_plot (see panel A). However, the data is again not aggregated within the grouping variable Worker. If we want to aggregate the individual data points for the grouping factor, we need to pass both the name of the grouping variable (Worker) and the data used for fitting.

b5 <- afex_plot(mm, "Machine")
## dv column detected: score
## No id column passed. Assuming all rows are independent samples.
b6 <- afex_plot(mm, "Machine", id = "Worker")
## dv column detected: score
plot_grid(b5, b6, labels = "AUTO")

brms

We can also fit the Machines data using brms.

library("brms")
data("Machines", package = "MEMSS") 
mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, 
           chains = 2, cores = 1, seed = 12345, iter = 500)

However, to pass a brms object to afex_plot we need to pass both, the data used for fitting as well as the name of the dependent variable (here score) via the dv argument. We again build the plot such that the left panel shows the raw data without aggregation and the right panel shows the data aggregated within the grouping factor Worker.

bb1 <- afex_plot(mrt, "Machine", data = Machines, dv = "score")
## No id column passed. Assuming all rows are independent samples.
bb2 <- afex_plot(mm, "Machine", id = "Worker", 
          data = Machines, dv = "score")
plot_grid(bb1, bb2)

Not Yet Supported: GLMMadaptive

Some models are unfortunately not yet supported. For example, models fit with the new and pretty cool looking GLMMadaptive package using some of the special families do not seem to produce reasonable results. The following unfortunately does not produce a reasonable plot.

library("GLMMadaptive")
data(Salamanders, package = "glmmTMB")
gm1 <- mixed_model(count~spp * mined, random = ~ 1 | site, data = Salamanders,
                   family = zi.poisson(), zi_fixed = ~ mined)

afex_plot(gm1, "spp", data = Salamanders)
afex/inst/doc/afex_mixed_example.Rmd0000644000176200001440000007024413531256325017223 0ustar liggesusers--- title: "Mixed Model Reanalysis of RT data" author: "Henrik Singmann" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Mixed Model Example Analysis: Reanalysis of Freeman et al. (2010)} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r set-options, echo=FALSE, cache=FALSE} options(width = 90) knitr::opts_chunk$set(dpi=72) ``` ## Overview This documents reanalysis response time data from an Experiment performed by Freeman, Heathcote, Chalmers, and Hockley (2010) using the mixed model functionality of __afex__ implemented in function `mixed` followed by post-hoc tests using package __emmeans__ (Lenth, 2017). After a brief description of the data set and research question, the code and results are presented. ## Description of Experiment and Data The data are lexical decision and word naming latencies for 300 words and 300 nonwords from 45 participants presented in Freeman et al. (2010). The 300 items in each `stimulus` condition were selected to form a balanced $2 \times 2$ design with factors neighborhood `density` (low versus high) and `frequency` (low versus high). The `task` was a between subjects factor: 25 participants worked on the lexical decision task and 20 participants on the naming task. After excluding erroneous responses each participants responded to between 135 and 150 words and between 124 and 150 nonwords. We analyzed log RTs which showed an approximately normal picture. ## Data and R Preperation We start with loading some packages we will need throughout this example. For data manipulation we will be using the `dplyr` and `tidyr` packages from the [`tidyverse`](http://tidyverse.org/). A thorough introduction to these packages is beyond this example, but well worth it, and can be found in ['R for Data Science'](http://r4ds.had.co.nz/) by Wickham and Grolemund. For plotting we will be diverging from the `tidyverse` and use `lattice` instead. At some later point in time I will change this to `ggplot2` plots. After loading the packages, we will load the data (which comes with `afex`), remove the errors, and take a look at the variables in the data. ```{r message=FALSE, warning=FALSE} library("afex") # needed for mixed() and attaches lme4 automatically. library("emmeans") # emmeans is needed for follow-up tests (and not anymore loaded automatically). library("multcomp") # for advanced control for multiple testing/Type 1 errors. library("dplyr") # for working with data frames library("tidyr") # for transforming data frames from wide to long and the other way round. library("lattice") # for plots library("latticeExtra") # for combining lattice plots, etc. lattice.options(default.theme = standard.theme(color = FALSE)) # black and white lattice.options(default.args = list(as.table = TRUE)) # better ordering data("fhch2010") # load fhch <- droplevels(fhch2010[ fhch2010$correct,]) # remove errors str(fhch2010) # structure of the data ``` To make sure our expectations about the data match the data we use some `dplyr` magic to confirm the number of participants per condition and items per participant. ```{r} ## are all participants in only one task? fhch2010 %>% group_by(id) %>% summarise(task = n_distinct(task)) %>% as.data.frame() %>% {.$task == 1} %>% all() ## participants per condition: fhch2010 %>% group_by(id) %>% summarise(task = first(task)) %>% ungroup() %>% group_by(task) %>% summarise(n = n()) ## number of different items per participant: fhch2010 %>% group_by(id, stimulus) %>% summarise(items = n_distinct(item)) %>% ungroup() %>% group_by(stimulus) %>% summarise(min = min(items), max = max(items), mean = mean(items)) ``` Before running the analysis we should make sure that our dependent variable looks roughly normal. To compare `rt` with `log_rt` within the same graph using `lattice` we first need to transform the data from the wide format (where both rt types occupy one column each) into the long format (in which the two rt types are combined into a single column with an additional indicator column). To do so we use `tidyr::gather`. Then we simply call the `histogram` function on the new `data.frame` and make a few adjustments to the defaults to obtain a nice looking output. The plot shows that `log_rt` looks clearly more normal than `rt`, although not perfectly so. An interesting exercise could be to rerun the analysis below using a transformation that provides an even better 'normalization'. ```{r, fig.width=7, fig.height=4} fhch_long <- fhch %>% gather("rt_type", "rt", rt, log_rt) histogram(~rt|rt_type, fhch_long, breaks = "Scott", type = "density", scale = list(x = list(relation = "free"))) ``` ## Descriptive Analysis The main factors in the experiment were the between-subjects factor `task` (`naming` vs. `lexdec`), and the within-subjects factors `stimulus` (`word` vs. `nonword`), `density` (`low` vs. `high`), and `frequency` (`low` vs. `high`). Before running an analysis it is a good idea to visually inspect the data to gather some expectations regarding the results. Should the statistical results dramatically disagree with the expectations this suggests some type of error along the way (e.g., model misspecification) or at least encourages a thorough check to make sure everything is correct. We first begin by plotting the data aggregated by-participant. In each plot we plot the raw data in the background. To make the individual data points visible we add some `jitter` on the x-axis and choose `pch` and `alpha` values such that we see where more data points are (i.e., where plot overlaps it is darker). Then we add the mean as a x in a circle. Both of this is done in the same call to `xyplot` using a custom panel function. Finally, we combine this plot with a simple boxplot using `bwplot`. ```{r, fig.width=7, fig.height=6} agg_p <- fhch %>% group_by(id, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_p, jitter.x = TRUE, pch = 20, alpha = 0.5, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_p, pch="|", do.out = FALSE) ``` Now we plot the same data but aggregated across items: ```{r, fig.width=7, fig.height=6} agg_i <- fhch %>% group_by(item, task, stimulus, density, frequency) %>% summarise(mean = mean(log_rt)) %>% ungroup() xyplot(mean ~ density:frequency|task+stimulus, agg_i, jitter.x = TRUE, pch = 20, alpha = 0.2, panel = function(x, y, ...) { panel.xyplot(x, y, ...) tmp <- aggregate(y, by = list(x), mean) panel.points(tmp$x, tmp$y, pch = 13, cex =1.5) }) + bwplot(mean ~ density:frequency|task+stimulus, agg_i, pch="|", do.out = FALSE) ``` These two plots show a very similar pattern and suggest several things: * Responses to `nonwords` appear slower than responses to `words`, at least for the `naming` task. * `lexdec` responses appear to be slower than `naming` responses, particularly in the `word` condition. * In the `nonword` and `naming` condition we see a clear effect of `frequency` with slower responses to `high` than `low` `frequency` words. * In the `word` conditions the `frequency` pattern appears to be in the opposite direction to the pattern described in the previous point: faster responses to `low` `frequency` than to `high` `frequency` words. * `density` appears to have no effect, perhaps with the exception of the `nonword` `lexdec` condition. ## Model Setup To set up a mixed model it is important to identify which factors vary within which grouping factor generating random variability (i.e., grouping factors are sources of stochastic variability). The two grouping factors are participants (`id`) and items (`item`). The within-participant factors are `stimulus`, `density`, and `frequency`. The within-item factor is `task`. The 'maximal model' (Barr, Levy, Scheepers, and Tily, 2013) therefore is the model with by-participant random slopes for `stimulus`, `density`, and `frequency` and their interactions and by-item random slopes for `task`. Occasionally, the maximal model does not converge successfully. In this case a good first approach for dealing with this problem is to remove the corelations among the random terms. In our example, there are two sets of correlations, one for each random effect grouping variable. Consequently, we can build four model that have the maximal structure in terms of random-slopes and only differ in which correlations among random terms are calculated: 1. With all correlations. 2. No correlation among by-item random effects (i.e., no correlation between random intercept and `task` random slope). 3. No correlation among by-participant random effect terms (i.e., no correlation among random slopes themselves and between the random slopes and the random intercept). 4. No correlation among either random grouping factor. The next decision to be made is which method to use for obtaining $p$-values. The default method is `KR` (=Kenward-Roger) which provides the best control against anti-conservative results. However, `KR` needs quite a lot of RAM, especially with complicated random effect structures and large data sets. As in this case we have both, relatively large data (i.e., many levels on each random effect, especially the item random effect) and a complicated random effect structure, it seems a reasonable decision to choose another method. The second 'best' method (in terms of controlling for Type I errors) is the 'Satterthwaite' approximation, `method='S'`. It provides a similar control of Type I errors as the Kenward-Roger approximation and needs less RAM, however one downside is that it simply fails in some cases. ## Results ### Satterthwaite Results The following code fits the four models using the Satterthwaite method. To suppress random effects we use the `||` notation. Note that it is necessary to set `expand_re=TRUE` when suppressing random effects among variables that are entered as factors and not as numerical variables (as done here). Also note that `mixed` automatically uses appropriate contrast codings if factors are included in interactions (`contr.sum`) in contrast to the `R` default (which is `contr.treatment`). To make sure the estimation does not end prematurely we set the allowed number of function evaluations to a very high value (using `lmerControl`). ```{r, eval = FALSE} m1s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task|item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6))) m2s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task||item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m3s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task|item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m4s <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task||item), fhch, method = "S", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ``` As the estimation of these model may take some time, `afex` inlcudes the estimated models which can be loaded with the following code. Note that when using the `print` or `anova` method for `mixed` objects, the `warnings` emitted during estimation of the model by `lmer` will be printed again. So there is no downside of loading the already estimated models. We then inspect the four results. ```{r} load(system.file("extdata/", "freeman_models.rda", package = "afex")) m1s m2s m3s m4s ``` Before looking at the results we can see that for models 1 and 2, `lmer` emmited a warning that the model failed to converge. These warnings do not necessarily mean that the results cannot be used. As we will see below, model 2 (`m2s`) produces essentially the same results as models 3 and 4 suggesting that this warning is indeed a false positive. However, the results also show that estimating the Satterthwaite approximation failed for `m1s`, we have no denominator degrees of freedom and no $p$-values. If this happens, we can only try another method or a reduced model. Models 2 to 4 produce results and the results are extremely similar across models. A total of 9 or 10 effects reached significance. We found main effects for `task` and `stimulus`, two-way interactions of `task:stimulus`, `task:density`, `task:frequency`, and `stimulus:frequency`, three-way interactions of `task:stimulus:density`, `task:stimulus:frequency`, and `task:density:frequency`, a marginal three-way interaction (for two of three models) of `stimulus:density:frequency`, and the four-way interaction of `task:stimulus:density:frequency`. Additionally, all $F$ and $p$ values are very similar to each other across the three models. The only difference in terms of significant versus non-significant effects between the three models is the three-way interaction of `stimulus:density:frequency` which is only significant for model 3 with $F(1, 88.40) = 4.16$, $p = .04$, and only reaches marginal significance for the other two models with $p > .05$ and a very similar $F$-value. ### LRT Results It is instructive to compare those results with results obtained using the comparatively 'worst' method for obtaining $p$-value simplmeneted in `afex`, likelihood ratio tests. Likelihood ratio-tests should in principle deliver reasonable results for large data sets such as the current one, so we should expect not too many deviations. We again fit all four models, this time using `method='LRT'`. ```{r, eval = FALSE} m1lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task|item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6))) m2lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency|id)+ (task||item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m3lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task|item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) m4lrt <- mixed(log_rt ~ task*stimulus*density*frequency + (stimulus*density*frequency||id)+ (task||item), fhch, method = "LRT", control = lmerControl(optCtrl = list(maxfun = 1e6)), expand_re = TRUE) ``` Because the resulting `mixed` objects are of considerable size, we do not include the full objects, but only the resulting ANOVA tables and `data.frames` (`nice_lrt` is a list containing the result from calling `nice` on the objects, `anova_lrt` contains the result from calling `anova`). Before considering the results, we again first consider the warnings emitted when fitting the models. Because methods `'LRT'` and `'PB'` fit one `full_model` and one `restricted_model` for each effect (i.e., term), there can be more warnings than for methods `'KR'` and `'S'` which only fit one model (the `full_model`). And this is exactly what happens. For `m1lrt` there are 11 convergence warnings, almost one per fitted model. However, none of those immediately invalidates the results. This is different for models 2 and 3 for both of which warnings indicate that `nested model(s) provide better fit than full model`. What this warning means is that the `full_model` does not provide a better fit than at least one of the `restricted_model`, which is mathematically impossible as the `restricted_models` are nested within the full model (i.e., they result from setting one or several parameters equal to 0, so the `full_model` can always provide an at least as good account as the `restricted_models`). Model 4 finally shows no warnings. The following code produces a single output comparing models 1 and 4 next to each other. The results show basically the same pattern as obtained with the Satterthwaite approximation. Even the $p$-values are extremely similar to the $p$-values of the Satterthwaite models. The only 'difference' is that the `stimulus:density:frequency` three-way interaction is significant in each case now, although only barely so. ```{r} res_lrt <- cbind(nice_lrt[[1]], " " = " ", nice_lrt[[4]][,-(1:2)]) colnames(res_lrt)[c(3,4,6,7)] <- paste0( rep(c("m1_", "m4_"), each =2), colnames(res_lrt)[c(3,4)]) res_lrt ``` We can also compare this with the results from model 3. Although the `full_model` cannot be the maximum-likelihood estimate (as it provides a worse than the `density:frequency` model), the difference seems to be minimal as it also shows exactly the same pattern as the other models. ```{r} nice_lrt[[2]] ``` ### Summary of Results Fortunately, the results from all models that actually produced results and converged without a critical warning (e.g., one critical warning is that a `restricted_model` provides a better fit than the `full_model`) agreed very strongly providing a high degree of confidence in the results. This might not be too surprising given the comparatively large number of total data points and the fact that each random effect grouping factor has a considerable number of levels (way above 20 for both participants and items). This also suggests that the convergence warnings are likely false positives; the models seem to have converged successfully to the maximum likelihood estimate, or at least to a value very near the maximum likelihood estimate. How further reducing the random effects structure (e.g., removing the random slopes for the highest interaction) affects the results is left as an exercise for the reader. In terms of the significant findings, there are many that seem to be in line with the descriptive results described above. For example, the highly significant effect of `task:stimulus:frequency` with $F(1, 190.61) = 109.33$, $p < .0001$ (values from `m2s`), appears to be in line with the observation that the frequency effect appears to change its sign depending on the `task:stimulus` cell (with `nonword` and `naming` showing the opposite patterns than the other three conditions). Consequently, we start by investigating this interaction further below. ## Follow-Up Analyses Before investigating the significant interaction in detail it is a good idea to remind oneself what a significant interaction represents on a conceptual level; that one or multiple of the variables in the interaction moderate (i.e., affect) the effect of the other variable or variables. Consequently, there are several ways to investigate a significant interaction. Each of the involved variables can be seen as the moderating variables and each of the variables can be seen as the effect of interest. Which one of those possible interpretations is of interest in a given situation highly depends on the actual data and research question and multiple views can be 'correct' in a given situation. In addition to this conceptual issue, there are also multiple technical ways to investigate a significant interaction. One approach not followed here is to split the data according to the moderating variables and compute the statistical model again for the splitted data sets with the effect variable(s) as remaining fixed effect. This approach, also called _simple effects_ analysis, is, for example, recommended by Maxwell and Delaney (2004) as it does not assume variance homogeneity and is faithful to the data at each level. The approach taken here is to simply perform the test on the fitted full model. This approach assumes variance homogeneity (i.e., that the variances in all groups are homogeneous) and has the added benefit that it is computationally relatively simple. In addition, it can all be achieved using the framework provided by [`emmeans`](https://cran.r-project.org/package=emmeans) (Lenth, 2017). ### task:stimulus:frequency Interaction Our interest in the beginning is on the effect of `frequency` by `task:stimulus` combination. So let us first look at the estimated marginal means os this effect. In `emmeans` parlance these estimated means are called 'least-square means' because of historical reasons, but because of the lack of least-square estimation in mixed models we prefer the term estimated marginal means, or EMMs for short. Those can be obtained in the following way. To prevent `emmeans` from calculating the *df* for the EMMs (which can be quite costly), we use asymptotic *df*s (i.e., $z$ values and tests). `emmeans` requires to first specify the variable(s) one wants to treat as the effect variable(s) (here `frequency`) and then allows to specify condition variables. ```{r} emm_options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- emmeans(m2s, "frequency", by = c("stimulus", "task")) emm_i1 ``` The returned values are in line with our observation that the `nonword` and `naming` condition diverges from the other three. But is there actual evidence that the effect flips? We can test this using additional `emmeans` functionality. Specifically, we first use the `pairs` function which provides us with a pairwise test of the effect of `frequency` in each `task:stimulus` combination. Then we need to combine the four tests within one object to obtain a familywise error rate correction which we do via `update(..., by = NULL)` (i.e., we revert the effect of the `by` statement from the earlier `emmeans` call) and finally we select the `holm` method for controlling for family wise error rate (the Holm method is uniformly more powerful than the Bonferroni). ```{r} update(pairs(emm_i1), by = NULL, adjust = "holm") ``` We could also use a slightly more powerful method than the Holm method, method `free` from package `multcomp`, which takes the correlation of the model parameters into account (note that due a bug in the current emmenas version this is currently deactivated): ```{r, eval=FALSE} summary(as.glht(update(pairs(emm_i1), by = NULL)), test = adjusted("free")) ``` We see that the results are exactly as expected. In the `nonword` and `naming` condition we have a clear negative effect of frequency while in the other three conditions it is clearly positive. We could now also use the EMMs and retransform them onto the response scale (i.e., RTs) which we could use for plotting. Note that the $p$-values in this ouput are for the $z$ test of whether or not a value is significantly above 0 on the `log_rt`-scale (i.e., above 1 second on the response scale). That seems not the most interesting test, but the output is interesting because of the EMMs and standard errors that could be used for printing. ```{r} emm_i1b <- summary(contrast(emm_i1, by = NULL)) emm_i1b[,c("estimate", "SE")] <- exp(emm_i1b[,c("estimate", "SE")]) emm_i1b ``` ### task:stimulus:density:frequency Interaction As the last example, let us take a look at the significant four-way interaction of `task:stimulus:density:frequency`, $F(1, 111.32) = 10.07$, $p = .002$. Here we might be interested in a slightly more difficult question namely whether the `density:frequency` interaction varies across `task:stimulus` conditions. If we again look at the figures above, it appears that there is a difference between `low:low` and `high:low` in the `nonword` and `lexdec` condition, but not in the other conditions. We again first begin by obtaining the EMMs. However, the actual values are not interesting at the moment, we are basically only interested in the interaction for each `task:stimulus` condition. Therefore, we use the EMMs to create two consecutive contrasts, the first one for `density` and then for `frequency` using the fist contrast. Then we run a joint test conditional on the `task:stimulus` conditions. ```{r} emm_i2 <- emmeans(m2s, c("density", "frequency"), by = c("stimulus", "task")) con1 <- contrast(emm_i2, "trt.vs.ctrl1", by = c("frequency", "stimulus", "task")) # density con2 <- contrast(con1, "trt.vs.ctrl1", by = c("contrast", "stimulus", "task")) test(con2, joint = TRUE, by = c("stimulus", "task")) ``` This test indeed shows that the `density:frequency` interaction is only significant in the `nonword` and `lexdec` condition. Next, let's see if we can unpack this interaction in a meaningful manner. For this we compare `low:low` and `high:low` in each of the four groups. And just for the sake of making the example more complex, we also compare `low:high` and `high:high`. This can simply be done by specifying a list of custom contrasts on the EMMs (or reference grid in `emmeans` parlance) which can be passed again to the `contrast` function. The contrasts are a `list` where each element should sum to one (i.e., be a proper contrast) and be of length equal to the number of EMMs (although we have 16 EMMs in total, we only need to specify it for a length of four due to conditiong by `c("stimulus", "task")`). To control for the family wise error rate across all tests, we again use `update(..., by = NULL)` on the result this time again specifying `by = NULL` to revert the effect of conditiong. Note that although we entered the variables into `emmeans` in the same order as into our plot call above, the order of the four EMMs differs. ```{r} emm_i2 # desired contrats: des_c <- list( ll_hl = c(1, -1, 0, 0), lh_hh = c(0, 0, 1, -1) ) update(contrast(emm_i2, des_c), by = NULL, adjust = "holm") ``` In contrast to our expectation, the results show two significant effects and not only one. In line with our expectations, in the `nonword` and `lexdec` condition the EMM of `low:high` is smaller than the EMM for `high:high`, $z = -6.30$, $p < .0001$. However, in the `nonword` and `naming` condition we found the opposite pattern; the EMM of `low:high` is larger than the EMM for `high:high`, $z = 3.65$, $p = .002$. For all other effects $|z| < 1.3$, $p > .99$. In addition, there is no difference between `low:high` and `high:high` in any condition. ## References * Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. _Journal of Memory and Language_, 68(3), 255-278. https://doi.org/10.1016/j.jml.2012.11.001 * Bretz, F., Hothorn, T., & Westfall, P. H. (2011). _Multiple comparisons using R_. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp * Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. _Journal of Memory and Language_, 62(1), 1-18. https://doi.org/10.1016/j.jml.2009.09.004 * Lenth, R. (2017). _emmeans: Estimated Marginal Means, aka Least-Squares Means_. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans * Maxwell, S. E., & Delaney, H. D. (2004). _Designing experiments and analyzing data: a model-comparisons perspective_. Mahwah, N.J.: Lawrence Erlbaum Associates. ```{r, echo=FALSE, eval = FALSE} ### OLD STUFF BELOW. PLEASE IGNORE. load("freeman_models.rda") load("../freeman_models_all.rda") m1lrt$restricted_models <- list(NULL) m2lrt$restricted_models <- list(NULL) m3lrt$restricted_models <- list(NULL) m4lrt$restricted_models <- list(NULL) save(m1lrt, file = "freeman_models1.rda", compress = "xz") save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models.rda", compress = "xz") anovas_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), anova) nice_lrt <- lapply(list(m1lrt, m2lrt, m3lrt, m4lrt), nice) res_lrt <- cbind(nice_lrt[[1]], " " = " ", nice_lrt[[2]][,-(1:2)], " " = " ", nice_lrt[[3]][,-(1:2)], " " = " ", nice_lrt[[4]][,-(1:2)]) colnames(res_lrt)[c(3,4,6,7, 9,10, 12,13)] <- paste0( rep(c("m1_", "m2_", "m3_","m4_"), each =2), colnames(res_lrt)[c(3,4)]) ## warnings: m1s # fails and 1 warning m2s # 1 warning m3s # 0 warnings m4s # 0 warnings m1lrt # 11 warnings m2lrt # 1 nested model(s) provide better, 7 other warnings m3lrt # 7 nested models provide better fit, 9 other warnings m4lrt # 0 warnings cbind(nice_lrt[[1]]$Effect, do.call("cbind", lapply(nice_lrt, function(x) x[,3:4]))) save(m1s, m2s, m3s, m4s, anovas_lrt, nice_lrt,file = "freeman_models.rda", compress = "xz") save(m1s, m2s, m3s, m4s, m1lrt, m2lrt, m3lrt, m4lrt, file = "freeman_models2.rda", compress = "bzip2") tools::resaveRdaFiles("freeman_models1.rda") ``` afex/inst/doc/afex_anova_example.html0000644000176200001440000116154713607676755017474 0ustar liggesusers ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)

ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)

Henrik Singmann

2020-01-15

Overview

This documents reanalysis a dataset from an Experiment performed by Singmann and Klauer (2011) using the ANOVA functionality of afex followed by post-hoc tests using package emmeans (Lenth, 2017). After a brief description of the dataset and research question, the code and results are presented.

Description of Experiment and Data

Singmann and Klauer (2011) were interested in whether or not conditional reasoning can be explained by a single process or whether multiple processes are necessary to explain it. To provide evidence for multiple processes we aimed to establish a double dissociation of two variables: instruction type and problem type. Instruction type was manipulated between-subjects, one group of participants received deductive instructions (i.e., to treat the premises as given and only draw necessary conclusions) and a second group of participants received probabilistic instructions (i.e., to reason as in an everyday situation; we called this “inductive instruction” in the manuscript). Problem type consisted of two different orthogonally crossed variables that were manipulated within-subjects, validity of the problem (formally valid or formally invalid) and plausibility of the problem (inferences which were consisted with the background knowledge versus problems that were inconsistent with the background knowledge). The critical comparison across the two conditions was among problems which were valid and implausible with problems that were invalid and plausible. For example, the next problem was invalid and plausible:

If a person is wet, then the person fell into a swimming pool.
A person fell into a swimming pool.
How valid is the conclusion/How likely is it that the person is wet?

For those problems we predicted that under deductive instructions responses should be lower (as the conclusion does not necessarily follow from the premises) as under probabilistic instructions. For the valid but implausible problem, an example is presented next, we predicted the opposite pattern:

If a person is wet, then the person fell into a swimming pool.
A person is wet.
How valid is the conclusion/How likely is it that the person fell into a swimming pool?

Our study also included valid and plausible and invalid and implausible problems.

In contrast to the analysis reported in the manuscript, we initially do not separate the analysis into affirmation and denial problems, but first report an analysis on the full set of inferences, MP, MT, AC, and DA, where MP and MT are valid and AC and DA invalid. We report a reanalysis of our Experiment 1 only. Note that the factor plausibility is not present in the original manuscript, there it is a results of a combination of other factors.

Data and R Preperation

We begin by loading the packages we will be using throughout.

library("afex")     # needed for ANOVA functions.
library("emmeans")  # emmeans must now be loaded explicitly for follow-up tests.
library("multcomp") # for advanced control for multiple testing/Type 1 errors.
library("ggplot2")  # for customizing plots.
afex_options(emmeans_model = "multivariate") # use multivariate model for all follow-up tests.

Note that for ANOVAs involving repeated-measures factors, follow-up tests based on the multivariate model are generally preferrably to univariate follow-up tests. Consequently, we set this option globally. Future versions of afex will likely use the multivariate model as the default.

data(sk2011.1)
str(sk2011.1)
## 'data.frame':    640 obs. of  9 variables:
##  $ id          : Factor w/ 40 levels "8","9","10","12",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ instruction : Factor w/ 2 levels "deductive","probabilistic": 2 2 2 2 2 2 2 2 2 2 ...
##  $ plausibility: Factor w/ 2 levels "plausible","implausible": 1 2 2 1 2 1 1 2 1 2 ...
##  $ inference   : Factor w/ 4 levels "MP","MT","AC",..: 4 2 1 3 4 2 1 3 4 2 ...
##  $ validity    : Factor w/ 2 levels "valid","invalid": 2 1 1 2 2 1 1 2 2 1 ...
##  $ what        : Factor w/ 2 levels "affirmation",..: 2 2 1 1 2 2 1 1 2 2 ...
##  $ type        : Factor w/ 2 levels "original","reversed": 2 2 2 2 1 1 1 1 2 2 ...
##  $ response    : int  100 60 94 70 100 99 98 49 82 50 ...
##  $ content     : Factor w/ 4 levels "C1","C2","C3",..: 1 1 1 1 2 2 2 2 3 3 ...

An important feature in the data is that each participant provided two responses for each cell of the design (the content is different for each of those, each participant saw all four contents). These two data points will be aggregated automatically by afex.

with(sk2011.1, table(inference, id, plausibility))
## , , plausibility = plausible
## 
##          id
## inference 8 9 10 12 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
##        MP 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        MT 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        AC 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        DA 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##          id
## inference 37 38 39 40 41 42 43 44 46 47 48 49 50
##        MP  2  2  2  2  2  2  2  2  2  2  2  2  2
##        MT  2  2  2  2  2  2  2  2  2  2  2  2  2
##        AC  2  2  2  2  2  2  2  2  2  2  2  2  2
##        DA  2  2  2  2  2  2  2  2  2  2  2  2  2
## 
## , , plausibility = implausible
## 
##          id
## inference 8 9 10 12 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
##        MP 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        MT 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        AC 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##        DA 2 2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
##          id
## inference 37 38 39 40 41 42 43 44 46 47 48 49 50
##        MP  2  2  2  2  2  2  2  2  2  2  2  2  2
##        MT  2  2  2  2  2  2  2  2  2  2  2  2  2
##        AC  2  2  2  2  2  2  2  2  2  2  2  2  2
##        DA  2  2  2  2  2  2  2  2  2  2  2  2  2

ANOVA

To get the full ANOVA table for the model, we simply pass it to aov_ez using the design as described above. We save the returned object for further analysis.

a1 <- aov_ez("id", "response", sk2011.1, between = "instruction", 
       within = c("inference", "plausibility"))
## Warning: More than one observation per cell, aggregating the data using mean (i.e,
## fun_aggregate = mean)!
## Contrasts set to contr.sum for the following variables: instruction
a1 # the default print method prints a data.frame produced by nice 
## Anova Table (Type 3 tests)
## 
## Response: response
##                               Effect           df     MSE         F  ges p.value
## 1                        instruction        1, 38 2027.42      0.31 .003     .58
## 2                          inference 2.66, 101.12  959.12   5.81 **  .06    .002
## 3              instruction:inference 2.66, 101.12  959.12   6.00 **  .07    .001
## 4                       plausibility        1, 38  468.82 34.23 ***  .07  <.0001
## 5           instruction:plausibility        1, 38  468.82  10.67 **  .02    .002
## 6             inference:plausibility  2.29, 87.11  318.91    2.87 + .009     .06
## 7 instruction:inference:plausibility  2.29, 87.11  318.91    3.98 *  .01     .02
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
## 
## Sphericity correction method: GG

The equivalent calls (i.e., producing exactly the same output) of the other two ANOVA functions aov_car or aov4 is shown below.

aov_car(response ~ instruction + Error(id/inference*plausibility), sk2011.1)
aov_4(response ~ instruction + (inference*plausibility|id), sk2011.1)

As mentioned before, the two responses per cell of the design and participants are aggregated for the analysis as indicated by the warning message. Furthermore, the degrees of freedom are Greenhouse-Geisser corrected per default for all effects involving inference, as inference is a within-subject factor with more than two levels (i.e., MP, MT, AC, & DA). In line with our expectations, the three-way interaction is significant.

The object printed per default for afex_aov objects (produced by nice) can also be printed nicely using knitr:

knitr::kable(nice(a1))
Effect df MSE F ges p.value
instruction 1, 38 2027.42 0.31 .003 .58
inference 2.66, 101.12 959.12 5.81 ** .06 .002
instruction:inference 2.66, 101.12 959.12 6.00 ** .07 .001
plausibility 1, 38 468.82 34.23 *** .07 <.0001
instruction:plausibility 1, 38 468.82 10.67 ** .02 .002
inference:plausibility 2.29, 87.11 318.91 2.87 + .009 .06
instruction:inference:plausibility 2.29, 87.11 318.91 3.98 * .01 .02

Alternatively, the anova method for afex_aov objects returns a data.frame of class anova that can be passed to, for example, xtable for nice formatting:

print(xtable::xtable(anova(a1), digits = c(rep(2, 5), 3, 4)), type = "html")
num Df den Df MSE F ges Pr(>F)
instruction 1.00 38.00 2027.42 0.31 0.003 0.5830
inference 2.66 101.12 959.12 5.81 0.063 0.0016
instruction:inference 2.66 101.12 959.12 6.00 0.065 0.0013
plausibility 1.00 38.00 468.82 34.23 0.068 0.0000
instruction:plausibility 1.00 38.00 468.82 10.67 0.022 0.0023
inference:plausibility 2.29 87.11 318.91 2.87 0.009 0.0551
instruction:inference:plausibility 2.29 87.11 318.91 3.98 0.013 0.0177

Post-Hoc Contrasts and Plotting

To further analyze the data we need to pass it to package emmeans, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on emmeans can be obtained in its vignettes and faq. emmeans can work with afex_aov objects directly as afex comes with the necessary methods for the generic functions defined in emmeans. When using the multivariate options as described above, emmeans uses the ANOVA model estimated via base R’s lm method (which in the case of a multivariate response is an object of class c("mlm", "lm")). In the default setting (i.e., emmeans_model = "univariate"), emmeans uses the object created by base R’s aov function, which for now is also part of an afex_aov object.

Some First Contrasts

Main Effects Only

This object can now be passed to emmeans, for example to obtain the marginal means of the four inferences:

m1 <- emmeans(a1, ~ inference)
m1
##  inference emmean   SE df lower.CL upper.CL
##  MP          87.5 1.80 38     83.9     91.2
##  MT          76.7 4.06 38     68.5     84.9
##  AC          69.4 4.77 38     59.8     79.1
##  DA          83.0 3.84 38     75.2     90.7
## 
## Results are averaged over the levels of: instruction, plausibility 
## Confidence level used: 0.95

This object can now also be used to compare whether or not there are differences between the levels of the factor:

pairs(m1)
##  contrast estimate   SE df t.ratio p.value
##  MP - MT     10.83 4.33 38  2.501  0.0759 
##  MP - AC     18.10 5.02 38  3.607  0.0047 
##  MP - DA      4.56 4.20 38  1.086  0.7002 
##  MT - AC      7.27 3.98 38  1.825  0.2778 
##  MT - DA     -6.28 4.70 38 -1.334  0.5473 
##  AC - DA    -13.54 5.30 38 -2.556  0.0672 
## 
## Results are averaged over the levels of: instruction, plausibility 
## P value adjustment: tukey method for comparing a family of 4 estimates

To obtain more powerful p-value adjustments, we can furthermore pass it to multcomp (Bretz, Hothorn, & Westfall, 2011):

summary(as.glht(pairs(m1)), test=adjusted("free"))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##              Estimate Std. Error t value Pr(>|t|)   
## MP - MT == 0   10.831      4.331   2.501  0.05915 . 
## MP - AC == 0   18.100      5.018   3.607  0.00443 **
## MP - DA == 0    4.556      4.196   1.086  0.31350   
## MT - AC == 0    7.269      3.984   1.825  0.19409   
## MT - DA == 0   -6.275      4.703  -1.334  0.31350   
## AC - DA == 0  -13.544      5.299  -2.556  0.05915 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)

A Simple interaction

We could now also be interested in the marginal means of the inferences across the two instruction types. emmeans offers two ways to do so. The first splits the contrasts across levels of the factor using the by argument.

m2 <- emmeans(a1, "inference", by = "instruction")
## equal: emmeans(a1, ~ inference|instruction)
m2
## instruction = deductive:
##  inference emmean   SE df lower.CL upper.CL
##  MP          97.3 2.54 38     92.1    102.4
##  MT          70.4 5.75 38     58.8     82.0
##  AC          61.5 6.75 38     47.8     75.1
##  DA          81.8 5.43 38     70.8     92.8
## 
## instruction = probabilistic:
##  inference emmean   SE df lower.CL upper.CL
##  MP          77.7 2.54 38     72.6     82.9
##  MT          83.0 5.75 38     71.3     94.6
##  AC          77.3 6.75 38     63.7     91.0
##  DA          84.1 5.43 38     73.1     95.1
## 
## Results are averaged over the levels of: plausibility 
## Confidence level used: 0.95

Consequently, tests are also only performed within each level of the by factor:

pairs(m2)
## instruction = deductive:
##  contrast estimate   SE df t.ratio p.value
##  MP - MT     26.89 6.13 38  4.389  0.0005 
##  MP - AC     35.80 7.10 38  5.045  0.0001 
##  MP - DA     15.47 5.93 38  2.608  0.0599 
##  MT - AC      8.91 5.63 38  1.582  0.4007 
##  MT - DA    -11.41 6.65 38 -1.716  0.3297 
##  AC - DA    -20.32 7.49 38 -2.712  0.0471 
## 
## instruction = probabilistic:
##  contrast estimate   SE df t.ratio p.value
##  MP - MT     -5.22 6.13 38 -0.853  0.8287 
##  MP - AC      0.40 7.10 38  0.056  0.9999 
##  MP - DA     -6.36 5.93 38 -1.072  0.7084 
##  MT - AC      5.62 5.63 38  0.998  0.7512 
##  MT - DA     -1.14 6.65 38 -0.171  0.9982 
##  AC - DA     -6.76 7.49 38 -0.902  0.8036 
## 
## Results are averaged over the levels of: plausibility 
## P value adjustment: tukey method for comparing a family of 4 estimates

The second version considers all factor levels together. Consequently, the number of pairwise comparisons is a lot larger:

m3 <- emmeans(a1, c("inference", "instruction"))
## equal: emmeans(a1, ~inference*instruction)
m3
##  inference instruction   emmean   SE df lower.CL upper.CL
##  MP        deductive       97.3 2.54 38     92.1    102.4
##  MT        deductive       70.4 5.75 38     58.8     82.0
##  AC        deductive       61.5 6.75 38     47.8     75.1
##  DA        deductive       81.8 5.43 38     70.8     92.8
##  MP        probabilistic   77.7 2.54 38     72.6     82.9
##  MT        probabilistic   83.0 5.75 38     71.3     94.6
##  AC        probabilistic   77.3 6.75 38     63.7     91.0
##  DA        probabilistic   84.1 5.43 38     73.1     95.1
## 
## Results are averaged over the levels of: plausibility 
## Confidence level used: 0.95
pairs(m3)
##  contrast                            estimate   SE df t.ratio p.value
##  MP,deductive - MT,deductive            26.89 6.13 38  4.389  0.0020 
##  MP,deductive - AC,deductive            35.80 7.10 38  5.045  0.0003 
##  MP,deductive - DA,deductive            15.47 5.93 38  2.608  0.1848 
##  MP,deductive - MP,probabilistic        19.55 3.59 38  5.439  0.0001 
##  MP,deductive - MT,probabilistic        14.32 6.29 38  2.279  0.3310 
##  MP,deductive - AC,probabilistic        19.95 7.21 38  2.767  0.1342 
##  MP,deductive - DA,probabilistic        13.19 5.99 38  2.201  0.3741 
##  MT,deductive - AC,deductive             8.91 5.63 38  1.582  0.7577 
##  MT,deductive - DA,deductive           -11.41 6.65 38 -1.716  0.6772 
##  MT,deductive - MP,probabilistic        -7.34 6.29 38 -1.167  0.9363 
##  MT,deductive - MT,probabilistic       -12.56 8.13 38 -1.545  0.7783 
##  MT,deductive - AC,probabilistic        -6.94 8.86 38 -0.783  0.9931 
##  MT,deductive - DA,probabilistic       -13.70 7.91 38 -1.733  0.6666 
##  AC,deductive - DA,deductive           -20.32 7.49 38 -2.712  0.1501 
##  AC,deductive - MP,probabilistic       -16.25 7.21 38 -2.254  0.3446 
##  AC,deductive - MT,probabilistic       -21.48 8.86 38 -2.423  0.2600 
##  AC,deductive - AC,probabilistic       -15.85 9.54 38 -1.661  0.7111 
##  AC,deductive - DA,probabilistic       -22.61 8.66 38 -2.611  0.1834 
##  DA,deductive - MP,probabilistic         4.08 5.99 38  0.680  0.9971 
##  DA,deductive - MT,probabilistic        -1.15 7.91 38 -0.145  1.0000 
##  DA,deductive - AC,probabilistic         4.47 8.66 38  0.517  0.9995 
##  DA,deductive - DA,probabilistic        -2.29 7.68 38 -0.298  1.0000 
##  MP,probabilistic - MT,probabilistic    -5.22 6.13 38 -0.853  0.9885 
##  MP,probabilistic - AC,probabilistic     0.40 7.10 38  0.056  1.0000 
##  MP,probabilistic - DA,probabilistic    -6.36 5.93 38 -1.072  0.9588 
##  MT,probabilistic - AC,probabilistic     5.62 5.63 38  0.998  0.9719 
##  MT,probabilistic - DA,probabilistic    -1.14 6.65 38 -0.171  1.0000 
##  AC,probabilistic - DA,probabilistic    -6.76 7.49 38 -0.902  0.9840 
## 
## Results are averaged over the levels of: plausibility 
## P value adjustment: tukey method for comparing a family of 8 estimates

Running Custom Contrasts

Objects returned from emmeans can also be used to test specific contrasts. For this, we can simply create a list, where each element corresponds to one contrasts. A contrast is defined as a vector of constants on the reference grid (i.e., the object returned from emmeans, here m3). For example, we might be interested in whether there is a difference between the valid and invalid inferences in each of the two conditions.

c1 <- list(
  v_i.ded = c(0.5, 0.5, -0.5, -0.5, 0, 0, 0, 0),
  v_i.prob = c(0, 0, 0, 0, 0.5, 0.5, -0.5, -0.5)
  )

contrast(m3, c1, adjust = "holm")
##  contrast estimate   SE df t.ratio p.value
##  v_i.ded    12.194 4.12 38  2.960  0.0105 
##  v_i.prob   -0.369 4.12 38 -0.090  0.9291 
## 
## Results are averaged over the levels of: plausibility 
## P value adjustment: holm method for 2 tests
summary(as.glht(contrast(m3, c1)), test = adjusted("free"))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##               Estimate Std. Error t value Pr(>|t|)  
## v_i.ded == 0   12.1937     4.1190    2.96   0.0105 *
## v_i.prob == 0  -0.3687     4.1190   -0.09   0.9291  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)

The results can be interpreted as in line with expectations. Responses are larger for valid than invalid problems in the deductive, but not the probabilistic condition.

Plotting

Since version 0.22, afex comes with its own plotting function based on ggplot2, afex_plot, which works directly with afex_aov objects.

As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. As we saw above, this interaction was significant. Consequently, we are interested in plotting this interaction.

Basic Plots

For afex_plot, we need to specify the x-factor(s), which determine which factor-levels or combinations of factor-levels are plotted on the x-axis. We can also define trace factor(s), which determine which factor levels are connected by lines. Finally, we can also define panel factor(s), which determine if the plot is split into subplots. afex_plot then plots the estimated marginal means obtained from emmeans, confidence intervals, and the raw data in the background. Note that the raw data in the background is per default drawn using an alpha blending of .5 (i.e., 50% semi-transparency). Thus, in case of several points lying directly on top of each other, this point appears noticeably darker.

afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility")
## Warning: Panel(s) show a mixed within-between-design.
## Error bars do not allow comparisons across all means.
## Suppress error bars with: error = "none"

In the default settings, the error bars show 95%-confidence intervals based on the standard error of the underlying model (i.e., the lm model in the present case). In the present case, in which each subplot (defined by x- and trace-factor) shows a combination of a within-subjects factor (i.e., inference) and a between-subjects (i.e., instruction) factor, this is not optimal. The error bars only allow to assess differences regarding the between-subjects factor (i.e., across the lines), but not inferences regarding the within-subjects factor (i.e., within one line). This is also indicated by a warning.

An alternative would be within-subject confidence intervals:

afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", 
          error = "within")
## Warning: Panel(s) show a mixed within-between-design.
## Error bars do not allow comparisons across all means.
## Suppress error bars with: error = "none"

However, those only allow inferences regarding the within-subject factors and not regarding the between-subjecta factor. So the same warning is emitted again.

A further alternative is to suppress the error bars altogether. This is the approach used in our original paper and probably a good idea in general when figures show both between- and within-subjects factors within the same panel. The presence of the raw data in the background still provides a visual depiction of the variability of the data.

afex_plot(a1, x = "inference", trace = "instruction", panel = "plausibility", 
          error = "none")

Customizing Plots

afex_plot allows to customize the plot in a number of different ways. For example, we can easily change the aesthetic mapping associated with the trace factor. So instead of using lineytpe and shape of the symbols, we can use color. Furthermore, we can change the graphical element used for plotting the data points in the background. For example, instead of plotting the raw data, we can replace this with a boxplot. Finally, we can also make both the points showing the means and the lines connecting the means larger.

p1 <- afex_plot(a1, x = "inference", trace = "instruction", 
                panel = "plausibility", error = "none", 
                mapping = c("color", "fill"), 
                data_geom = geom_boxplot, data_arg = list(width = 0.4), 
                point_arg = list(size = 1.5), line_arg = list(size = 1))
p1

Note that afex_plot returns a ggplot2 plot object which can be used for further customization. For example, one can easily change the theme to something that does not have a grey background:

p1 + theme_light()

We can also set the theme globally for the remainder of the R session.

theme_set(theme_light())

The full set of customizations provided by afex_plot is beyond the scope of this vignette. The examples on the help page at ?afex_plot provide a good overview.

Replicate Analysis from Singmann and Klauer (2011)

However, the plots shown so far are not particularly helpful with respect to the research question. Next, we fit a new ANOVA model in which we separate the data in affirmation and denial inferences. This was also done in the original manuscript. We then lot the data a second time.

a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", 
       within = c("validity", "plausibility", "what"))
## Warning: More than one observation per cell, aggregating the data using mean (i.e,
## fun_aggregate = mean)!
## Contrasts set to contr.sum for the following variables: instruction
a2
## Anova Table (Type 3 tests)
## 
## Response: response
##                                    Effect    df     MSE         F    ges p.value
## 1                             instruction 1, 38 2027.42      0.31   .003     .58
## 2                                validity 1, 38  678.65    4.12 *    .01     .05
## 3                    instruction:validity 1, 38  678.65    4.65 *    .01     .04
## 4                            plausibility 1, 38  468.82 34.23 ***    .07  <.0001
## 5                instruction:plausibility 1, 38  468.82  10.67 **    .02    .002
## 6                                    what 1, 38  660.52      0.22  .0007     .64
## 7                        instruction:what 1, 38  660.52      2.60   .008     .11
## 8                   validity:plausibility 1, 38  371.87      0.14  .0002     .71
## 9       instruction:validity:plausibility 1, 38  371.87    4.78 *   .008     .04
## 10                          validity:what 1, 38 1213.14   9.80 **    .05    .003
## 11              instruction:validity:what 1, 38 1213.14   8.60 **    .05    .006
## 12                      plausibility:what 1, 38  204.54   9.97 **   .009    .003
## 13          instruction:plausibility:what 1, 38  204.54    5.23 *   .005     .03
## 14             validity:plausibility:what 1, 38  154.62      0.03 <.0001     .85
## 15 instruction:validity:plausibility:what 1, 38  154.62      0.42  .0003     .52
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Then we plot the data from this ANOVA. Because each panel would again show a mixed-design, we suppress the error bars.

afex_plot(a2, x = c("plausibility", "validity"), 
          trace = "instruction", panel = "what", 
          error = "none")

We see the critical and predicted cross-over interaction in the left of those two graphs. For implausible but valid problems deductive responses are larger than probabilistic responses. The opposite is true for plausible but invalid problems. We now tests these differences at each of the four x-axis ticks in each plot using custom contrasts (diff_1 to diff_4). Furthermore, we test for a validity effect and plausibility effect in both conditions.

(m4 <- emmeans(a2, ~instruction+plausibility+validity|what))
## what = affirmation:
##  instruction   plausibility validity emmean   SE df lower.CL upper.CL
##  deductive     plausible    valid      99.5 1.16 38     97.1    101.8
##  probabilistic plausible    valid      95.3 1.16 38     93.0     97.6
##  deductive     implausible  valid      95.1 5.01 38     85.0    105.2
##  probabilistic implausible  valid      60.2 5.01 38     50.0     70.3
##  deductive     plausible    invalid    67.0 6.95 38     52.9     81.0
##  probabilistic plausible    invalid    90.5 6.95 38     76.5    104.6
##  deductive     implausible  invalid    56.0 7.97 38     39.9     72.2
##  probabilistic implausible  invalid    64.1 7.97 38     48.0     80.3
## 
## what = denial:
##  instruction   plausibility validity emmean   SE df lower.CL upper.CL
##  deductive     plausible    valid      70.5 6.18 38     58.0     83.1
##  probabilistic plausible    valid      93.0 6.18 38     80.5    105.5
##  deductive     implausible  valid      70.2 6.36 38     57.4     83.1
##  probabilistic implausible  valid      73.0 6.36 38     60.1     85.8
##  deductive     plausible    invalid    86.5 5.32 38     75.8     97.3
##  probabilistic plausible    invalid    87.5 5.32 38     76.7     98.2
##  deductive     implausible  invalid    77.1 6.62 38     63.7     90.5
##  probabilistic implausible  invalid    80.8 6.62 38     67.4     94.1
## 
## Confidence level used: 0.95
c2 <- list(
  diff_1 = c(1, -1, 0, 0, 0, 0, 0, 0),
  diff_2 = c(0, 0, 1, -1, 0, 0, 0, 0),
  diff_3 = c(0, 0, 0, 0,  1, -1, 0, 0),
  diff_4 = c(0, 0, 0, 0,  0, 0, 1, -1),
  val_ded  = c(0.5, 0, 0.5, 0, -0.5, 0, -0.5, 0),
  val_prob = c(0, 0.5, 0, 0.5, 0, -0.5, 0, -0.5),
  plau_ded   = c(0.5, 0, -0.5, 0, -0.5, 0, 0.5, 0),
  plau_prob  = c(0, 0.5, 0, -0.5, 0, 0.5, 0, -0.5)
  )
contrast(m4, c2, adjust = "holm")
## what = affirmation:
##  contrast  estimate    SE df t.ratio p.value
##  diff_1       4.175  1.64 38  2.543  0.0759 
##  diff_2      34.925  7.08 38  4.931  0.0001 
##  diff_3     -23.600  9.83 38 -2.401  0.0854 
##  diff_4      -8.100 11.28 38 -0.718  0.9538 
##  val_ded     35.800  7.10 38  5.045  0.0001 
##  val_prob     0.400  7.10 38  0.056  0.9553 
##  plau_ded    -3.275  3.07 38 -1.068  0.8761 
##  plau_prob   30.775  4.99 38  6.164  <.0001 
## 
## what = denial:
##  contrast  estimate    SE df t.ratio p.value
##  diff_1     -22.425  8.74 38 -2.565  0.1007 
##  diff_2      -2.700  8.99 38 -0.300  1.0000 
##  diff_3      -0.925  7.52 38 -0.123  1.0000 
##  diff_4      -3.650  9.36 38 -0.390  1.0000 
##  val_ded    -11.412  6.65 38 -1.716  0.5658 
##  val_prob    -1.137  6.65 38 -0.171  1.0000 
##  plau_ded    -4.562  4.11 38 -1.109  1.0000 
##  plau_prob   13.363  2.96 38  4.519  0.0005 
## 
## P value adjustment: holm method for 8 tests

We can also pass these tests to multcomp which gives us more powerful Type 1 error corrections.

summary(as.glht(contrast(m4, c2)), test = adjusted("free"))
## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps

## Warning in tmp$pfunction("adjusted", ...): Completion with error > abseps
## $`what = affirmation`
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##                Estimate Std. Error t value Pr(>|t|)    
## diff_1 == 0       4.175      1.641   2.543   0.0651 .  
## diff_2 == 0      34.925      7.082   4.931 8.08e-05 ***
## diff_3 == 0     -23.600      9.830  -2.401   0.0709 .  
## diff_4 == 0      -8.100     11.275  -0.718   0.6882    
## val_ded == 0     35.800      7.096   5.045 6.08e-05 ***
## val_prob == 0     0.400      7.096   0.056   0.9553    
## plau_ded == 0    -3.275      3.065  -1.068   0.6036    
## plau_prob == 0   30.775      4.992   6.164 2.38e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)
## 
## 
## $`what = denial`
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##                Estimate Std. Error t value Pr(>|t|)    
## diff_1 == 0     -22.425      8.742  -2.565 0.081066 .  
## diff_2 == 0      -2.700      8.987  -0.300 0.984919    
## diff_3 == 0      -0.925      7.522  -0.123 0.984919    
## diff_4 == 0      -3.650      9.358  -0.390 0.984919    
## val_ded == 0    -11.412      6.651  -1.716 0.379647    
## val_prob == 0    -1.137      6.651  -0.171 0.984919    
## plau_ded == 0    -4.562      4.115  -1.109 0.725912    
## plau_prob == 0   13.363      2.957   4.519 0.000404 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)

Unfortunately, in the present case this function throws several warnings. Nevertheless, the p-values from both methods are very similar and agree on whether or not they are below or above .05. Because of the warnings it seems advisable to use the one provided by emmeans directly and not use the ones from multcomp.

The pattern for the affirmation problems is in line with the expectations: We find the predicted differences between the instruction types for valid and implausible (diff_2) and invalid and plausible (diff_3) and the predicted non-differences for the other two problems (diff_1 and diff_4). Furthermore, we find a validity effect in the deductive but not in the probabilistic condition. Likewise, we find a plausibility effect in the probabilistic but not in the deductive condition.

Some Cautionary Notes

  • Choosing the right correction for multiple testing can be difficult. In fact multcomp comes with an accompanying book (Bretz et al., 2011). If the degrees-of-freedom of all contrasts are identical using multcomp’s method free is more powerful than simply using the Bonferroni-Holm method. free is a generalization of the Bonferroni-Holm method that takes the correlations among the model parameters into account and uniformly more powerful.
  • For data sets with many within-subject factors, creating the aov object can take some time (i.e., compared to producing the ANOVA table which is usually very fast). Those objects are also comparatively large, often multiple MB. If speed is important and one is not interested in employing emmeans one can set return = "nice" in the call to the ANOVA function to only receive the ANOVA table (this can also be done globally: afex_options(return_aov = "nice")).

References

  • Bretz, F., Hothorn, T., & Westfall, P. H. (2011). Multiple comparisons using R. Boca Raton, FL: CRC Press. https://CRAN.R-project.org/package=multcomp
  • Singmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning. Thinking & Reasoning, 17(3), 247-281. doi: 10.1080/13546783.2011.572718
  • Lenth, R. (2017). emmeans: Estimated Marginal Means, aka Least-Squares Means. R package version 0.9.1. https://CRAN.R-project.org/package=emmeans
afex/inst/doc/afex_plot_supported_models.R0000644000176200001440000002711613607677016020517 0ustar liggesusers## ----set-options, echo=FALSE, cache=FALSE----------------------------------------------- options(width = 90) knitr::opts_chunk$set(dpi=72) knitr::knit_hooks$set(document = function(x){ gsub("```\n*```r*\n*", "", x) }) ## ----message=FALSE, warning=FALSE------------------------------------------------------- library("afex") library("ggplot2") library("cowplot") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) ## --------------------------------------------------------------------------------------- set_sum_contrasts() ## --------------------------------------------------------------------------------------- warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks) ## ----fig.width=7, fig.height=3---------------------------------------------------------- p1 <- afex_plot(warp.lm, "tension") p2 <- afex_plot(warp.lm, "tension", "wool") plot_grid(p1, p2) ## --------------------------------------------------------------------------------------- ins <- data.frame( n = c(500, 1200, 100, 400, 500, 300), size = factor(rep(1:3,2), labels = c("S","M","L")), age = factor(rep(1:2, each = 3)), claims = c(42, 37, 1, 101, 73, 14)) ## ----fig.width=3, fig.height=3---------------------------------------------------------- ins.glm <- glm(claims ~ size + age + offset(log(n)), data = ins, family = "poisson") afex_plot(ins.glm, "size", "age") ## --------------------------------------------------------------------------------------- ## binomial glm adapted from ?predict.glm ldose <- factor(rep(0:5, 2)) numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16) sex <- factor(rep(c("M", "F"), c(6, 6))) SF <- numdead/20 ## dv should be a vector, no matrix budworm.lg <- glm(SF ~ sex*ldose, family = binomial, weights = rep(20, length(numdead))) ## ----fig.width=8, fig.height=3---------------------------------------------------------- a <- afex_plot(budworm.lg, "ldose") b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! c <- afex_plot(budworm.lg, "ldose", "sex", data_arg = list(size = 4, color = "red")) plot_grid(a, b, c, labels = "AUTO", nrow = 1) ## ----fig.width=8, fig.height=6---------------------------------------------------------- ## nlme mixed model data(Oats, package = "nlme") Oats$nitro <- factor(Oats$nitro) oats.1 <- nlme::lme(yield ~ nitro * Variety, random = ~ 1 | Block / Variety, data = Oats) plot_grid( afex_plot(oats.1, "nitro", "Variety", data = Oats), # A afex_plot(oats.1, "nitro", "Variety", data = Oats), # B afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block"), # C afex_plot(oats.1, "nitro", data = Oats), # D afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")), # E afex_plot(oats.1, "nitro", data = Oats, id = "Block"), # F labels = "AUTO" ) ## ---- eval=FALSE------------------------------------------------------------------------ # library("glmmTMB") # tmb <- glmmTMB(count~spp * mined + (1|site), # ziformula = ~spp * mined, # family=nbinom2, Salamanders) # ## ---- eval=FALSE, include=FALSE--------------------------------------------------------- # library("glmmTMB") # set_sum_contrasts() # tmb <- glmmTMB(count~spp * mined + (1|site), # ziformula = ~spp * mined, # family=nbinom2, Salamanders) # save(tmb, file = "inst/extdata/tmb_example_fit.rda", compress = "xz") ## ---- echo=FALSE, include=FALSE--------------------------------------------------------- library("glmmTMB") data(Salamanders, package = "glmmTMB") load(system.file("extdata/", "tmb_example_fit.rda", package = "afex")) ## ----fig.width=8, fig.height=3---------------------------------------------------------- plot_grid( afex_plot(tmb, "spp"), afex_plot(tmb, "spp", data_geom = geom_violin), afex_plot(tmb, "spp", id = "site", data = Salamanders), labels = "AUTO", nrow = 1 ) ## ----fig.width=8.5, fig.height=3.5------------------------------------------------------ a <- afex_plot(tmb, "spp", "mined") b <- afex_plot(tmb, "spp", "mined", data_alpha = 0.3, data_arg = list( position = ggplot2::position_jitterdodge( jitter.width = 0.2, jitter.height = 0.5, dodge.width = 0.5 ## needs to be same as dodge ), color = "darkgrey")) plot_grid(a, b, labels = "AUTO") ## ----fig.width=5.5, fig.height=3.5------------------------------------------------------ afex_plot(tmb, "spp", "mined", id = "site", data = Salamanders, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list(dodge.width = 0.5, cex = 0.4, color = "darkgrey") ) ## ---- eval=FALSE------------------------------------------------------------------------ # library("rstanarm") ## requires resetting the ggplot2 theme # theme_set(theme_bw(base_size = 14) + # theme(legend.position="bottom", # panel.grid.major.x = element_blank(), # panel.grid.minor.x = element_blank())) # cbpp <- lme4::cbpp # cbpp$prob <- with(cbpp, incidence / size) # example_model <- stan_glmer(prob ~ period + (1|herd), # data = cbpp, family = binomial, weight = size, # chains = 2, cores = 1, seed = 12345, iter = 500) ## ---- eval=FALSE------------------------------------------------------------------------ # b1 <- afex_plot(example_model, "period") # ## dv column detected: prob # ## No id column passed. Assuming all rows are independent samples. # b2 <- afex_plot(example_model, "period", data_geom = geom_violin) # ## dv column detected: prob # ## No id column passed. Assuming all rows are independent samples. # plot_grid(b1, b2, labels = "AUTO") ## ----fig.width=7, fig.height=3, echo=FALSE---------------------------------------------- load(system.file("extdata/", "plots_rstanarm.rda", package = "afex")) plot_grid(b1, b2, labels = "AUTO") ## ---- eval=FALSE------------------------------------------------------------------------ # cbpp_l <- vector("list", nrow(cbpp)) # for (i in seq_along(cbpp_l)) { # cbpp_l[[i]] <- data.frame( # herd = cbpp$herd[i], # period = cbpp$period[i], # incidence = rep(0, cbpp$size[i]) # ) # cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 # } # cbpp_l <- do.call("rbind", cbpp_l) # cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) # cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) # example_model2 <- stan_glmer(incidence ~ period + (1|herd), # data = cbpp_l, family = binomial, # chains = 2, cores = 1, seed = 12345, iter = 500) ## ---- eval=FALSE------------------------------------------------------------------------ # b3 <- afex_plot(example_model2, "period") # ## dv column detected: incidence # ## No id column passed. Assuming all rows are independent samples. # b4 <- afex_plot(example_model2, "period", id = "herd") # ## dv column detected: incidence # plot_grid(b3, b4, labels = "AUTO") ## ----fig.width=7, fig.height=3, echo=FALSE---------------------------------------------- plot_grid(b3, b4, labels = "AUTO") ## ---- eval=FALSE------------------------------------------------------------------------ # data("Machines", package = "MEMSS") # mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, # chains = 2, cores = 1, seed = 12345, iter = 500) ## ---- eval=FALSE------------------------------------------------------------------------ # b5 <- afex_plot(mm, "Machine") # ## dv column detected: score # ## No id column passed. Assuming all rows are independent samples. # b6 <- afex_plot(mm, "Machine", id = "Worker") # ## dv column detected: score # plot_grid(b5, b6, labels = "AUTO") ## ----fig.width=7, fig.height=3, echo=FALSE---------------------------------------------- plot_grid(b5, b6, labels = "AUTO") ## ---- eval=FALSE, include=FALSE--------------------------------------------------------- # library("rstanarm") ## requires resetting the ggplot2 theme # library("ggplot2") # theme_set(theme_bw(base_size = 14) + # theme(legend.position="bottom", # panel.grid.major.x = element_blank(), # panel.grid.minor.x = element_blank())) # set_sum_contrasts() # cbpp <- lme4::cbpp # cbpp$prob <- with(cbpp, incidence / size) # example_model <- stan_glmer(prob ~ period + (1|herd), # data = cbpp, family = binomial, weight = size, # chains = 2, cores = 1, seed = 12345, iter = 500) # b1 <- afex_plot(example_model, "period") # b2 <- afex_plot(example_model, "period", data_geom = geom_violin) # # cbpp_l <- vector("list", nrow(cbpp)) # for (i in seq_along(cbpp_l)) { # cbpp_l[[i]] <- data.frame( # herd = cbpp$herd[i], # period = cbpp$period[i], # incidence = rep(0, cbpp$size[i]) # ) # cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1 # } # cbpp_l <- do.call("rbind", cbpp_l) # cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd)) # cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period)) # example_model2 <- stan_glmer(incidence ~ period + (1|herd), # data = cbpp_l, family = binomial, # chains = 2, cores = 1, seed = 12345, iter = 500) # b3 <- afex_plot(example_model2, "period") # b4 <- afex_plot(example_model2, "period", id = "herd") # # data("Machines", package = "MEMSS") # mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, # chains = 2, cores = 1, seed = 12345, iter = 500) # b5 <- afex_plot(mm, "Machine") # b6 <- afex_plot(mm, "Machine", id = "Worker", data = Machines) # save(b1, b2, b3, b4, b5, b6, file = "../inst/extdata/plots_rstanarm.rda", # compress = "xz", version = 2) ## ---- eval=FALSE------------------------------------------------------------------------ # library("brms") # data("Machines", package = "MEMSS") # mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, # chains = 2, cores = 1, seed = 12345, iter = 500) ## ---- eval=FALSE------------------------------------------------------------------------ # bb1 <- afex_plot(mrt, "Machine", data = Machines, dv = "score") # ## No id column passed. 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