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

Henrik Singmann

2017-05-25

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 lsmeans (Lenth, 2015). 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

require(afex) # needed for ANOVA, lsmeans is loaded automatically.
require(multcomp) # for advanced control for multiple testing/Type 1 errors.
require(lattice) # for plots
lattice.options(default.theme = standard.theme(color = FALSE)) # black and white
lattice.options(default.args = list(as.table = TRUE)) # better ordering
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 (aov_car or aov4 would be alternatives producing the same results) 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

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 lsmeans, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on lsmeans can be obtained in its vignette. lsmeans can work with afex_aov objects directly as afex comes with the necessary methods for the generic functions defined in lsmeans. lsmeans uses the ANOVA model estimated via base R’s aov function that is part of an afex_aov object.

Some First Contrasts

Main Effects Only

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

m1 <- lsmeans(a1, ~ inference)
## NOTE: Results may be misleading due to involvement in interactions
m1
##  inference   lsmean       SE     df lower.CL upper.CL
##  MP        87.51250 3.783074 126.87 80.02641 94.99859
##  MT        76.68125 3.783074 126.87 69.19516 84.16734
##  AC        69.41250 3.783074 126.87 61.92641 76.89859
##  DA        82.95625 3.783074 126.87 75.47016 90.44234
## 
## 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   10.83125 4.611854 114   2.349  0.0933
##  MP - AC   18.10000 4.611854 114   3.925  0.0008
##  MP - DA    4.55625 4.611854 114   0.988  0.7566
##  MT - AC    7.26875 4.611854 114   1.576  0.3963
##  MT - DA   -6.27500 4.611854 114  -1.361  0.5266
##  AC - DA  -13.54375 4.611854 114  -2.937  0.0206
## 
## 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"))
## Note: df set to 114
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##              Estimate Std. Error t value Pr(>|t|)    
## MP - MT == 0   10.831      4.612   2.349 0.068825 .  
## MP - AC == 0   18.100      4.612   3.925 0.000922 ***
## MP - DA == 0    4.556      4.612   0.988 0.325273    
## MT - AC == 0    7.269      4.612   1.576 0.281791    
## MT - DA == 0   -6.275      4.612  -1.361 0.296932    
## AC - DA == 0  -13.544      4.612  -2.937 0.017561 *  
## ---
## 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. lsmeans offers two ways to do so. The first splits the contrasts across levels of the factor.

m2 <- lsmeans(a1, ~ inference|instruction)
## NOTE: Results may be misleading due to involvement in interactions
m2
## instruction = deductive:
##  inference  lsmean       SE     df lower.CL  upper.CL
##  MP        97.2875 5.350074 126.87 86.70057 107.87443
##  MT        70.4000 5.350074 126.87 59.81307  80.98693
##  AC        61.4875 5.350074 126.87 50.90057  72.07443
##  DA        81.8125 5.350074 126.87 71.22557  92.39943
## 
## instruction = probabilistic:
##  inference  lsmean       SE     df lower.CL  upper.CL
##  MP        77.7375 5.350074 126.87 67.15057  88.32443
##  MT        82.9625 5.350074 126.87 72.37557  93.54943
##  AC        77.3375 5.350074 126.87 66.75057  87.92443
##  DA        84.1000 5.350074 126.87 73.51307  94.68693
## 
## Results are averaged over the levels of: plausibility 
## Confidence level used: 0.95

Consequently test are also only performed within each level:

pairs(m2)
## instruction = deductive:
##  contrast estimate       SE  df t.ratio p.value
##  MP - MT   26.8875 6.522147 114   4.122  0.0004
##  MP - AC   35.8000 6.522147 114   5.489  <.0001
##  MP - DA   15.4750 6.522147 114   2.373  0.0882
##  MT - AC    8.9125 6.522147 114   1.366  0.5229
##  MT - DA  -11.4125 6.522147 114  -1.750  0.3031
##  AC - DA  -20.3250 6.522147 114  -3.116  0.0122
## 
## instruction = probabilistic:
##  contrast estimate       SE  df t.ratio p.value
##  MP - MT   -5.2250 6.522147 114  -0.801  0.8538
##  MP - AC    0.4000 6.522147 114   0.061  0.9999
##  MP - DA   -6.3625 6.522147 114  -0.976  0.7636
##  MT - AC    5.6250 6.522147 114   0.862  0.8241
##  MT - DA   -1.1375 6.522147 114  -0.174  0.9981
##  AC - DA   -6.7625 6.522147 114  -1.037  0.7282
## 
## Results are averaged over the levels of: plausibility 
## P value adjustment: tukey method for comparing a family of 4 estimates

The second version treats all factor combinations together, producing a considerably larger number of pairwise comparisons:

m3 <- lsmeans(a1, ~ inference:instruction)
## NOTE: Results may be misleading due to involvement in interactions
m3
##  inference instruction    lsmean       SE     df lower.CL  upper.CL
##  MP        deductive     97.2875 5.350074 126.87 86.70057 107.87443
##  MT        deductive     70.4000 5.350074 126.87 59.81307  80.98693
##  AC        deductive     61.4875 5.350074 126.87 50.90057  72.07443
##  DA        deductive     81.8125 5.350074 126.87 71.22557  92.39943
##  MP        probabilistic 77.7375 5.350074 126.87 67.15057  88.32443
##  MT        probabilistic 82.9625 5.350074 126.87 72.37557  93.54943
##  AC        probabilistic 77.3375 5.350074 126.87 66.75057  87.92443
##  DA        probabilistic 84.1000 5.350074 126.87 73.51307  94.68693
## 
## 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          26.8875 6.522147 114.00   4.122  0.0018
##  MP,deductive - AC,deductive          35.8000 6.522147 114.00   5.489  <.0001
##  MP,deductive - DA,deductive          15.4750 6.522147 114.00   2.373  0.2649
##  MP,deductive - MP,probabilistic      19.5500 7.566147 126.87   2.584  0.1716
##  MP,deductive - MT,probabilistic      14.3250 7.566147 126.87   1.893  0.5581
##  MP,deductive - AC,probabilistic      19.9500 7.566147 126.87   2.637  0.1527
##  MP,deductive - DA,probabilistic      13.1875 7.566147 126.87   1.743  0.6592
##  MT,deductive - AC,deductive           8.9125 6.522147 114.00   1.366  0.8704
##  MT,deductive - DA,deductive         -11.4125 6.522147 114.00  -1.750  0.6548
##  MT,deductive - MP,probabilistic      -7.3375 7.566147 126.87  -0.970  0.9779
##  MT,deductive - MT,probabilistic     -12.5625 7.566147 126.87  -1.660  0.7125
##  MT,deductive - AC,probabilistic      -6.9375 7.566147 126.87  -0.917  0.9839
##  MT,deductive - DA,probabilistic     -13.7000 7.566147 126.87  -1.811  0.6141
##  AC,deductive - DA,deductive         -20.3250 6.522147 114.00  -3.116  0.0462
##  AC,deductive - MP,probabilistic     -16.2500 7.566147 126.87  -2.148  0.3906
##  AC,deductive - MT,probabilistic     -21.4750 7.566147 126.87  -2.838  0.0948
##  AC,deductive - AC,probabilistic     -15.8500 7.566147 126.87  -2.095  0.4239
##  AC,deductive - DA,probabilistic     -22.6125 7.566147 126.87  -2.989  0.0644
##  DA,deductive - MP,probabilistic       4.0750 7.566147 126.87   0.539  0.9994
##  DA,deductive - MT,probabilistic      -1.1500 7.566147 126.87  -0.152  1.0000
##  DA,deductive - AC,probabilistic       4.4750 7.566147 126.87   0.591  0.9989
##  DA,deductive - DA,probabilistic      -2.2875 7.566147 126.87  -0.302  1.0000
##  MP,probabilistic - MT,probabilistic  -5.2250 6.522147 114.00  -0.801  0.9928
##  MP,probabilistic - AC,probabilistic   0.4000 6.522147 114.00   0.061  1.0000
##  MP,probabilistic - DA,probabilistic  -6.3625 6.522147 114.00  -0.976  0.9770
##  MT,probabilistic - AC,probabilistic   5.6250 6.522147 114.00   0.862  0.9887
##  MT,probabilistic - DA,probabilistic  -1.1375 6.522147 114.00  -0.174  1.0000
##  AC,probabilistic - DA,probabilistic  -6.7625 6.522147 114.00  -1.037  0.9677
## 
## 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 lsmeans 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 lsmeans, 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  12.19375 4.611854 114   2.644  0.0187
##  v_i.prob -0.36875 4.611854 114  -0.080  0.9364
## 
## 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"))
## Note: df set to 114
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##               Estimate Std. Error t value Pr(>|t|)  
## v_i.ded == 0   12.1937     4.6119   2.644   0.0186 *
## v_i.prob == 0  -0.3687     4.6119  -0.080   0.9364  
## ---
## 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

Function lsmip from package lsmeans can be used for plotting the data directly from an afex_aov object. As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. A plot of this interaction could be the following:

lsmip(a1, instruction ~ inference|plausibility)

Replicate Analysis from Singmann and Klauer (2011)

As this plot is not very helpful, we now fit a new ANOVA model in which we separate the data in affirmation and denial inferences, as done in the original manuscript and plot the data then 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.

lsmip(a2, ~instruction ~ plausibility+validity|what, 
      scales = list(x=list(
        at = 1:4,
        labels = c("pl:v", "im:v", "pl:i", "im:i")
        )))

We see the critical predicted cross-over interaction in the left of those two graphs. For valid but implausible problems (im:v) deductive responses are larger than probabilistic responses. The opposite is true for invalid but plausible problems (pl:i). 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 <- lsmeans(a2, ~instruction+plausibility+validity|what))
## what = affirmation:
##  instruction   plausibility validity lsmean      SE     df lower.CL upper.CL
##  deductive     plausible    valid    99.475 6.01019 183.89  87.6172 111.3328
##  probabilistic plausible    valid    95.300 6.01019 183.89  83.4422 107.1578
##  deductive     implausible  valid    95.100 6.01019 183.89  83.2422 106.9578
##  probabilistic implausible  valid    60.175 6.01019 183.89  48.3172  72.0328
##  deductive     plausible    invalid  66.950 6.01019 183.89  55.0922  78.8078
##  probabilistic plausible    invalid  90.550 6.01019 183.89  78.6922 102.4078
##  deductive     implausible  invalid  56.025 6.01019 183.89  44.1672  67.8828
##  probabilistic implausible  invalid  64.125 6.01019 183.89  52.2672  75.9828
## 
## what = denial:
##  instruction   plausibility validity lsmean      SE     df lower.CL upper.CL
##  deductive     plausible    valid    70.550 6.01019 183.89  58.6922  82.4078
##  probabilistic plausible    valid    92.975 6.01019 183.89  81.1172 104.8328
##  deductive     implausible  valid    70.250 6.01019 183.89  58.3922  82.1078
##  probabilistic implausible  valid    72.950 6.01019 183.89  61.0922  84.8078
##  deductive     plausible    invalid  86.525 6.01019 183.89  74.6672  98.3828
##  probabilistic plausible    invalid  87.450 6.01019 183.89  75.5922  99.3078
##  deductive     implausible  invalid  77.100 6.01019 183.89  65.2422  88.9578
##  probabilistic implausible  invalid  80.750 6.01019 183.89  68.8922  92.6078
## 
## 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      4.1750 8.499692 183.89   0.491  1.0000
##  diff_2     34.9250 8.499692 183.89   4.109  0.0004
##  diff_3    -23.6000 8.499692 183.89  -2.777  0.0303
##  diff_4     -8.1000 8.499692 183.89  -0.953  1.0000
##  val_ded    35.8000 6.877109  70.38   5.206  <.0001
##  val_prob    0.4000 6.877109  70.38   0.058  1.0000
##  plau_ded   -3.2750 3.627998  64.94  -0.903  1.0000
##  plau_prob  30.7750 4.102924  65.86   7.501  <.0001
## 
## what = denial:
##  contrast  estimate       SE     df t.ratio p.value
##  diff_1    -22.4250 8.499692 183.89  -2.638  0.0633
##  diff_2     -2.7000 8.499692 183.89  -0.318  1.0000
##  diff_3     -0.9250 8.499692 183.89  -0.109  1.0000
##  diff_4     -3.6500 8.499692 183.89  -0.429  1.0000
##  val_ded   -11.4125 6.877109  70.38  -1.659  0.6088
##  val_prob   -1.1375 6.877109  70.38  -0.165  1.0000
##  plau_ded   -4.5625 3.627998  64.94  -1.258  1.0000
##  plau_prob  13.3625 4.102924  65.86   3.257  0.0143
## 
## P value adjustment: holm method for 8 tests

As the resulting eight contrasts have different numbers of degrees-of-freedom, we can only pass them to multcomp in small batches. This gives us more powerful Type 1 error corrections but overall a reduced correction as we now control for three families of tests (i.e., overall Type 1 error probability of .15).

summary(as.glht(contrast(m4, c2[1:4])), test =adjusted("free"))
## Note: df set to 184
## $`what = affirmation`
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##             Estimate Std. Error t value Pr(>|t|)    
## diff_1 == 0    4.175      8.500   0.491 0.623874    
## diff_2 == 0   34.925      8.500   4.109 0.000243 ***
## diff_3 == 0  -23.600      8.500  -2.777 0.017281 *  
## diff_4 == 0   -8.100      8.500  -0.953 0.564739    
## ---
## 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      8.500  -2.638   0.0331 *
## diff_2 == 0   -2.700      8.500  -0.318   0.9554  
## diff_3 == 0   -0.925      8.500  -0.109   0.9554  
## diff_4 == 0   -3.650      8.500  -0.429   0.9554  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)
summary(as.glht(contrast(m4, c2[5:6])), test =adjusted("free"))
## Note: df set to 70
## $`what = affirmation`
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##               Estimate Std. Error t value Pr(>|t|)    
## val_ded == 0    35.800      6.877   5.206 3.69e-06 ***
## val_prob == 0    0.400      6.877   0.058    0.954    
## ---
## 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|)
## val_ded == 0   -11.412      6.877  -1.659    0.192
## val_prob == 0   -1.137      6.877  -0.165    0.869
## (Adjusted p values reported -- free method)
summary(as.glht(contrast(m4, c2[7:8])), test =adjusted("free"))
## Note: df set to 65
## $`what = affirmation`
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##                Estimate Std. Error t value Pr(>|t|)    
## plau_ded == 0    -3.275      3.628  -0.903     0.37    
## plau_prob == 0   30.775      4.103   7.501  4.5e-10 ***
## ---
## 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|)   
## plau_ded == 0    -4.562      3.628  -1.258  0.21304   
## plau_prob == 0   13.362      4.103   3.257  0.00358 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- free method)

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

  • While the df of the ANOVA tables are Greenhouse-Geisser corrected per default for within-subject factors with more than two levels, this is not the case for post-hoc tests or contrasts using lsmeans. The contrasts use uncorrected degrees of freedom that are Satterthwaite approximated. This most likely produces anti-conservative tests if compound symmetry/sphericity is violated.
  • For unbalanced samples, aov is usually not the correct choise. This is why the test of effects is based on car::Anova. However, for lsmeans we need to use aov models. However, lsmeans offers the option to weight the marginal means differently in case of different group sizes (i.e., unbalanced data). For example, it offers the option that each group is assumed to be of equal size (i.e., weights = "equal") or proportionally (i.e., weights = "proportional"). See help of lsmeans for more information.
  • 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 lsmeans 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. V. (2015). lsmeans: Least-Squares Means. R package version 2.16-4. https://CRAN.R-project.org/package=lsmeans
afex/inst/doc/afex_mixed_example.html0000644000176200001440000110073013111546473017440 0ustar liggesusers Mixed Model Reanalysis of RT data

Mixed Model Reanalysis of RT data

Henrik Singmann

2017-05-25

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 lsmeans (Lenth, 2015). 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. In my opinion lattice provides the best combination of expressive power and abstraction. Specifically, like in base graph, we can fully decide what gets plotted.

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.

require(afex) # needed for ANOVA, lsmeans is loaded automatically.
require(dplyr) # for working with data frames
require(tidyr) # for transforming data frames from wide to long and the other way round.
require(multcomp) # for advanced control for multiple testing/Type 1 errors.
require(lattice) # for plots
require(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
##   <fctr> <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
##     <fctr> <int> <int>    <dbl>
## 1     word   139   150 147.4667
## 2  nonword   134   150 146.3556

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 lsmeans (Lenth, 2015).

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 lsmeans 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 lsmeans from calculating the df for the EMMs (which can be quite costly), we use asymptotic dfs (i.e., \(z\) values and tests). lsmeans 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.

lsm.options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger'
emm_i1 <- lsmeans(m2s, "frequency", by = c("stimulus", "task"))
## NOTE: Results may be misleading due to involvement in interactions
emm_i1
## stimulus = word, task = naming:
##  frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low       -0.323260819 0.04154237 NA -0.40468237 -0.24183927
##  high      -0.381928410 0.04571233 NA -0.47152293 -0.29233389
## 
## stimulus = nonword, task = naming:
##  frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low       -0.143143471 0.04584628 NA -0.23300052 -0.05328642
##  high       0.063627305 0.04965563 NA -0.03369594  0.16095054
## 
## stimulus = word, task = lexdec:
##  frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low        0.023231980 0.03730914 NA -0.04989260  0.09635656
##  high      -0.039959811 0.04099368 NA -0.12030595  0.04038633
## 
## stimulus = nonword, task = lexdec:
##  frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low        0.104057173 0.04115486 NA  0.02339514  0.18471921
##  high      -0.006455104 0.04451011 NA -0.09369331  0.08078310
## 
## 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 lsmeans 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 contrast(..., by = NULL) (i.e., we revert the effect of the by statement from the earlier lsmeans 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).

contrast(pairs(emm_i1), by = NULL, adjust = "holm")
##  contrast                            estimate         SE df z.ratio p.value
##  low - high,word,naming effect     0.05226737 0.01358051 NA   3.849  0.0001
##  low - high,nonword,naming effect -0.21317100 0.01446402 NA -14.738  <.0001
##  low - high,word,lexdec effect     0.05679157 0.01318314 NA   4.308  <.0001
##  low - high,nonword,lexdec effect  0.10411206 0.01392627 NA   7.476  <.0001
## 
## Results are averaged over the levels of: density 
## 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:

summary(as.glht(contrast(pairs(emm_i1), by = NULL)), test = adjusted("holm"))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Linear Hypotheses:
##                                       Estimate Std. Error z value Pr(>|z|)    
## low - high,word,naming effect == 0     0.05227    0.01358   3.849 0.000119 ***
## low - high,nonword,naming effect == 0 -0.21317    0.01446 -14.738  < 2e-16 ***
## low - high,word,lexdec effect == 0     0.05679    0.01318   4.308  3.3e-05 ***
## low - high,nonword,lexdec effect == 0  0.10411    0.01393   7.476  2.3e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)

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     0.7903480 1.029560 NA  -8.076  <.0001
##  high,word,naming effect    0.7453141 1.033128 NA  -9.019  <.0001
##  low,nonword,naming effect  0.9463294 1.033081 NA  -1.695  0.1029
##  high,nonword,naming effect 1.1637019 1.035842 NA   4.305  <.0001
##  low,word,lexdec effect     1.1176306 1.029734 NA   3.796  0.0002
##  high,word,lexdec effect    1.0491907 1.032572 NA   1.498  0.1341
##  low,nonword,lexdec effect  1.2117142 1.032575 NA   5.991  <.0001
##  high,nonword,lexdec effect 1.0849390 1.034791 NA   2.384  0.0228
## 
## Results are averaged over the levels of: density 
## 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 <- lsmeans(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 p.value
##  word     naming   1  NA  0.105  0.7464
##  nonword  naming   1  NA  2.537  0.1112
##  word     lexdec   1  NA  1.790  0.1809
##  nonword  lexdec   1  NA 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 lsmeans 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 use contrast a second time on the result this time again specifying by = NULL to revert the effect of conditiong. Note that although we entered the variables into lsmeans 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       lsmean         SE df   asymp.LCL   asymp.UCL
##  low     low       -0.313843596 0.04478638 NA -0.40162328 -0.22606391
##  high    low       -0.332678043 0.04081261 NA -0.41266929 -0.25268679
##  low     high      -0.377406551 0.04662971 NA -0.46879910 -0.28601400
##  high    high      -0.386450269 0.04721965 NA -0.47899907 -0.29390146
## 
## stimulus = nonword, task = naming:
##  density frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low     low       -0.103989924 0.04996611 NA -0.20192171 -0.00605814
##  high    low       -0.182297019 0.04415685 NA -0.26884286 -0.09575118
##  low     high       0.078231630 0.05201926 NA -0.02372424  0.18018750
##  high    high       0.049022979 0.04947457 NA -0.04794540  0.14599136
## 
## stimulus = word, task = lexdec:
##  density frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low     low        0.037141777 0.04035764 NA -0.04195775  0.11624130
##  high    low        0.009322184 0.03679361 NA -0.06279198  0.08143634
##  low     high      -0.045127696 0.04192675 NA -0.12730261  0.03704722
##  high    high      -0.034791927 0.04243206 NA -0.11795723  0.04837338
## 
## stimulus = nonword, task = lexdec:
##  density frequency       lsmean         SE df   asymp.LCL   asymp.UCL
##  low     low        0.044799574 0.04490982 NA -0.04322205  0.13282120
##  high    low        0.163314772 0.03986203 NA  0.08518664  0.24144291
##  low     high      -0.007277516 0.04669875 NA -0.09880539  0.08425036
##  high    high      -0.005632691 0.04446001 NA -0.09277271  0.08150732
## 
## 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)
  )
contrast(contrast(emm_i2, des_c), by = NULL, adjust = "holm")
##  contrast                        estimate         SE df z.ratio p.value
##  ll_hl,word,naming effect     0.014744733 0.01949044 NA   0.757  1.0000
##  lh_hh,word,naming effect     0.004954004 0.01990869 NA   0.249  1.0000
##  ll_hl,nonword,naming effect  0.074217381 0.02034362 NA   3.648  0.0018
##  lh_hh,nonword,naming effect  0.025118937 0.01977667 NA   1.270  1.0000
##  ll_hl,word,lexdec effect     0.023729879 0.01867913 NA   1.270  1.0000
##  lh_hh,word,lexdec effect    -0.014425482 0.01882784 NA  -0.766  1.0000
##  ll_hl,nonword,lexdec effect -0.122604912 0.01945809 NA  -6.301  <.0001
##  lh_hh,nonword,lexdec effect -0.005734539 0.01870550 NA  -0.307  1.0000
## 
## 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. V. (2015). lsmeans: Least-Squares Means. R package version 2.16-4. https://CRAN.R-project.org/package=lsmeans
  • 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.Rmd0000644000176200001440000006772313111540031017213 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) ``` ## 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 __lsmeans__ (Lenth, 2015). 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. In my opinion `lattice` provides the best combination of expressive power and abstraction. Specifically, like in base graph, we can fully decide what gets plotted. 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} require(afex) # needed for ANOVA, lsmeans is loaded automatically. require(dplyr) # for working with data frames require(tidyr) # for transforming data frames from wide to long and the other way round. require(multcomp) # for advanced control for multiple testing/Type 1 errors. require(lattice) # for plots require(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 `lsmeans` (Lenth, 2015). ### 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 `lsmeans` 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 `lsmeans` from calculating the *df* for the EMMs (which can be quite costly), we use asymptotic *df*s (i.e., $z$ values and tests). `lsmeans` 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} lsm.options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- lsmeans(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 `lsmeans` 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 `contrast(..., by = NULL)` (i.e., we revert the effect of the `by` statement from the earlier `lsmeans` 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} contrast(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: ```{r} summary(as.glht(contrast(pairs(emm_i1), by = NULL)), test = adjusted("holm")) ``` 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 <- lsmeans(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 `lsmeans` 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 use `contrast` a second time on the result this time again specifying `by = NULL` to revert the effect of conditiong. Note that although we entered the variables into `lsmeans` 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) ) contrast(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. V. (2015). _lsmeans: Least-Squares Means_. R package version 2.16-4. https://CRAN.R-project.org/package=lsmeans * 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.Rmd0000644000176200001440000003151013111546363017210 0ustar liggesusers--- title: "ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)" author: "Henrik Singmann" date: "`r Sys.Date()`" output: rmarkdown::html_vignette 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) ``` # 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 __lsmeans__ (Lenth, 2015). 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 ```{r message=FALSE, warning=FALSE} require(afex) # needed for ANOVA, lsmeans is loaded automatically. require(multcomp) # for advanced control for multiple testing/Type 1 errors. require(lattice) # for plots lattice.options(default.theme = standard.theme(color = FALSE)) # black and white lattice.options(default.args = list(as.table = TRUE)) # better ordering ``` ```{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` (`aov_car` or `aov4` would be alternatives producing the same results) 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 ``` 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 `lsmeans`, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on `lsmeans` can be obtained in [its vignette](https://CRAN.R-project.org/package=lsmeans/vignettes/using-lsmeans.pdf). `lsmeans` can work with `afex_aov` objects directly as __afex__ comes with the necessary methods for the generic functions defined in `lsmeans`. `lsmeans` uses the ANOVA model estimated via base R's `aov` function that is part of an `afex_aov` object. ## Some First Contrasts ### Main Effects Only This object can now be passed to `lsmeans`, for example to obtain the marginal means of the four inferences: ```{r} m1 <- lsmeans(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. `lsmeans` offers two ways to do so. The first splits the contrasts across levels of the factor. ```{r} m2 <- lsmeans(a1, ~ inference|instruction) m2 ``` Consequently test are also only performed within each level: ```{r} pairs(m2) ``` The second version treats all factor combinations together, producing a considerably larger number of pairwise comparisons: ```{r} m3 <- lsmeans(a1, ~ inference:instruction) m3 pairs(m3) ``` ### Running Custom Contrasts Objects returned from `lsmeans` 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 `lsmeans`, 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 Function `lsmip` from package `lsmeans` can be used for plotting the data directly from an `afex_aov` object. As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. A plot of this interaction could be the following: ```{r fig.width=7.5, fig.height=4} lsmip(a1, instruction ~ inference|plausibility) ``` # Replicate Analysis from Singmann and Klauer (2011) As this plot is not very helpful, we now fit a new ANOVA model in which we separate the data in affirmation and denial inferences, as done in the original manuscript and plot the data then 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. ```{r fig.width=7.5, fig.height=4} lsmip(a2, ~instruction ~ plausibility+validity|what, scales = list(x=list( at = 1:4, labels = c("pl:v", "im:v", "pl:i", "im:i") ))) ``` We see the critical predicted cross-over interaction in the left of those two graphs. For valid but implausible problems (`im:v`) deductive responses are larger than probabilistic responses. The opposite is true for invalid but plausible problems (`pl:i`). 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 <- lsmeans(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") ``` As the resulting eight contrasts have different numbers of degrees-of-freedom, we can only pass them to `multcomp` in small batches. This gives us more powerful Type 1 error corrections but overall a reduced correction as we now control for three families of tests (i.e., overall Type 1 error probability of .15). ```{r} summary(as.glht(contrast(m4, c2[1:4])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[5:6])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[7:8])), test =adjusted("free")) ``` 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 * While the df of the ANOVA tables are Greenhouse-Geisser corrected per default for within-subject factors with more than two levels, this is not the case for post-hoc tests or contrasts using `lsmeans`. The contrasts use uncorrected degrees of freedom that are Satterthwaite approximated. This most likely produces anti-conservative tests if compound symmetry/sphericity is violated. * For unbalanced samples, `aov` is usually not the correct choise. This is why the test of effects is based on `car::Anova`. However, for `lsmeans` we need to use `aov` models. However, `lsmeans` offers the option to weight the marginal means differently in case of different group sizes (i.e., unbalanced data). For example, it offers the option that each group is assumed to be of equal size (i.e., `weights = "equal"`) or proportionally (i.e., `weights = "proportional"`). See help of `lsmeans` for more information. * 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 `lsmeans` 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. V. (2015). _lsmeans: Least-Squares Means_. 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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$", x)), NA)), is_true()) expect_that(m_mc1, equals(m_mc2, check.attributes = FALSE)) } }) test_that("print(mixed) works: only 1 or 2 fixed effects with all methods", { data(obk.long, package = "afex") expect_that(print(mixed(value ~ treatment+(1|id), data = obk.long)), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+phase+(1|id), data = obk.long)), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+(1|id), data = obk.long, method = "LRT")), is_a("data.frame")) expect_that(print(mixed(value ~ treatment+phase+(1|id), data = obk.long, method = "LRT")), is_a("data.frame")) skip_if_not_installed("mlmRev") require("mlmRev") # for the data, see ?Contraception expect_that(print(mixed(use ~ urban + (1 | district), method = "PB", family = binomial, data = Contraception, args_test=list(nsim=2))), is_a("data.frame")) expect_that(print(mixed(use ~ urban + livch + (1 | district), method = "PB", family = binomial, data = Contraception, args_test=list(nsim=2))), is_a("data.frame")) }) # test_that("mixed, Maxell & Delaney (2004), Table 16.4, p. 842: bobyqa not fitting well", { # data(md_16.4) # # F-values and p-values are relatively off: # expect_that(mixed(induct ~ cond*cog + (cog|room:cond), md_16.4, control=lmerControl(optimizer="bobyqa")), gives_warning("better fit")) # expect_that(mixed(induct ~ cond*cog + (cog|room:cond), md_16.4, type=2, control=lmerControl(optimizer="bobyqa")), gives_warning("better fit")) # }) test_that("mixed: set.data.arg", { data(obk.long, package = "afex") suppressWarnings(m1 <- mixed(value ~ treatment*phase +(1|id), obk.long, method = "LRT", progress=FALSE)) suppressWarnings(m2 <- mixed(value ~ treatment*phase +(1|id), obk.long, method = "LRT", progress=FALSE, set.data.arg = FALSE)) expect_that(m1$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) sk_m2 <- mixed(response ~ instruction+(1|id)+(1|content), sk2_aff, method = "LRT", progress = FALSE) 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") 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") expect_is(l2, "merMod") expect_equivalent(m2$full_model, l2) l3 <- lmer_alt(response ~ validity + (believability||id), ks2013.3) l4 <- lmer_alt(response ~ validity + (believability||id), ks2013.3, control = lmerControl(optimizer = "Nelder_Mead")) expect_equivalent(l2, l3) expect_equal(l3, l4, check.attributes = FALSE) l5 <- lmer_alt(response ~ validity + (believability||id), ks2013.3, control = lmerControl(optimizer = "Nelder_Mead"), check_contrasts = TRUE) expect_equal(l2, l5, check.attributes = FALSE ) expect_identical(names(coef(l2)$id), names(coef(l5)$id)) # parameter names need to be identical (same contrasts) expect_false(all(names(coef(l2)$id) == names(coef(l3)$id))) # parameter names need to be different (different contrasts) l7 <- lmer_alt(response ~ validity + (1|id) + (0+validity*condition||content), ks2013.3, control = lmerControl(optCtrl = list(maxfun=1e6))) expect_is(l7, "merMod") expect_error(lmer_alt(response ~ validity + (0|id) + (0+validity*condition||content), ks2013.3), "Invalid random effects term") expect_is(lmer_alt(response ~ validity + (validity||id) + (validity|content), ks2013.3), "merMod") }) test_that("mixed: expand_re argument (longer)", { if (packageVersion("testthat") >= "0.9") { testthat::skip_on_cran() testthat::skip_on_travis() data("ks2013.3") m4 <- mixed(response ~ validity + (believability*validity||id) + (validity*condition|content), ks2013.3, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE) m5 <- suppressWarnings(mixed(response ~ validity + (believability*validity|id) + (validity*condition||content), ks2013.3, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), expand_re = TRUE, progress=FALSE)) expect_identical(length(unlist(summary(m4)$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)$varcor, "sc"), tolerance = 0.02) } }) test_that("mixed: return=data, expand_re argument, and allFit", { #if (packageVersion("testthat") >= "0.9") { #testthat::skip_on_cran() #testthat::skip_on_travis() testthat::skip_if_not_installed("optimx") require(optimx) data("ks2013.3") ks2013.3_tmp <- ks2013.3 m6 <- mixed(response ~ validity + (believability*validity||id), ks2013.3_tmp, expand_re = TRUE, method = "LRT", control = lmerControl(optCtrl = list(maxfun=1e6)), progress=FALSE, return = "merMod") m6_all_1 <- all_fit(m6, verbose = FALSE, data = ks2013.3_tmp) expect_output(print(m6_all_1$`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: 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() sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) for (i in c(2, 3)) { sk2_aff_kr <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = FALSE, method = "KR", progress=FALSE, type = i) sk2_aff_s <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = FALSE, method = "S", progress=FALSE, type = i) sk2_aff_nkr <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, progress = FALSE, type = i, expand_re = TRUE, all_fit = FALSE, method = "nested-KR") sk2_aff_lrt <- mixed(response ~ instruction*type+(inference*type||id), sk2_aff, progress = FALSE, type = i, expand_re = TRUE, all_fit = FALSE, method = "LRT") sk2_aff_pb <- mixed(response ~ instruction*type+(inference||id), sk2_aff, progress = FALSE, type = i, args_test = list(nsim = 10), expand_re = TRUE, all_fit = FALSE, method = "PB") expect_is(sk2_aff_kr, "mixed") expect_is(sk2_aff_s, "mixed") expect_is(sk2_aff_nkr, "mixed") expect_is(sk2_aff_lrt, "mixed") expect_is(sk2_aff_pb, "mixed") expect_is(anova(sk2_aff_kr), "anova") expect_is(anova(sk2_aff_s), "anova") expect_is(anova(sk2_aff_nkr), "anova") expect_is(anova(sk2_aff_lrt), "anova") expect_is(anova(sk2_aff_pb), "anova") expect_output(print(sk2_aff_kr), "Effect") expect_output(print(sk2_aff_kr), "F") expect_output(print(sk2_aff_s), "Effect") expect_output(print(sk2_aff_s), "F") expect_output(print(sk2_aff_nkr), "Effect") expect_output(print(sk2_aff_nkr), "F") expect_output(print(sk2_aff_lrt), "Effect") expect_output(print(sk2_aff_lrt), "Chisq") expect_output(print(sk2_aff_pb), "Effect") expect_output(print(sk2_aff_pb), "Chisq") } }) test_that("mixed all_fit = TRUE works with old methods", { data("sk2011.2") # see example("mixed") sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk2_aff_b <- mixed(response ~ instruction+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE, method = "nested-KR") sk2_aff_b2 <- mixed(response ~ instruction*type+(inference||id), sk2_aff, type = 2, expand_re = TRUE, all_fit = TRUE, method = "nested-KR") 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") sk2_aff <- droplevels(sk2011.2[sk2011.2$what == "affirmation",]) sk2_aff_b <- mixed(response ~ instruction+(inference*type||id), sk2_aff, expand_re = TRUE, all_fit = TRUE, method = "KR") sk2_aff_b2 <- mixed(response ~ instruction*type+(inference||id), sk2_aff, type = 2, expand_re = TRUE, all_fit = TRUE, method = "KR") expect_is(sk2_aff_b, "mixed") expect_named(attr(sk2_aff_b, "all_fit_selected"), "full_model") expect_false(is.null(attr(sk2_aff_b, "all_fit_logLik"))) expect_is(sk2_aff_b2, "mixed") expect_named(attr(sk2_aff_b2, "all_fit_selected"), "full_model") expect_false(is.null(attr(sk2_aff_b2, "all_fit_logLik"))) }) test_that("anova_table attributes", { data(obk.long) symbol_test <- mixed(value ~ treatment * phase + (1|id), obk.long, sig_symbols = c("", "a", "aa", "aaa"), return = "nice") expect_output(print(symbol_test), "aaa") symbol_test <- mixed(value ~ treatment * phase + (1|id), obk.long, sig_symbols = c("", "a", "aa", "aaa")) expect_output(print(symbol_test), "aaa") expect_output(print(nice(symbol_test, sig_symbols = c("", "b", "bb", "bbb"))), "bbb") new_symbols <- c(" ", " b", " bb", " bbb") symbol_test <- anova(symbol_test, sig_symbols = c(" ", " b", " bb", " bbb")) expect_identical(attr(symbol_test, "sig_symbols"), new_symbols) expect_output(print(nice(symbol_test)), "bbb") # Test support for old afex objects old_afex_object <- default_options <- mixed(value ~ treatment * phase + (1|id), obk.long) attr(old_afex_object$anova_table, "sig_symbols") <- NULL expect_that(nice(old_afex_object), is_identical_to(nice(default_options))) }) afex/tests/testthat/test-compare_2_vectors.R0000644000176200001440000000043512642234726020725 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-aov_car-structural.R0000644000176200001440000001371613073233062021126 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$anova_table, "correction"), equals("none")) }) afex/tests/testthat/test-aov_car-bugs.R0000644000176200001440000002663313111507500017652 0ustar liggesusers context("ANOVAs: known bugs") test_that("regex works correctly in aov_car when also having within factors outside the Error term", { data(obk.long) expect_is(aov_car(value ~ treatment * gender*phase*hour + Error(id/phase*hour), data = obk.long), "afex_aov") }) test_that("another label bug (May 2014)", { data("sk2011.1") levels(sk2011.1$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_ez works with multiple covariates", { skip_if_not_installed("psych") require(psych) 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$condition) # that is somewhat stupid expect_is(aov_ez(data=msq2, dv="Extraversion", id = "ID", between = "condition", covariate=c("TOD", "MSQ_Time"), factorize=FALSE, fun_aggregate = mean), "afex_aov") })afex/tests/testthat/test-mixed-mw.R0000644000176200001440000000543113061013265017026 0ustar liggesusers context("Mixed LMMs: replicating Maxwell & Delaney (2004)") test_that("mixed: Maxell & Delaney (2004), Table 16.3, p. 837", { ### replicate results from Table 16.3 (Maxwell & Delaney, 2004, p. 837) data(md_16.1) # original results need treatment contrasts: mixed1_orig <- mixed(severity ~ sex + (1|id), md_16.1, check_contrasts=FALSE, progress=FALSE) expect_that(fixef(mixed1_orig$full_model), is_equivalent_to(c(60, -14))) expect_that(round(anova(mixed1_orig)[1,"F"],2), equals(9.97)) expect_that(round(anova(mixed1_orig)[1,"Pr(>F)"],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_that(round(fixef(mixed2_orig$full_model), 4), is_equivalent_to(c(35.6261, -8.1485))) expect_that(round(sqrt(Matrix::diag(vcov(mixed2_orig$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$cog, scale=FALSE) mixed4 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, progress=FALSE, check_contrasts=FALSE) expect_that(round(fixef(mixed4$full_model), 2), is_equivalent_to(c(36.1, -9.07, 0.64, 0.03))) }) afex/tests/testthat/test-lmerTest-support.R0000644000176200001440000000204213060231206020577 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")) expect_is(m1, "merMod") expect_true(inherits(m1b, "merModLmerTest")) afex_options(lmer_function = "lme4") m2 <- mixed(response ~ instruction*inference*plausibility +(1|id), sk2011.1, progress = FALSE, return = "merMod") expect_false(inherits(m2, "merModLmerTest")) expect_is(m2, "merMod") afex_options(aop) expect_true("Pr(>F)" %in% colnames(lmerTest::anova(m1))) expect_false("Pr(>F)" %in% colnames(anova(m1))) expect_true("Pr(>F)" %in% colnames(lmerTest::anova(m1b))) expect_false("Pr(>F)" %in% colnames(anova(m1b))) expect_false("Pr(>F)" %in% colnames(anova(m2))) expect_false("Pr(>F)" %in% colnames(lmerTest::anova(m2))) }) afex/tests/testthat/test-aov_car-basic.R0000644000176200001440000002003613071744203017772 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$anova_table[,"F"], 2), is_equivalent_to(f)) expect_that(suppressWarnings(summary(md_ez_r$Anova)$univariate.tests[,"SS"][-1]), is_equivalent_to(ss_num)) expect_that(suppressWarnings(summary(md_ez_r$Anova)$univariate.tests[,"Error SS"])[-1], is_equivalent_to(ss_error)) expect_that(anova(md_ez_r, correction = "none")[,"num Df"], is_equivalent_to(num_df)) expect_that(anova(md_ez_r, correction = "none")[,"den Df"], is_equivalent_to(den_df)) }) test_that("Analysis of Singmann & Klauer (2011, Exp. 1)", { data(sk2011.1, package = "afex") out1 <- aov_ez("id", "response", sk2011.1[ sk2011.1$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$what == "affirmation",], within = c("inference", "type"), between = "instruction", anova_table=(es = "pes"), fun_aggregate = mean, return = "afex_aov") expect_output(print(out_new), "Signif. codes") expect_output(print(anova(out_new)), "Signif. codes") expect_output(print(nice(out_new)), "Anova") load("afex_aov_16_1.rda") expect_output(print(out1), "Anova") expect_output(print(anova(out1)), "Signif. codes") expect_output(print(nice(out1)), "Anova") }) afex/tests/testthat/test-afex_aov.R0000644000176200001440000000532013055557465017106 0ustar liggesusers context("ANOVAs: check that afex_aov return value works") test_that("split-plot produces an afex_aov object without error", { data(obk.long, package = "afex") split_plot1 <- aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long, observed = "gender", return = "afex_aov") split_plot2 <- aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long, observed = "gender", return = "afex_aov") split_plot3 <- aov_ez("id", "value", obk.long, between = c("treatment", "gender"), within = c("phase", "hour"), observed = "gender", return = "afex_aov") expect_that(split_plot1, is_equivalent_to(split_plot2)) expect_that(split_plot1, is_equivalent_to(split_plot3)) expect_that(split_plot1, is_a("afex_aov")) ## is same with numeric factor: obk.long$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("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"))) }) afex/tests/testthat/mixed_with_dot.rda0000644000176200001440000147151013055625310017707 0ustar liggesusers}پvW|. 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=Fƾn='Xkٵ6yQؠ8#x?hW2c~OI}z}t:^N&_}>&˩7K,=}:y::}9|z~}>8SY}q:翷Nۋ^3VoN5ˇ?8H}?fއ=POĻGk8Z/Οyq8H66Gq&}3ގ;p 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+bOQ=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/data/0000755000176200001440000000000013055500353012105 5ustar liggesusersafex/data/sk2011.2.rda0000644000176200001440000000460712612772357013702 0ustar liggesusersBZh91AY&SY(wߠ@ {Hϫj0y<|54dM44`<yLPh j R!ʩ@<Lj '=S)S!M4I$PTdڧ P4bP TЏSOP@he4g3Q62=&d 6Y{u=bܐh-#r&9S]zuVӪ>zm&EJJjB$` nq^/s4ٚ05[ak3QVEfi"JQA`c uJEZW@hJERFEZCeՑ$e xr$FTVYII3G7w)CjmR.:5}^)Ǖjݐyd%!t~3/[Cϻxrw}_Wz޾"2 s09=J֋^Kxnc.LMrst|vUN44nBu!tŇWUߛL/PԾ̬G)]fi[َ)E^HcIt7T&SWv 55PC%-r˩h{ @ц6$ ǎ"+`j8剏#pIfU(5 6YKQC߬r .LSZTƫTDӸ/^jh nYA0+yj%=象TMeNw ^ }Wi}tY\ T3츦n%ғoWH*WԼE 1EPH qFm!ڶPӌtأΨ&rʳGTR7hw?^i1H7Fǖv  =1鶀EpF'U|;Z2(p]fApO<&& "^{g(Epa%t*b !! 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V֪;x9@Kinx~ޟb9F*"۔^q><2~.u.B"LiVZJ+Z7Gafex/data/md_12.1.rda0000644000176200001440000000054412612772357013656 0ustar liggesusersSNP̥MLHWM\p튝M( u' ~'%Ź)ƄI93s!{o 0Hm$b6`2yҘM ʹyҔZee3V_@s~Azn4>Li{etWᶝ<Ŕ@IuBQw{&YB>㣮/G6?d*ïafex/R/0000755000176200001440000000000013111507500011367 5ustar liggesusersafex/R/md_16.4-data.R0000644000176200001440000000473412612772711013516 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/ems.R0000644000176200001440000001171513055500353012311 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/round_ps.R0000644000176200001440000000137212612772711013363 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/utils.R0000644000176200001440000000353513073233062012666 0ustar liggesusers 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(" " , stringr::str_trim(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/aov_car.R0000644000176200001440000010137113111507500013127 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{lsmeans} 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}. #' #' @usage #' aov_ez(id, dv, data, between = NULL, within = NULL, covariate = NULL, #' 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(), ..., print.formula = FALSE) #' #' aov_car(formula, data, fun_aggregate = NULL, type = afex_options("type"), #' factorize = afex_options("factorize"), #' check_contrasts = afex_options("check_contrasts"), #' return = afex_options("return_aov"), observed = NULL, #' anova_table = list(), ...) #' #' 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(), ..., print.formula = FALSE) #' #' #' @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. #' @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 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. he default is given by \code{afex_options("factorize")}, which is initially \code{TRUE}. If one wants to run an ANCOVA, 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 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). 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). Other values are currently still supported for backward compatibility. # Possible values are \code{c("Anova", "lm", "data", "nice", "full", "all", "univariate", "marginal", "aov")} (possibly abbreviated). #' @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 ... Further arguments passed to \code{fun_aggregate}. #' #' @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{lsmeans} 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{lsmeans::lsmeans} 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[lsmeans]{ref.grid}} object by running \code{\link[lsmeans]{lsmeans}} on the \code{afex_aov} object from step 1 using the factors involved in the contrast. For example: \code{r <- lsmeans(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[lsmeans]{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{lsmeans} allows for a variety of advanced settings and simplifiations, for example: all pairwise comparison of a single factor using one command (e.g., \code{lsmeans(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=lsmeans}{here}). #' #' A caveat regarding the use of \pkg{lsmeans} concerns the assumption of sphericity for ANOVAs including within-subjects/repeated-measures factors (with more than two levels). While the ANOVA tables per default report results using the Greenhousse-Geisser correction, no such correction is available when using \pkg{lsmeans}. This may result in anti-conservative tests. #' #' \pkg{lsmeans} is loaded/attached automatically when loading \pkg{afex} via \code{library} or \code{require}. #' } #' #' \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} and \code{anova}. #' #' 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. #' } #' #' @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 the return argument to \code{"nice"}. This can also be done globally via \code{afex_options(return_aov = "nice")}. \code{return = "nice"} also produces the default output of previous versions of afex (versions 0.13 and earlier). #' #' 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}. #' #' @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} #' #' @name aov_car #' @aliases aov_ez aov_car aov_4 #' @export aov_ez aov_car aov_4 #' @importFrom car Anova #' @importFrom stringr str_c str_detect str_replace_all str_extract #' @importFrom reshape2 dcast #' @importFrom lme4 findbars nobars #' @importFrom stats terms as.formula xtabs contrasts<- coef #' #' @example examples/examples.aov_car.R #' #' #' @encoding UTF-8 #' aov_car <- function(formula, data, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), observed = NULL, anova_table = list(), ...) { 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$fun.aggregate dots <- dots[names(dots) != "fun.aggregate"] } # stuff copied from aov: Terms <- terms(formula, "Error", data = data) indError <- attr(Terms, "specials")$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) dv <- vars[1] # transform to data.frame if necessary (e.g., when using dplyr) data <- as.data.frame(data) #check if dv is numeric: if (!is.numeric(data[,dv])) stop("dv needs to be numeric.") vars <- vars[-1] parts <- attr(terms(formula, "Error", data = data), "term.labels") error.term <- parts[str_detect(parts, "^Error\\(")] 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[!str_detect(parts, "^Error\\(")] 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(str_c("Converting to factor: ", str_c(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(str_c("Numerical variables NOT centered on 0 (i.e., likely bogus results): ", str_c(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) str_c(effect.parts.no.within, collapse = "+") else "1" lh1 <- str_c(id, if (length(between.escaped) > 0) str_c(between.escaped, collapse = "+") else NULL, sep = "+") rh1 <- str_c(within.escaped, collapse = "+") rh3 <- str_c(within.escaped, collapse = "*") # converting all within subject factors to factors and adding 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(str_c("Following ids are in more than one between subjects condition:\n", str_c(ids.in.more.condition, collapse = ", "))) } # Is fun_aggregate NULL and aggregation necessary? if (is.null(fun_aggregate)) { if (any(xtabs(as.formula(str_c("~", 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 } } # if return = "lme4" return the (aggregated) data fitted with lmer! # if (return == "lme4") { # warning("lme4 return is experimental!\nAlso: Missing values and contrasts not checked for return = 'lme4'!") # n.dat <- dcast(data, formula = as.formula(str_c(lh1, if (length(within) > 0) paste0("+", rh1) else "", "~ .", sep = "")), fun.aggregate = fun.aggregate, ..., value.var = dv) # colnames(n.dat)[length(colnames(n.dat))] <- "value" # f.within.new <- str_replace_all(rh1, pattern="\\+", replacement="*") # return(lmer(as.formula(str_c("value~", rh2, if (length(within) > 0) paste0("*", f.within.new) else "", "+ (1", if (length(within) > 0) paste0("+", f.within.new) else "", "|", id, ")" , sep = "")), data = n.dat)) # } # prepare the data: tmp.dat <- do.call(dcast, args = c(data = list(data), formula = as.formula(str_c(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))) warning(str_c("Missing values for following ID(s):\n", str_c(tmp.dat[missing.values,1], collapse = ", "), "\nRemoving those cases from the analysis."), call. = FALSE) } # 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 <- do.call(dcast, args = c(data = list(data), formula = as.formula(str_c(str_c(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 # full.formula <- as.formula(str_c(dv, " ~ ", str_c(c(between.factors, within), collapse = "*"))) # all.terms <- attr(terms(full.formula), "term.labels") # marginals.out <- lapply(all.terms, function(x) aggregate(as.formula(str_c(dv, " ~ ", x)), dat.ret, mean)) # names(marginals.out) <- all.terms # grand.mean <- data.frame(mean(dat.ret[,dv])) # colnames(grand.mean) <- dv # marginals.out <- c(grand_mean = list(grand.mean), marginals.out) # if (return == "marginal") { # return(marginals.out) # } if (length(between) > 0) { if (check_contrasts) { resetted <- NULL for (i in between) { 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(str_c("Contrasts set to contr.sum for the following variables: ", str_c(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(str_c("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", "afex_aov")) include.aov <- TRUE else include.aov <- FALSE 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] } #return(aov(formula(paste(dv, "~", paste(c(between, within), collapse = "*"), if (length(within) > 0) paste0("+Error(", id, "/(",paste(within, collapse="*"), "))") else NULL)), data=dat.ret, contrasts = contrasts)) aov <- aov(formula(paste(dv.escaped, "~", paste(c(between.escaped, within.escaped), collapse = "*"), if (length(within) > 0) paste0("+Error(", id.escaped, "/(",paste(within.escaped, collapse="*"), "))") else NULL)), data=dat.ret, contrasts = contrasts) } 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])) colnames(idata) <- within } # print(as.formula(str_c("cbind(",str_c(colnames(tmp.dat[-(seq_along(c(id, between)))]), collapse = ", "), ") ~ ", rh2))) # browser() tmp.lm <- do.call("lm", list(formula = as.formula(str_c("cbind(",str_c(colnames(tmp.dat[-(seq_along(c(id, between)))]), collapse = ", "), ") ~ ", rh2)), data = tmp.dat)) # browser() 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(str_c("~", 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(str_c("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") <- within attr(afex_aov, "between") <- between attr(afex_aov, "type") <- type 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 (class(Anova.out) == "Anova.mlm") return(summary(Anova.out, multivariate = FALSE)) 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") <- within attr(afex_aov, "between") <- between attr(afex_aov, "type") <- type afex_aov$anova_table <- do.call("anova", args = c(object = list(afex_aov), observed = list(observed), anova_table)) #afex_aov$anova_table <- do.call("anova", args = c(object = list(afex_aov), observed = list(observed), args.return)) return(do.call("nice", args = c(object = list(afex_aov), observed = list(observed), anova_table))) } } 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(), ..., print.formula = FALSE) { #browser() 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 <- str_c(" + Error(", id, if (length(within) > 0) "/(" else "", str_c(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 <- str_c(dv, " ~ ", rh, error) if (print.formula) message(str_c("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, ...) } aov_ez <- function(id, dv, data, between = NULL, within = NULL, covariate = NULL, 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(), ..., 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 <- str_c(covariate, collapse = "+") } #browser() id <- escape_vars(id) dv <- escape_vars(dv) between <- escape_vars(between) within <- escape_vars(within) rh <- if (!is.null(between) || !is.null(covariate)) str_c(if (!is.null(between)) str_c(between, collapse = " * ") else NULL, covariate, sep = " + ") else "1" error <- str_c(" + Error(", id, if (!is.null(within)) "/(" else "", str_c(within, collapse = " * "), if (length(within) > 0) ")" else "", ")") formula <- str_c(dv, " ~ ", rh, error) if (print.formula) message(str_c("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, ...) } afex/R/helpers.R0000644000176200001440000000733313071473343013176 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{return_aov}: Return value of the ANOVA functions (see \code{\link{aov_car}}), default is \code{"nice"}. #' \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{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}}. There should be no difference between the two. The latter could be minimally faster, but does not allow to use \code{lmerTest::anova()}. #' } #' #' @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[str_detect(names(op), "^afex.")] names(afex_op) <- str_replace(names(afex_op), "^afex.", "") return(afex_op) } else if (is.list(dots[[1]])) { # set several afex options as a list: newop <- dots[[1]] names(newop) <- str_c("afex.", names(newop)) options(newop) } else if (!is.null(names(dots))) { newop <- dots names(newop) <- str_c("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(str_c("afex.", unlist(dots)))) } else { warning("Unsopported command to afex_options(), nothing done.", call. = FALSE) } } afex/R/sk2011.2-data.R0000644000176200001440000000565112612772711013526 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/afex-package.R0000644000176200001440000000260713111541054014035 0ustar liggesusers#' Analysis of Factorial Experiments. #' #' \tabular{ll}{ #' Package: \tab afex\cr #' Type: \tab Package\cr #' Version: \tab 0.18-0\cr #' Date: \tab 2017-05-25\cr #' Depends: \tab R (>= 3.1.0), lme4 (>= 1.1-8), lsmeans (>= 2.17)\cr #' Encoding: \tab UTF-8\cr #' License: \tab GPL (>=2)\cr #' URL: \tab http://afex.singmann.science/, https://github.com/singmann/afex\cr #' } #' #' 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 between-within (i.e., split-plot) ANOVAs for data in long format (i.e., #' one observation per row), 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 uses type 3 sums of squares as default (imitating commercial statistical software). #' #' @aliases afex-package #' @name afex-package #' @docType package #' @title The afex Package #' @author Henrik Singmann, Ben Bolker, Jake Westfall, Frederik Aust, with contributions from Søren Højsgaard, John Fox, Michael A. Lawrence, Ulf Mertens, Jonathan Love #' @keywords package NULL afex/R/set_contrasts.R0000644000176200001440000000266112642221125014416 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/ks2013.3-data.R0000644000176200001440000000643212612772711013527 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_16.1-data.R0000644000176200001440000000350612612772711013507 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/obk.long-data.R0000644000176200001440000000553312612772711014155 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[car]{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 = "car") #' 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/compare.2.vectors.R0000644000176200001440000001535212612772711015007 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 = approximate(100000), #' 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}}. Defaults to \code{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{oneway_test}} (the only test in this selction not using a rank transformation), #' \item the \code{Wilcoxon} test \code{\link{wilcox_test}} (\code{coin::Wilcoxon}), and #' \item the \code{median} test \code{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 = approximate(100000), wilcox.exact = NULL, wilcox.correct = TRUE) { #browser() 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.") out <- list() if (paired) if (!length(x) == length(y)) stop("length(x) needs to be equal to length(y) when paired is TRUE!") 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)) { dv <- c(x, y) iv <- factor(rep(c("A", "B"), c(length(x), length(y)))) 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 <- oneway_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "permutation", test.statistic = "Z", test.value = statistic(res.perm), test.df = NA, p = pvalue(res.perm)[1], stringsAsFactors = FALSE)) }, error = function(e) warning(paste("coin::permutation test failed:", e))) tryCatch(if ("Wilcoxon" %in% coin) { res.coin.wilcox <- wilcox_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "coin::Wilcoxon", test.statistic = "Z", test.value = statistic(res.coin.wilcox), test.df = NA, p = pvalue(res.coin.wilcox)[1], stringsAsFactors = FALSE)) }, error = function(e) warning(paste("coin::Wilcoxon test failed:", e))) tryCatch(if ("median" %in% coin) { res.median <- median_test(formula.coin, distribution=perm.distribution, alternative = alternative) nonparametric <- rbind(nonparametric, data.frame(test = "median", test.statistic = "Z", test.value = statistic(res.median), test.df = NA, p = 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/sk2011.1-data.R0000644000176200001440000000564313055557535013535 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/md_15.1-data.R0000644000176200001440000000635512612772711013513 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/mixed.R0000644000176200001440000013562513073276162012652 0ustar liggesusers#' p-values for fixed effects of mixed-model via lme4::lmer() #' #' Calculates p-values for all fixed effects in a mixed model. The default method \code{"KR"} (= Kenward-Roger) as well as \code{method="S"} (Satterthwaite) support LMMs and fit the model with \code{\link[lme4]{lmer}}) and then pass it to either \code{\link[lmerTest]{anova.merModLmerTest}} (or \code{\link[car]{Anova}}). The other methods (\code{"LRT"} = likelihood-ratio tests and \code{"PB"} = parametric bootstrap) support both LMMs and GLMMs (i.e., with \code{family} argument) and fit a full model and restricted models in which the parameters corresponding to the effect (i.e., model term) are withhold (i.e., fixed to 0) and tests statistics are based on comparing the full model with the restricted models. The default is tests based on Type 3 sums of squares. \code{print}, \code{summary}, and \code{anova} methods for the returned object of class \code{"mixed"} are available (the last two return the same data.frame). \code{lmer_alt} is simply a wrapper for mixed that only returns the \code{"merMod"} object and correctly uses the \code{||} notation to remove correlation among factors, but otherwise behaves like \code{g/lmer} (as for \code{mixed}, it calls \code{glmer} as soon as a \code{family} argument is present). #' #' #' @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? Otherwise the name will be \code{data}. Helpful if fitted objects are used afterwards (e.g., using \pkg{lsmeans}). Default is \code{TRUE}. #' @param progress if \code{TRUE}, shows progress with a text progress bar and other status messages during fitting. #' @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}, 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 fitted with lmer. 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 fitting 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}) passed to \code{\link{lmer}}/\code{\link{glmer}}, such as \code{control}. #' #' #' @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{"lmerMod"} object returned from fitting the full mixed model. #' \item \code{restricted_models} a list of \code{"lmerMod"} objects from fitting 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 fitting (i.e., after excluding missing rows and applying expand_re if requested). #' } #' #' 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"}, an object of class \code{"merMod"}, as returned from \code{g/lmer}, is returned. #' #' @details For an introduction to mixed-modeling for experimental designs see Barr, Levy, Scheepers, & Tily (2013; I highly recommend reading this paper if you use this function), 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]{anova.merModLmerTest}} (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]{anova.merModLmerTest}} 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://glmm.wikidot.com/faq}{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"}. This is done to avoid R's "feature" to not allow this behavior. #' #' 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 to use \code{||} with factors correctly (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{"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 uzsed for fitting is also returned as part of the \code{mixed} object so can be used from there. #' } #' #' @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 stringr str_replace #' @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 = TRUE, progress = TRUE, cl = NULL, return = "mixed", sig_symbols = afex_options("sig_symbols"), ...) { dots <- list(...) ### 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: if (check_contrasts) { #browser() vars.to.check <- all.vars(formula) resetted <- NULL for (i in vars.to.check) { 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(str_c("Contrasts set to contr.sum for the following variables: ", str_c(resetted, collapse=", "))) } #warning(str_c("Calculating Type 3 sums with contrasts = ", options("contrasts")[[1]][1], ".\n Use options(contrasts=c('contr.sum','contr.poly')) instead")) # browser() 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() #browser() formula.f <- as.formula(formula) #if (class(formula) != "formula") message("Formula (the first argument) converted to 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 <- str_c(str_c("(", 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(str_c(vars.to.check[1], "~", str_c(vars.to.check[-1], collapse = "+"))), data = data) m.matrix <- model.matrix(rh2, data = data) warning(str_c("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(str_c("Numerical variables NOT centered on 0 (i.e., interpretation of all main effects might be difficult if in interactions): ", str_c(non.null, collapse = ", "))) } if (expand_re) { random_parts <- str_c(all.terms[grepl("\\|", all.terms)]) which_random_double_bars <- str_detect(random_parts, "\\|\\|") random_units <- str_replace(random_parts, "^.+\\|\\s+", "") tmp_random <- lapply(str_replace(random_parts, "\\|.+$", ""), function(x) as.formula(str_c("~", 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]]) <- str_c("re", i, ".", str_replace_all(colnames(tmp_model.matrix[[i]]), ":", "_by_")) new_random[i] <- str_c("(", as.numeric(re_contains_intercept[i]), "+", str_c(colnames(tmp_model.matrix[[i]]), collapse = "+"), if (which_random_double_bars[i]) "||" else "|", random_units[i], ")") } else { new_random[i] <- str_c("(", 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 <- str_c(new_random, collapse = "+") } 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")] mf[["formula"]] <-as.formula(str_c(dv,deparse(rh2, width.cutoff = 500L),"+",random)) #formula.f 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") 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 } #browser() if (return == "merMod") { out <- eval(mf) return(out) } if ("family" %in% names(mf)) { if (!(method[1] %in% c("LRT", "PB"))) stop("GLMMs can only be estimated with 'LRT' or 'PB'.") } if (method[1] %in% c("KR", "S")) { ## do not calculate nested models for these methods if (progress) cat(str_c("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(str_c("[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) anova_table <- anova_table[, c("NumDF", "DenDF", "F.value", "Pr(>F)")] 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_ } anova_table <- anova_table[, c("NumDF", "DenDF", "F.value", "Pr(>F)")] colnames(anova_table) <- c("num Df", "den Df", "F", "Pr(>F)") } if (progress) cat(str_c("[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 <- str_c(deparse(-which(mapping == (i-1))), collapse = "") formulas[[i+1]] <- as.formula(str_c(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") { #warning("Implementation of Type 2 method not unproblematic.\n Check documentation or use car::Anova (Wald tests).") 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 <- str_c(deparse(-which(mapping %in% which(effect.order > c))), collapse = "") full_model.formulas[[c]] <- as.formula(str_c(dv, "~ 0 + m.matrix[,", tmp.columns, "] +", random)) } for (c in seq_along(fixed.effects)) { order.c <- effect.order[c] tmp.columns <- str_c(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(str_c(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(str_c("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 <- clusterEvalQ(cl = cl, library("lme4", character.only = TRUE)) junk <- clusterCall(cl = cl, "require", package = "afex", character.only = TRUE) #junk <- clusterEvalQ(cl = cl, loadNamespace("lme4")) 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(all_fit(fits[[1]], data=md_16.4b), function(y) try(logLik(y))) 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!")) } 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(str_c("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 #df.out <- data.frame(Effect = fixed.effects, stringsAsFactors = FALSE) anova_table <- data.frame(t(vapply(tests, function(x) unlist(x[["test"]][1,]), unlist(tests[[1]][["test"]][1,])))) #FtestU <- vapply(tests, function(x) unlist(x[["test"]][2,]), unlist(tests[[1]][["test"]][2,])) #row.names(FtestU) <- str_c(row.names(FtestU), ".U") #anova_table <- cbind(anova_table, t(FtestU)) 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(str_c("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 #browser() #df.out<- data.frame(Effect = fixed.effects, stringsAsFactors = FALSE) 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) <- str_c(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) # # attr(anova_table, "heading") <- c(paste0("Mixed Model Anova Table (Type ", type , " tests)\n"), paste0("Response: ", dv) #title <- "Analysis of Variance Table\n" #topnote <- paste("Model ", format(1L:nmodels), ": ", variables, # sep = "", collapse = "\n") } 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) #, 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 } 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$anova_table)[logLik_restricted > logLik_full]) } else if (attr(object, "type") == 2 | attr(object, "type") == "II") { NULL # logLik_full <- as.numeric(vapply(fits[1:max.effect.order],logLik, 0)) # logLik_restricted <- as.numeric(vapply(fits[(max.effect.order+1):length(fits)], logLik, 0)) # warn_logLik <- c() # for (c in seq_along(fixed.effects)) { # order.c <- effect.order[c] # if(logLik_restricted[[c]] > logLik_full[[order.c]]) warn_logLik <- c(warn_logLik, fixed.effects[c]) # } # if(length(warn_logLik)>0) return(warn_logLik) } return(TRUE) } #' @rdname mixed #' @export lmer_alt <- function(formula, data, check_contrasts = FALSE, ...) { mc <- match.call() #assign(all.vars(mc[["data"]]), data) mc[[1]] <- as.name("mixed") mc[["return"]] <- "merMod" mc[["expand_re"]] <- TRUE mc[["progress"]] <- FALSE mc[["check_contrasts"]] <- check_contrasts #browser() eval(mc) } #' @method print mixed #' @export print.mixed <- function(x, ...) { full_model_name <- names(x)[[2]] try(if(!isREML(x[[full_model_name]]) && !isTRUE(check_likelihood(x))) warning(paste("Following nested model(s) provide better fit than full model:", paste(check_likelihood(x), collapse = ", "), "\n Results cannot be trusted. Try all_fit=TRUE!"), call. = FALSE), silent = TRUE) get_mixed_warnings(x) tmp <- nice.mixed(x, ...) print(tmp) invisible(tmp) } #anova.mixed <- #' @method summary mixed #' @export summary.mixed <- function(object, ...) { if ("full_model" %in% names(object)) summary(object = if (length(object[["full_model"]]) == 1) object[["full_model"]] else object[["full_model"]][[length(object[["full_model"]])]], ...) else if("full.model" %in% names(object)) summary(object = if (length(object[["full.model"]]) == 1) object[["full.model"]] else object[["full.model"]][[length(object[["full.model"]])]], ...) } #' @method anova mixed #' @export anova.mixed <- function(object, ..., sig_symbols = attr(object$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 lsmeans for mixed objects: #' @importFrom lsmeans recover.data lsm.basis #' @method recover.data mixed #' @export recover.data.mixed <- function(object, ...) { full_model_name <- names(object)[[2]] recover.data(object[[full_model_name]], ...) } #' @method lsm.basis mixed #' @export lsm.basis.mixed <- function(object, trms, xlev, grid, ...) { full_model_name <- names(object)[[2]] lsm.basis(object[[full_model_name]], trms, xlev, grid, ...) } afex/R/nice.R0000644000176200001440000003420013073233062012435 0ustar liggesusers#' Make nice ANOVA table for printing. #' #' This generic function produces a nice ANOVA table for printin 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 packages \pkg{ascii} or \pkg{xtable} (nowadays \pkg{knitr} is probably the best approach, see \href{http://yihui.name/knitr/}{here}). \pkg{ascii} provides conversion to \href{http://www.methods.co.nz/asciidoc/}{AsciiDoc} and \href{http://orgmode.org/}{org-mode} (see \code{\link[ascii]{ascii}} and \code{\link[ascii]{print-ascii}}). \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$double.eps^0.5) abs(x - round(x)) < tol make.fs <- function(anova, symbols) { ifelse(anova[["Pr(>F)"]] < 0.001, str_c(formatC(anova[["F"]], digits = 2, format = "f"), symbols[4]), ifelse(anova[["Pr(>F)"]] < 0.01, str_c(formatC(anova[["F"]], digits = 2, format = "f"), symbols[3]), ifelse(anova[["Pr(>F)"]] < 0.05, str_c(formatC(anova[["F"]], digits = 2, format = "f"), symbols[2]), ifelse(anova[["Pr(>F)"]] < 0.1, str_c(formatC(anova[["F"]], digits = 2, format = "f"), symbols[1]), formatC(anova[["F"]], digits = 2, format = "f"))))) } anova_table <- object anova_table[,"df"] <- paste(ifelse(is.wholenumber(anova_table[,"num Df"]), anova_table[,"num Df"], formatC(anova_table[,"num Df"], digits = 2, format = "f")), ifelse(is.wholenumber(anova_table[,"den Df"]),anova_table[,"den Df"], formatC(anova_table[,"den Df"], digits = 2, format = "f")), sep = ", ") symbols.use <- c(" +", " *", " **", " ***") symbols.use[seq_along(sig_symbols)] <- sig_symbols df.out <- data.frame(Effect = row.names(anova_table), df = anova_table[,"df"], stringsAsFactors = FALSE) if (MSE) df.out <- cbind(df.out, data.frame(MSE = formatC(anova_table[,"MSE"], digits = 2, format = "f"), stringsAsFactors = FALSE)) df.out <- cbind(df.out, data.frame(F = make.fs(anova_table, symbols.use), stringsAsFactors = FALSE)) if (!is.null(anova_table$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, str_c(formatC(anova[[stat]], digits = 2, format = "f"), symbols[4]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.01, str_c(formatC(anova[[stat]], digits = 2, format = "f"), symbols[3]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.05, str_c(formatC(anova[[stat]], digits = 2, format = "f"), symbols[2]), ifelse(anova[[paste0("Pr(>", stat,")")]] < 0.1, str_c(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") { 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 stop("method of mixed object not supported.") rownames(df.out) <- NULL attr(df.out, "heading") <- attr(anova_table, "heading") attr(df.out, "sig_symbols") <- symbols.use class(df.out) <- c("nice_table", class(df.out)) df.out } #' @rdname nice #' @method print nice_table #' @export print.nice_table <- function(x, ...) { if(!is.null(heading <- attr(x, "heading"))) { cat(heading, sep = "\n") } print.data.frame(x) if(!is.null(attr(x, "sig_symbols"))) print_legend(x) if(!is.null(correction_method <- attr(x, "correction")) && correction_method != "none") { cat("\nSphericity correction method:", correction_method, "\n") } invisible(x) } afex/R/md_12.1-data.R0000644000176200001440000000515712612772711013507 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/deprecated.R0000644000176200001440000000206012704737012013622 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/allFit.R0000644000176200001440000001202113055776111012736 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 code taken from \url{https://github.com/lme4/lme4/blob/master/inst/utils/allFit.R} #' #' @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/reexport.R0000644000176200001440000000010313073236302013362 0ustar liggesusers### lme4 #' @importFrom lmerTest lmer #' @export lmerTest::lmer afex/R/methods.afex_aov.R0000644000176200001440000002343213073233062014756 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{lsm.basis}}. #' #' @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{lsm.basis}}{Provide the backbone for using \code{\link{lsmeans}} and related functions from \pkg{lsmeans} directly on \code{afex_aov} objects by returning a \code{\link{ref.grid}} object. Should not be called directly but through the functionality provided by \pkg{lsmeans}.} #' #' } #' #' @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 (class(object$Anova)[1] == "Anova.mlm") { if (inherits(object$Anova, "Anova.mlm")) { tmp <- suppressWarnings(summary(object$Anova, multivariate = FALSE)) t.out <- tmp[["univariate.tests"]] #browser() #t.out <- cbind(t.out, orig_den_df = t.out[, "den Df"]) if (correction[1] == "GG") { tmp[["pval.adjustments"]] <- tmp[["pval.adjustments"]][!is.na(tmp[["pval.adjustments"]][,"GG eps"]),, drop = FALSE] t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] * tmp[["pval.adjustments"]][,"GG eps"] t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] * tmp[["pval.adjustments"]][,"GG eps"] t.out[row.names(tmp[["pval.adjustments"]]), "Pr(>F)"] <- tmp[["pval.adjustments"]][,"Pr(>F[GG])"] } else { if (correction[1] == "HF") { if (any(tmp[["pval.adjustments"]][,"HF eps"] > 1)) warning("HF eps > 1 treated as 1", call. = FALSE) tmp[["pval.adjustments"]] <- tmp[["pval.adjustments"]][!is.na(tmp[["pval.adjustments"]][,"HF eps"]),, drop = FALSE] t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "num Df"] * pmin(1, tmp[["pval.adjustments"]][,"HF eps"]) t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] <- t.out[row.names(tmp[["pval.adjustments"]]), "den Df"] * pmin(1, tmp[["pval.adjustments"]][,"HF eps"]) t.out[row.names(tmp[["pval.adjustments"]]), "Pr(>F)"] <- tmp[["pval.adjustments"]][,"Pr(>F[HF])"] } else { if (correction[1] == "none") { TRUE } else stop("None supported argument to correction.") } } tmp.df <- t.out tmp2 <- as.data.frame(unclass(tmp.df)) #} else if (class(object$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"] # calculate es es_df <- data.frame(row.names = rownames(tmp2)) if ("pes" %in% es) { es_df$pes <- tmp2$SS/(tmp2$SS + tmp2[,"Error SS"]) } if ("ges" %in% es) { # This code is basically a copy from ezANOVA by Mike Lawrence! if(!is.null(observed) & length(observed) > 0){ obs <- rep(FALSE,nrow(tmp2)) for(i in observed){ if (!any(str_detect(rownames(tmp2),str_c("\\b",i,"\\b")))) stop(str_c("Observed variable not in data: ", i)) obs <- obs | str_detect(rownames(tmp2),str_c("\\b",i,"\\b")) } obs_SSn1 <- sum(tmp2$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) } anova_table <- cbind(tmp2[,c("num Df", "den Df", "MSE", "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$long[, attr(object, "within"), drop = FALSE], nlevels, 0) > 2)) correction else "none" attr(anova_table, "observed") <- if(!is.null(observed) & length(observed) > 0) observed else character(0) attr(anova_table, "sig_symbols") <- if(!is.null(sig_symbols)) sig_symbols else afex_options("sig_symbols") anova_table } #' @rdname afex_aov-methods #' @method print afex_aov #' @importFrom stats symnum #' @export print.afex_aov <- function(x, ...) { out <- nice(x$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$anova_table) } else stop("Non-supported object passed. Slot 'Anova' needs to be of class 'Anova.mlm' or 'anova'.") } #-------------------------------------------------------------- ### afex package - mixed objects ### # just need to provide an 'lsmeans' method here #' @rdname afex_aov-methods #' @importFrom lsmeans recover.data lsm.basis #' @method recover.data afex_aov #' @export recover.data.afex_aov = function(object, ...) { #do.call(do.call(":::", args = list(pkg = "lsmeans", name = "recover.data.aovlist")), args = list(object = object$aov, data = object$data$long, list(...))) recover.data(object = object$aov, ...) } #' @rdname afex_aov-methods #' @method lsm.basis afex_aov #' @export lsm.basis.afex_aov = function(object, trms, xlev, grid, ...) { #do.call(do.call(":::", args = list(pkg = "lsmeans", name = "lsm.basis.aovlist")), args = list(object = object$aov, trms = trms, xlev = xlev, grid = grid)) lsm.basis(object$aov, trms, xlev, grid, ...) } afex/R/fhch2010-data.R0000644000176200001440000000561713055500353013653 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/zzz.R0000644000176200001440000000414013073236720012360 0ustar liggesusers ## set default options for afex_options: .onLoad <- function(libname, pkgname) { op <- options() op.afex <- list( afex.type = 3, 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(" +", " *", " **", " ***") ) toset <- !(names(op.afex) %in% names(op)) if(any(toset)) options(op.afex[toset]) 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 lsmeans() for follow-up tests\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/vignettes/0000755000176200001440000000000013111546473013212 5ustar liggesusersafex/vignettes/afex_mixed_example.Rmd0000644000176200001440000006772313111540031017501 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) ``` ## 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 __lsmeans__ (Lenth, 2015). 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. In my opinion `lattice` provides the best combination of expressive power and abstraction. Specifically, like in base graph, we can fully decide what gets plotted. 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} require(afex) # needed for ANOVA, lsmeans is loaded automatically. require(dplyr) # for working with data frames require(tidyr) # for transforming data frames from wide to long and the other way round. require(multcomp) # for advanced control for multiple testing/Type 1 errors. require(lattice) # for plots require(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 `lsmeans` (Lenth, 2015). ### 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 `lsmeans` 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 `lsmeans` from calculating the *df* for the EMMs (which can be quite costly), we use asymptotic *df*s (i.e., $z$ values and tests). `lsmeans` 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} lsm.options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- lsmeans(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 `lsmeans` 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 `contrast(..., by = NULL)` (i.e., we revert the effect of the `by` statement from the earlier `lsmeans` 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} contrast(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: ```{r} summary(as.glht(contrast(pairs(emm_i1), by = NULL)), test = adjusted("holm")) ``` 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 <- lsmeans(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 `lsmeans` 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 use `contrast` a second time on the result this time again specifying `by = NULL` to revert the effect of conditiong. Note that although we entered the variables into `lsmeans` 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) ) contrast(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. V. (2015). _lsmeans: Least-Squares Means_. R package version 2.16-4. https://CRAN.R-project.org/package=lsmeans * 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/vignettes/afex_anova_example.Rmd0000644000176200001440000003151013111546363017476 0ustar liggesusers--- title: "ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)" author: "Henrik Singmann" date: "`r Sys.Date()`" output: rmarkdown::html_vignette 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) ``` # 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 __lsmeans__ (Lenth, 2015). 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 ```{r message=FALSE, warning=FALSE} require(afex) # needed for ANOVA, lsmeans is loaded automatically. require(multcomp) # for advanced control for multiple testing/Type 1 errors. require(lattice) # for plots lattice.options(default.theme = standard.theme(color = FALSE)) # black and white lattice.options(default.args = list(as.table = TRUE)) # better ordering ``` ```{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` (`aov_car` or `aov4` would be alternatives producing the same results) 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 ``` 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 `lsmeans`, a package that offers great functionality for both plotting and contrasts of all kind. A lot of information on `lsmeans` can be obtained in [its vignette](https://CRAN.R-project.org/package=lsmeans/vignettes/using-lsmeans.pdf). `lsmeans` can work with `afex_aov` objects directly as __afex__ comes with the necessary methods for the generic functions defined in `lsmeans`. `lsmeans` uses the ANOVA model estimated via base R's `aov` function that is part of an `afex_aov` object. ## Some First Contrasts ### Main Effects Only This object can now be passed to `lsmeans`, for example to obtain the marginal means of the four inferences: ```{r} m1 <- lsmeans(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. `lsmeans` offers two ways to do so. The first splits the contrasts across levels of the factor. ```{r} m2 <- lsmeans(a1, ~ inference|instruction) m2 ``` Consequently test are also only performed within each level: ```{r} pairs(m2) ``` The second version treats all factor combinations together, producing a considerably larger number of pairwise comparisons: ```{r} m3 <- lsmeans(a1, ~ inference:instruction) m3 pairs(m3) ``` ### Running Custom Contrasts Objects returned from `lsmeans` 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 `lsmeans`, 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 Function `lsmip` from package `lsmeans` can be used for plotting the data directly from an `afex_aov` object. As said initially, we are interested in the three-way interaction of instruction with inference, plausibility, and instruction. A plot of this interaction could be the following: ```{r fig.width=7.5, fig.height=4} lsmip(a1, instruction ~ inference|plausibility) ``` # Replicate Analysis from Singmann and Klauer (2011) As this plot is not very helpful, we now fit a new ANOVA model in which we separate the data in affirmation and denial inferences, as done in the original manuscript and plot the data then 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. ```{r fig.width=7.5, fig.height=4} lsmip(a2, ~instruction ~ plausibility+validity|what, scales = list(x=list( at = 1:4, labels = c("pl:v", "im:v", "pl:i", "im:i") ))) ``` We see the critical predicted cross-over interaction in the left of those two graphs. For valid but implausible problems (`im:v`) deductive responses are larger than probabilistic responses. The opposite is true for invalid but plausible problems (`pl:i`). 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 <- lsmeans(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") ``` As the resulting eight contrasts have different numbers of degrees-of-freedom, we can only pass them to `multcomp` in small batches. This gives us more powerful Type 1 error corrections but overall a reduced correction as we now control for three families of tests (i.e., overall Type 1 error probability of .15). ```{r} summary(as.glht(contrast(m4, c2[1:4])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[5:6])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[7:8])), test =adjusted("free")) ``` 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 * While the df of the ANOVA tables are Greenhouse-Geisser corrected per default for within-subject factors with more than two levels, this is not the case for post-hoc tests or contrasts using `lsmeans`. The contrasts use uncorrected degrees of freedom that are Satterthwaite approximated. This most likely produces anti-conservative tests if compound symmetry/sphericity is violated. * For unbalanced samples, `aov` is usually not the correct choise. This is why the test of effects is based on `car::Anova`. However, for `lsmeans` we need to use `aov` models. However, `lsmeans` offers the option to weight the marginal means differently in case of different group sizes (i.e., unbalanced data). For example, it offers the option that each group is assumed to be of equal size (i.e., `weights = "equal"`) or proportionally (i.e., `weights = "proportional"`). See help of `lsmeans` for more information. * 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 `lsmeans` 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. V. (2015). _lsmeans: Least-Squares Means_. 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optimx, nloptr, knitr, rmarkdown, lattice, latticeExtra, multcomp, testthat, mlmRev, dplyr, tidyr, dfoptim, Matrix, psych Imports: stringr, coin, pbkrtest (>= 0.4-1), lmerTest, car, reshape2, stats, methods 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 between-within (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), 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 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 Authors@R: c(person(given="Henrik", family="Singmann", role=c("aut", "cre"), email="singmann+afex@gmail.com"), person(given="Ben", family="Bolker", role=c("aut")), person(given="Jake", family="Westfall", role=c("aut")), person(given="Frederik", family="Aust", 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="Jonathan", family="Love", role=c("ctb")) ) Version: 0.18-0 Date: 2017-05-25 RoxygenNote: 6.0.1 NeedsCompilation: no Packaged: 2017-05-25 12:25:31 UTC; henrik Author: Henrik Singmann [aut, cre], Ben Bolker [aut], Jake Westfall [aut], Frederik Aust [aut], Søren Højsgaard [ctb], John Fox [ctb], Michael A. Lawrence [ctb], Ulf Mertens [ctb], Jonathan Love [ctb] Maintainer: Henrik Singmann Repository: CRAN Date/Publication: 2017-05-25 22:17:48 UTC afex/man/0000755000176200001440000000000013067717665011772 5ustar liggesusersafex/man/deprecated.Rd0000644000176200001440000000115513055750375014353 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/mixed.Rd0000644000176200001440000007100013073276377013362 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 = TRUE, 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? Otherwise the name will be \code{data}. Helpful if fitted objects are used afterwards (e.g., using \pkg{lsmeans}). Default is \code{TRUE}.} \item{progress}{if \code{TRUE}, shows progress with a text progress bar and other status messages during fitting.} \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}, 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 fitted with lmer. 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 fitting 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}) passed to \code{\link{lmer}}/\code{\link{glmer}}, such as \code{control}.} } \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{"lmerMod"} object returned from fitting the full mixed model. \item \code{restricted_models} a list of \code{"lmerMod"} objects from fitting 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 fitting (i.e., after excluding missing rows and applying expand_re if requested). } 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"}, an object of class \code{"merMod"}, as returned from \code{g/lmer}, is returned. } \description{ Calculates p-values for all fixed effects in a mixed model. The default method \code{"KR"} (= Kenward-Roger) as well as \code{method="S"} (Satterthwaite) support LMMs and fit the model with \code{\link[lme4]{lmer}}) and then pass it to either \code{\link[lmerTest]{anova.merModLmerTest}} (or \code{\link[car]{Anova}}). The other methods (\code{"LRT"} = likelihood-ratio tests and \code{"PB"} = parametric bootstrap) support both LMMs and GLMMs (i.e., with \code{family} argument) and fit a full model and restricted models in which the parameters corresponding to the effect (i.e., model term) are withhold (i.e., fixed to 0) and tests statistics are based on comparing the full model with the restricted models. The default is tests based on Type 3 sums of squares. \code{print}, \code{summary}, and \code{anova} methods for the returned object of class \code{"mixed"} are available (the last two return the same data.frame). \code{lmer_alt} is simply a wrapper for mixed that only returns the \code{"merMod"} object and correctly uses the \code{||} notation to remove correlation among factors, but otherwise behaves like \code{g/lmer} (as for \code{mixed}, it calls \code{glmer} as soon as a \code{family} argument is present). } \details{ For an introduction to mixed-modeling for experimental designs see Barr, Levy, Scheepers, & Tily (2013; I highly recommend reading this paper if you use this function), 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]{anova.merModLmerTest}} (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]{anova.merModLmerTest}} 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://glmm.wikidot.com/faq}{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"}. This is done to avoid R's "feature" to not allow this behavior. 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 to use \code{||} with factors correctly (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{"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 uzsed for fitting is also returned as part of the \code{mixed} object so can be used from there. } } \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{ ########################### ## 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: lmerTest::anova(sk_m1$full_model) # suppressing correlation among random slopes: # very similar results, but significantly faster and often less convergence warnings. sk_m2 <- mixed(response ~ instruction*inference*type+(inference*type||id), sk2_aff, expand_re = TRUE) sk_m2 ## mixed objects can be passed to lsmeans directly: # recreates basically Figure 4 (S&K, 2011, upper panel) # only the 4th and 6th x-axis position are flipped lsmip(sk_m1, instruction~type+inference) # set up reference grid for custom contrasts: # this can be made faster via: lsm.options(lmer.df = "Kenward-Roger") # set df for lsmeans to KR # lsm.options(lmer.df = "Satterthwaite") # the default # lsm.options(lmer.df = "asymptotic") # the fastest, no df (rg1 <- lsmeans(sk_m1, c("instruction", "type", "inference"))) # set up contrasts on reference grid: contr_sk2 <- list( ded_validity_effect = c(rep(0, 4), 1, rep(0, 5), -1, 0), ind_validity_effect = c(rep(0, 5), 1, rep(0, 5), -1), counter_MP = c(rep(0, 4), 1, -1, rep(0, 6)), counter_AC = c(rep(0, 10), 1, -1) ) # test the main double dissociation (see S&K, p. 268) contrast(rg1, contr_sk2, adjust = "holm") # only plausibility effect is not significant here. } ################################################### ## Replicating Maxwell & Delaney (2004) Examples ## ################################################### ### replicate results from Table 15.4 (Maxwell & Delaney, 2004, p. 789) data(md_15.1) # random intercept plus random slope (t15.4a <- mixed(iq ~ timecat + (1+time|id),data=md_15.1)) # to also replicate exact parameters use treatment.contrasts and the last level as base level: contrasts(md_15.1$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$cog, scale=FALSE) # F-values and p-values are relatively off: (mixed4 <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b)) # contrast has a relatively important influence on cog (mixed4_orig <- mixed(induct ~ cond*cog + (cog|room:cond), md_16.4b, check_contrasts=FALSE)) # parameters are again almost perfectly recovered: summary(mixed4_orig) #################### ## Other Examples ## #################### \dontrun{ # use the obk.long data (not reasonable, no random slopes) data(obk.long) mixed(value ~ treatment * phase + (1|id), obk.long) # Examples for using the per.parammeter argument: data(obk.long, package = "afex") obk.long$hour <- ordered(obk.long$hour) # tests only the main effect parameters of hour individually per parameter. mixed(value ~ treatment*phase*hour +(1|id), per_parameter = "^hour$", data = obk.long) # tests all parameters including hour individually mixed(value ~ treatment*phase*hour +(1|id), per_parameter = "hour", data = obk.long) # tests all parameters individually mixed(value ~ treatment*phase*hour +(1|id), per_parameter = ".", data = obk.long) # 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! ####################### ### Using 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") ## There are two ways to use multicore: # 1. Obtain fits with multicore: mixed(value ~ treatment*phase*hour +(1|id), data = obk.long, method = "LRT", cl = cl) # 2. Obtain PB samples via multicore: mixed(use ~ age + I(age^2) + urban + livch + (1 | district), family = binomial, method = "PB", data = Contraception, args_test = list(nsim = 10, cl = cl)) ## Both ways can be combined: mixed(use ~ age + I(age^2) + urban + livch + (1 | district), family = binomial, method = "PB", data = Contraception, args_test = list(nsim = 10, cl = cl), cl = cl) #### use all_fit = TRUE and expand_re = TRUE: data("sk2011.2") 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) } } \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/ems.Rd0000644000176200001440000000533413055750375013042 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/sk2011.1.Rd0000644000176200001440000000570513055750375013340 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/man/afex-package.Rd0000644000176200001440000000265513111507576014571 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-package} \title{The afex Package} \description{ Analysis of Factorial Experiments. } \details{ \tabular{ll}{ Package: \tab afex\cr Type: \tab Package\cr Version: \tab 0.18-0\cr Date: \tab 2017-05-25\cr Depends: \tab R (>= 3.1.0), lme4 (>= 1.1-8), lsmeans (>= 2.17)\cr Encoding: \tab UTF-8\cr License: \tab GPL (>=2)\cr URL: \tab http://afex.singmann.science/, https://github.com/singmann/afex\cr } 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 between-within (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), 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 uses type 3 sums of squares as default (imitating commercial statistical software). } \author{ Henrik Singmann, Ben Bolker, Jake Westfall, Frederik Aust, with contributions from Søren Højsgaard, John Fox, Michael A. Lawrence, Ulf Mertens, Jonathan Love } \keyword{package} afex/man/sk2011.2.Rd0000644000176200001440000001060213055750375013331 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")) lsmip(a1_b,instruction~type2, ylim = c(0, 100)) lsmip(a2_b,instruction~type2, ylim = c(0, 100)) } \keyword{dataset} afex/man/md_16.1.Rd0000644000176200001440000000357413055750375013327 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/round_ps.Rd0000644000176200001440000000107313055750375014103 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/compare.2.vectors.Rd0000644000176200001440000001040413055750375015522 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 = approximate(100000), 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}}. Defaults to \code{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{oneway_test}} (the only test in this selction not using a rank transformation), \item the \code{Wilcoxon} test \code{\link{wilcox_test}} (\code{coin::Wilcoxon}), and \item the \code{median} test \code{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 ## ## $nonparametric ## test test.statistic test.value test.df p ## 1 stats::Wilcoxon W 25.500 NA 0.06933 ## 2 permutation Z -1.751 NA 0.08154 ## 3 coin::Wilcoxon Z -1.854 NA 0.06487 ## 4 median Z -1.744 NA 0.17867 # compare with: with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], alternative = "less")) with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], alternative = "greater")) # doesn't make much sense as the data is not paired, but whatever: with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], paired = TRUE)) # from ?t.test: compare.2.vectors(1:10,y=c(7:20, 200)) } afex/man/afex_aov-methods.Rd0000644000176200001440000001162313073235514015476 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/methods.afex_aov.R \name{afex_aov-methods} \alias{afex_aov-methods} \alias{anova.afex_aov} \alias{print.afex_aov} \alias{summary.afex_aov} \alias{recover.data.afex_aov} \alias{lsm.basis.afex_aov} \title{Methods for afex_aov objects} \usage{ \method{anova}{afex_aov}(object, es = afex_options("es_aov"), observed = NULL, correction = afex_options("correction_aov"), MSE = TRUE, intercept = FALSE, p_adjust_method = NULL, sig_symbols = attr(object$anova_table, "sig_symbols"), ...) \method{print}{afex_aov}(x, ...) \method{summary}{afex_aov}(object, ...) \method{recover.data}{afex_aov}(object, ...) \method{lsm.basis}{afex_aov}(object, trms, xlev, grid, ...) } \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{trms, xlev, grid}{same as for \code{\link{lsm.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{lsm.basis}}{Provide the backbone for using \code{\link{lsmeans}} and related functions from \pkg{lsmeans} directly on \code{afex_aov} objects by returning a \code{\link{ref.grid}} object. Should not be called directly but through the functionality provided by \pkg{lsmeans}.} } } \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/nice.Rd0000644000176200001440000001740113073235514013163 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 printin 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 packages \pkg{ascii} or \pkg{xtable} (nowadays \pkg{knitr} is probably the best approach, see \href{http://yihui.name/knitr/}{here}). \pkg{ascii} provides conversion to \href{http://www.methods.co.nz/asciidoc/}{AsciiDoc} and \href{http://orgmode.org/}{org-mode} (see \code{\link[ascii]{ascii}} and \code{\link[ascii]{print-ascii}}). \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/fhch2010.Rd0000644000176200001440000000662713061021625013461 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) lsmip(a1, frequency~length|task+stimulus) lsmip(a1, frequency~density|task+stimulus) \dontrun{ a2 <- aov_ez("id", "rt", fhch2010, between = "task", within = c("density", "frequency", "length", "stimulus")) nice(a2) lsmip(a2, frequency~length|task+stimulus) lsmip(a2, frequency~density|task+stimulus) } } \keyword{dataset} afex/man/ks2013.3.Rd0000644000176200001440000000735513055750375013347 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/all_fit.Rd0000644000176200001440000000665013056223642013663 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{ code taken from \url{https://github.com/lme4/lme4/blob/master/inst/utils/allFit.R} } \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/reexports.Rd0000644000176200001440000000061313060223542014267 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/obk.long.Rd0000644000176200001440000000554413055750375013772 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[car]{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 = "car") 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/aov_car.Rd0000644000176200001440000006141713073235514013665 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_ez} \alias{aov_4} \title{Convenient ANOVA estimation for factorial designs} \usage{ aov_ez(id, dv, data, between = NULL, within = NULL, covariate = NULL, 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(), ..., print.formula = FALSE) aov_car(formula, data, fun_aggregate = NULL, type = afex_options("type"), factorize = afex_options("factorize"), check_contrasts = afex_options("check_contrasts"), return = afex_options("return_aov"), observed = NULL, anova_table = list(), ...) 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(), ..., 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. he default is given by \code{afex_options("factorize")}, which is initially \code{TRUE}. If one wants to run an ANCOVA, 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{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). 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). Other values are currently still supported for backward compatibility.} \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{...}{Further arguments passed to \code{fun_aggregate}.} \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.} \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.} } \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{lsmeans} 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{lsmeans} 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{lsmeans::lsmeans} 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[lsmeans]{ref.grid}} object by running \code{\link[lsmeans]{lsmeans}} on the \code{afex_aov} object from step 1 using the factors involved in the contrast. For example: \code{r <- lsmeans(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[lsmeans]{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{lsmeans} allows for a variety of advanced settings and simplifiations, for example: all pairwise comparison of a single factor using one command (e.g., \code{lsmeans(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=lsmeans}{here}). A caveat regarding the use of \pkg{lsmeans} concerns the assumption of sphericity for ANOVAs including within-subjects/repeated-measures factors (with more than two levels). While the ANOVA tables per default report results using the Greenhousse-Geisser correction, no such correction is available when using \pkg{lsmeans}. This may result in anti-conservative tests. \pkg{lsmeans} is loaded/attached automatically when loading \pkg{afex} via \code{library} or \code{require}. } \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} and \code{anova}. 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. } } \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 the return argument to \code{"nice"}. This can also be done globally via \code{afex_options(return_aov = "nice")}. \code{return = "nice"} also produces the default output of previous versions of afex (versions 0.13 and earlier). 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") # 1b. plot data: lsmip(a1, gender ~ hour | treatment+phase) # 2. obtain reference grid object: r1 <- lsmeans(a1, ~treatment +phase) r1 # 3. create list of contrasts on the reference grid: c1 <- list( A_B_pre = c(0, -1, 1, rep(0, 6)), # A versus B for pretest A_B_comb = c(0, 0, 0, 0, -0.5, 0.5, 0, -0.5, 0.5), # 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(0, 0, 0, 0, 0, 0, -1, 0.5, 0.5), # control versus A&B follow-up effect_comb = c(0, 0, 0, -0.5, 0.25, 0.25, -0.5, 0.25, 0.25) # 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: lsmeans(a1, "treatment", contr = "pairwise") ####################### ## 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}. } \author{ Henrik Singmann The design of these functions was influenced by \code{\link[ez]{ezANOVA}} from package \pkg{ez}. } afex/man/md_16.4.Rd0000644000176200001440000000501613055750375013323 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/set_sum_contrasts.Rd0000644000176200001440000000152613055750375016034 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/md_12.1.Rd0000644000176200001440000000520513055750375013314 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/md_15.1.Rd0000644000176200001440000000632413055750375013322 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/afex_options.Rd0000644000176200001440000000561613071473525014754 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{return_aov}: Return value of the ANOVA functions (see \code{\link{aov_car}}), default is \code{"nice"}. \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{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}}. There should be no difference between the two. The latter could be minimally faster, but does not allow to use \code{lmerTest::anova()}. } } \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 }

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ordering ## --------------------------------------------------------------------------------------- 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 ## ---- results='asis'-------------------------------------------------------------------- knitr::kable(nice(a1)) ## ---- results='asis'-------------------------------------------------------------------- print(xtable::xtable(anova(a1), digits = c(rep(2, 5), 3, 4)), type = "html") ## --------------------------------------------------------------------------------------- m1 <- lsmeans(a1, ~ inference) m1 ## --------------------------------------------------------------------------------------- pairs(m1) ## --------------------------------------------------------------------------------------- summary(as.glht(pairs(m1)), test=adjusted("free")) ## --------------------------------------------------------------------------------------- m2 <- lsmeans(a1, ~ inference|instruction) m2 ## --------------------------------------------------------------------------------------- pairs(m2) ## --------------------------------------------------------------------------------------- m3 <- lsmeans(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-------------------------------------------------------- lsmip(a1, instruction ~ inference|plausibility) ## --------------------------------------------------------------------------------------- a2 <- aov_ez("id", "response", sk2011.1, between = "instruction", within = c("validity", "plausibility", "what")) a2 ## ----fig.width=7.5, fig.height=4-------------------------------------------------------- lsmip(a2, ~instruction ~ plausibility+validity|what, scales = list(x=list( at = 1:4, labels = c("pl:v", "im:v", "pl:i", "im:i") ))) ## --------------------------------------------------------------------------------------- (m4 <- lsmeans(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[1:4])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[5:6])), test =adjusted("free")) summary(as.glht(contrast(m4, c2[7:8])), test =adjusted("free")) afex/inst/doc/afex_mixed_example.R0000644000176200001440000002065013111546473016676 0ustar liggesusers## ----set-options, echo=FALSE, cache=FALSE----------------------------------------------- options(width = 90) ## ----message=FALSE, warning=FALSE------------------------------------------------------- require(afex) # needed for ANOVA, lsmeans is loaded automatically. require(dplyr) # for working with data frames require(tidyr) # for transforming data frames from wide to long and the other way round. require(multcomp) # for advanced control for multiple testing/Type 1 errors. require(lattice) # for plots require(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]] ## --------------------------------------------------------------------------------------- lsm.options(lmer.df = "asymptotic") # also possible: 'satterthwaite', 'kenward-roger' emm_i1 <- lsmeans(m2s, "frequency", by = c("stimulus", "task")) emm_i1 ## --------------------------------------------------------------------------------------- contrast(pairs(emm_i1), by = NULL, adjust = "holm") ## --------------------------------------------------------------------------------------- summary(as.glht(contrast(pairs(emm_i1), by = NULL)), test = adjusted("holm")) ## --------------------------------------------------------------------------------------- emm_i1b <- summary(contrast(emm_i1, by = NULL)) emm_i1b[,c("estimate", "SE")] <- exp(emm_i1b[,c("estimate", "SE")]) emm_i1b ## --------------------------------------------------------------------------------------- emm_i2 <- lsmeans(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) ) contrast(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/afex_anova_example.html0000644000176200001440000026507613111546466017456 0ustar liggesusers ANOVA and Post-Hoc Contrasts: Reanalysis of Singmann and Klauer (2011)