Amelia/0000755000176200001440000000000013566771575011470 5ustar liggesusersAmelia/NAMESPACE0000644000176200001440000000230113277366020012663 0ustar liggesusersexport(amelia, write.amelia, AmeliaView, ## amelia.prep, ameliabind, compare.density, overimpute, disperse, tscsPlot, missmap, moPrep, transform.amelia, mi.meld, amelia.molist, amelia.default) import(foreign) import(utils) import(Rcpp) S3method(print, amelia) S3method(plot, amelia) S3method(summary, amelia) S3method(summary, mi) S3method(amelia, amelia) S3method(amelia, default) S3method(amelia, molist) S3method(moPrep, molist) S3method(moPrep, default) S3method(transform, amelia) useDynLib(Amelia) importFrom("grDevices", "chull", "colorRampPalette", "dev.copy2pdf", "dev.new", "devAskNewPage", "heat.colors", "rainbow", "rgb") importFrom("graphics", "abline", "arrows", "axis", "hist", "image", "legend", "lines", "matplot", "par", "plot", "plot.new", "plot.window", "points", "rect", "segments", "text", "xinch", "xyinch", "layout") importFrom("methods", "hasArg", "is") importFrom("stats", "coef", "complete.cases", "cov", "density", "lm", "na.omit", "prcomp", "qnorm", "quantile", "rbinom", "reshape", "rnorm", "runif", "sd", "var") Amelia/README0000644000176200001440000000212012064425632012321 0ustar liggesusers################################################## ## ## ## Amelia II: A Package for Missing Data ## ## README ## ## ## ## James Honaker ## ## Gary King ## ## Matthew Blackwell ## ## ## ################################################## Amelia II is an R package for the multiple imputation of multivariate incomplete data. It uses an algorithm that combines bootstrapping and the EM algorithm to take draws from the posterior of the missing data. The Amelia package includes normalizing transformations, cell-level priors, and methods for handling time-series cross-sectional data. Please feel free to contact us or the Amelia mailing list for any questions you might have about the package. Amelia mailing list -- Maintainer: Matthew Blackwell Amelia/.Rinstignore0000644000176200001440000000002612064423557013754 0ustar liggesusersMakefile doc/.*[.]png$Amelia/README.md0000644000176200001440000000166113277343165012740 0ustar liggesusers# Amelia II [![Travis-CI Build Status](https://travis-ci.org/IQSS/Amelia.svg?branch=master)](https://travis-ci.org/IQSS/Amelia) [![CRAN version](http://www.r-pkg.org/badges/version/Amelia)](https://cran.r-project.org/package=Amelia) [Amelia II][] is an R package for the multiple imputation of multivariate incomplete data. It uses an algorithm that combines bootstrapping and the EM algorithm to take draws from the posterior of the missing data. The Amelia package includes normalizing transformations, cell-level priors, and methods for handling time-series cross-sectional data. ## How to install ### Installation requirements `Amelia` requires [R][] version 2.14.0 or higher. ### Manual installation ```R install.packages("Amelia") ``` ### Installing unstable developer version: ```R require(devtools) install_github("IQSS/Amelia", ref = "develop") ``` [Amelia II]: http://gking.harvard.edu/amelia [R]: https://cran.r-project.org Amelia/data/0000755000176200001440000000000012526406344012361 5ustar liggesusersAmelia/data/africa.RData0000644000176200001440000000406712064423557014534 0ustar liggesusersWP*D ZA4/IP͌I {JmsΥ;vֵkYvժԩiNVX+{Ivr[|>y<MmNlm,H@p*G,e첚E)8B#:=B)<ǏId>ɐN2"&[osbko2ᛍSV[Dlu\εٛ:/x#؏N>d2I.TIOH%Yz3z*Lto+S Q )N'`?\`|q YPs/aa>ٿ{ڳBH;O<(Pl/m#?)=G!55g%em ޡ~Agi,qX.P<9lĿZ:H>~>p}RMvMɯq7٭sK|WF=3M/SzOIкap+J!?X9JNP6nx<(L-{rP-i !ol ˷}g|NB_@쇊gڙ(9>?-/·Wۡ}_`AK%alzapŨU xt86.iͧᅧ] V}yJ$Or NBJɠv4h;# P5W`uڍh;#gة}<ïjzybA# $b!ZSja+ ~$x!y<L?~ fffA ^)AR`^Hs.E'T2^ TCz FJ7, Š%w'4eX߹ 7q, \FP?P^(PkPolAV4js~4"lȧVhpCa:v|1VGtEt(vq49rf[%6YvubgMt[}q9-?I~opl4PXAmelia/data/freetrade.RData0000644000176200001440000000651312064423557015246 0ustar liggesusers[yX1EeZZ7^U!@ԺI-VŽRQ_} .-ok}דv~;Ld>-0 #0ޚ L9jLԆsɖ0n|ÍC(anF7r%8ƍ(F7Np'/n2r\.%9fOPGJR([ sP*dJgGICϗh!;CuC C']G+;S\a>e87n?zG:?':4EG<}m|=ްTO=YZ_#<|߇e믧)i > 4_>Gy麲u%b=)sp MQn ' NMLnrxOdž9B1C-04صo`{ k5~е_TD5n= !+bO pCN/԰˷MEd17Gt@Лa׎2z2|Q٥+Lb}$P=ٌ+A.tC]Crt[#K^9FDxG* zN'L0c2x+cz$cDŜ"[G|v)A[avڏ>j3#x 䅌j/zl"lSMļT!6 ʮïvχΗ=n ߢ|ZCtM'x7d9mWuHtC'˦tF< }*Q<}0SKʮt_~x_㊿E}Nt7% PTˑ`OBi'[DA'N-O1Ϋyl]_>OM:r _!𒔯g4 2tU [NOl;/ر[\/aǫ/t}V|XZ:T"/EzAiJ_$M Pe سwB6ȋa~s<Y:,ݍ3k]$O?ދz}|T#vB3%^+lMē}~)^Rtm+{`+& {'}6>x( <p~` /~W="S ^tP +M/^숼ckA 0crw3B~@Il1gFuY['Zoa7Z)pk>- +E>py'Ζ mgG}_ww%~5g[fM;'ulw;~?9<䉸fegFw;mB{OGDno;כSȟW7& <gQ#[> qvlė~\z^|.B^ã<$w$'ݡW0|DŸʡVI^KX˙i·Ӫj |/Aw$>g[Yc GMяy/tXm2q9QZ~yUuvC#߾ԥɸ>`dM~h &Mc`t"竖7V:=\oM9@~Sk7J_ަq*PcDW^%s`\M:>_r/wJ aߝ?}KS ~%f{u/:t%f9eMwC\඄-yؾ~O[/˸c|!2k>?k/"RrZzaf.uَgW)+Qo&?,=9ijַ*QVM]!@ܦ|?Y~V6Րw`;Ӷ[ t|qmc^\/ȧ.nvh66 q]7IMS5_y<< y4rcܸ&ƾOkz"R~g+TqGx'X/r$}k?Boa-~@VǬ*h{Gud%';ۙ @/y<7fWcת woO`< r]f:l -][X/3-˄yD@k_a-i/ޖgXCu[7弊/]}sOv'N}\:ϙ0+ 9Ȩ˨˨˨/sU=b V$vy9瑜'ӕTl#0UBxJ I^1JNwIxP_u( E?`Af2)Zu$5hjy@R)CZ}TT^*?jL*G5@_o#dupM,ooYJ[F|[[[tBtN V+@s .֟3Amelia/man/0000755000176200001440000000000013277350632012225 5ustar liggesusersAmelia/man/plot.amelia.Rd0000644000176200001440000000156013566552200014717 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plot.amelia.R \name{plot.amelia} \alias{plot.amelia} \title{Summary plots for Amelia objects} \usage{ \method{plot}{amelia}(x, which.vars, compare = TRUE, overimpute = FALSE, ask = TRUE, ...) } \arguments{ \item{x}{an object of class "amelia"; typically output from the function \code{amelia}.} \item{which.vars}{a vector indicating the variables to plot. The default is to plot all of the numeric variables that were actually imputed.} \item{compare}{plot the density comparisons for each variable (True or False)} \item{overimpute}{plot the overimputation for each variable (True or False)} \item{ask}{prompt user before changing pages of a plot (True or False)} \item{...}{further graphical arguments.} } \description{ Plots diagnostic plots for the output from the \code{amelia} function. } Amelia/man/amelia.Rd0000644000176200001440000003366013566552200013750 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/emb.r \name{amelia} \alias{amelia} \alias{amelia.amelia} \alias{amelia.molist} \alias{amelia.default} \title{AMELIA: Multiple Imputation of Incomplete Multivariate Data} \usage{ amelia(x, ...) \method{amelia}{amelia}(x, m = 5, p2s = 1, frontend = FALSE, ...) \method{amelia}{molist}(x, ...) \method{amelia}{default}(x, m = 5, p2s = 1, frontend = FALSE, idvars = NULL, ts = NULL, cs = NULL, polytime = NULL, splinetime = NULL, intercs = FALSE, lags = NULL, leads = NULL, startvals = 0, tolerance = 1e-04, logs = NULL, sqrts = NULL, lgstc = NULL, noms = NULL, ords = NULL, incheck = TRUE, collect = FALSE, arglist = NULL, empri = NULL, priors = NULL, autopri = 0.05, emburn = c(0, 0), bounds = NULL, max.resample = 100, overimp = NULL, boot.type = "ordinary", parallel = c("no", "multicore", "snow"), ncpus = getOption("amelia.ncpus", 1L), cl = NULL, ...) } \arguments{ \item{x}{either a matrix, data.frame, a object of class "amelia", or an object of class "molist". The first two will call the default S3 method. The third a convenient way to perform more imputations with the same parameters. The fourth will impute based on the settings from \code{moPrep} and any additional arguments.} \item{...}{further arguments to be passed.} \item{m}{the number of imputed datasets to create.} \item{p2s}{an integer value taking either 0 for no screen output, 1 for normal screen printing of iteration numbers, and 2 for detailed screen output. See "Details" for specifics on output when p2s=2.} \item{frontend}{a logical value used internally for the GUI.} \item{idvars}{a vector of column numbers or column names that indicates identification variables. These will be dropped from the analysis but copied into the imputed datasets.} \item{ts}{column number or variable name indicating the variable identifying time in time series data.} \item{cs}{column number or variable name indicating the cross section variable.} \item{polytime}{integer between 0 and 3 indicating what power of polynomial should be included in the imputation model to account for the effects of time. A setting of 0 would indicate constant levels, 1 would indicate linear time effects, 2 would indicate squared effects, and 3 would indicate cubic time effects.} \item{splinetime}{interger value of 0 or greater to control cubic smoothing splines of time. Values between 0 and 3 create a simple polynomial of time (identical to the polytime argument). Values \code{k} greater than 3 create a spline with an additional \code{k-3} knotpoints.} \item{intercs}{a logical variable indicating if the time effects of \code{polytime} should vary across the cross-section.} \item{lags}{a vector of numbers or names indicating columns in the data that should have their lags included in the imputation model.} \item{leads}{a vector of numbers or names indicating columns in the data that should have their leads (future values) included in the imputation model.} \item{startvals}{starting values, 0 for the parameter matrix from listwise deletion, 1 for an identity matrix.} \item{tolerance}{the convergence threshold for the EM algorithm.} \item{logs}{a vector of column numbers or column names that refer to variables that require log-linear transformation.} \item{sqrts}{a vector of numbers or names indicating columns in the data that should be transformed by a sqaure root function. Data in this column cannot be less than zero.} \item{lgstc}{a vector of numbers or names indicating columns in the data that should be transformed by a logistic function for proportional data. Data in this column must be between 0 and 1.} \item{noms}{a vector of numbers or names indicating columns in the data that are nominal variables.} \item{ords}{a vector of numbers or names indicating columns in the data that should be treated as ordinal variables.} \item{incheck}{a logical indicating whether or not the inputs to the function should be checked before running \code{amelia}. This should only be set to \code{FALSE} if you are extremely confident that your settings are non-problematic and you are trying to save computational time.} \item{collect}{a logical value indicating whether or not the garbage collection frequency should be increased during the imputation model. Only set this to \code{TRUE} if you are experiencing memory issues as it can significantly slow down the imputation process} \item{arglist}{an object of class "ameliaArgs" from a previous run of Amelia. Including this object will use the arguments from that run.} \item{empri}{number indicating level of the empirical (or ridge) prior. This prior shrinks the covariances of the data, but keeps the means and variances the same for problems of high missingness, small N's or large correlations among the variables. Should be kept small, perhaps 0.5 to 1 percent of the rows of the data; a reasonable upper bound is around 10 percent of the rows of the data.} \item{priors}{a four or five column matrix containing the priors for either individual missing observations or variable-wide missing values. See "Details" for more information.} \item{autopri}{allows the EM chain to increase the empirical prior if the path strays into an nonpositive definite covariance matrix, up to a maximum empirical prior of the value of this argument times \code{n}, the number of observations. Must be between 0 and 1, and at zero this turns off this feature.} \item{emburn}{a numeric vector of length 2, where \code{emburn[1]} is a the minimum EM chain length and \code{emburn[2]} is the maximum EM chain length. These are ignored if they are less than 1.} \item{bounds}{a three column matrix to hold logical bounds on the imputations. Each row of the matrix should be of the form \code{c(column.number, lower.bound,upper.bound)} See Details below.} \item{max.resample}{an integer that specifies how many times Amelia should redraw the imputed values when trying to meet the logical constraints of \code{bounds}. After this value, imputed values are set to the bounds.} \item{overimp}{a two-column matrix describing which cells are to be overimputed. Each row of the matrix should be a \code{c(row,column)} pair. Each of these cells will be treated as missing and replaced with draws from the imputation model.} \item{boot.type}{choice of bootstrap, currently restricted to either \code{"ordinary"} for the usual non-parametric bootstrap and \code{"none"} for no bootstrap.} \item{parallel}{the type of parallel operation to be used (if any). If missing, the default is taken from the option \code{"amelia.parallel"} (and if that is not set, \code{"no"}).} \item{ncpus}{integer: the number of processes to be used in parallel operation: typically one would choose the number of available CPUs.} \item{cl}{an optional \pkg{parallel} or \pkg{snow} cluster for use if \code{parallel = "snow"}. If not supplied, a cluster on the local machine is created for the duration of the \code{amelia} call.} } \value{ An instance of S3 class "amelia" with the following objects: \item{imputations}{a list of length \code{m} with an imputed dataset in each entry. The class (matrix or data.frame) of these entries will match \code{x}.} \item{m}{an integer indicating the number of imputations run.} \item{missMatrix}{a matrix identical in size to the original dataset with 1 indicating a missing observation and a 0 indicating an observed observation.} \item{theta}{An array with dimensions \eqn{(p+1)} by \eqn{(p+1)} by \eqn{m} (where \eqn{p} is the number of variables in the imputations model) holding the converged parameters for each of the \code{m} EM chains.} \item{mu}{A \eqn{p} by \eqn{m} matrix of of the posterior modes for the complete-data means in each of the EM chains.} \item{covMatrices}{An array with dimensions \eqn{(p)} by \eqn{(p)} by \eqn{m} where the first two dimensions hold the posterior modes of the covariance matrix of the complete data for each of the EM chains.} \item{code}{a integer indicating the exit code of the Amelia run.} \item{message}{an exit message for the Amelia run} \item{iterHist}{a list of iteration histories for each EM chain. See documentation for details.} \item{arguments}{a instance of the class "ameliaArgs" which holds the arguments used in the Amelia run.} \item{overvalues}{a vector of values removed for overimputation. Used to reformulate the original data from the imputations. } Note that the \code{theta}, \code{mu} and \code{covMatrcies} objects refers to the data as seen by the EM algorithm and is thusly centered, scaled, stacked, tranformed and rearranged. See the manual for details and how to access this information. } \description{ Runs the bootstrap EM algorithm on incomplete data and creates imputed datasets. } \details{ Multiple imputation is a method for analyzing incomplete multivariate data. This function will take an incomplete dataset in either data frame or matrix form and return \code{m} imputed datatsets with no missing values. The algorithm first creates a bootstrapped version of the original data, estimates the sufficient statistics (with priors if specified) by EM on this bootstrapped sample, and then imputes the missing values of the original data using the estimated sufficient statistics. It repeats this process \code{m} times to produce the \code{m} complete datasets where the observed values are the same and the unobserved values are drawn from their posterior distributions. The function will start a "fresh" run of the algorithm if \code{x} is either a incomplete matrix or data.frame. In this method, all of the options will be user-defined or set to their default. If \code{x} is the output of a previous Amelia run (that is, an object of class "amelia"), then Amelia will run with the options used in that previous run. This is a convenient way to run more imputations of the same model. You can provide Amelia with informational priors about the missing observations in your data. To specify priors, pass a four or five column matrix to the \code{priors} argument with each row specifying a different priors as such: \code{ one.prior <- c(row, column, mean,standard deviation)} or, \code{ one.prior <- c(row, column, minimum, maximum, confidence)}. So, in the first and second column of the priors matrix should be the row and column number of the prior being set. In the other columns should either be the mean and standard deviation of the prior, or a minimum, maximum and confidence level for the prior. You must specify your priors all as distributions or all as confidence ranges. Note that ranges are converted to distributions, so setting a confidence of 1 will generate an error. Setting a priors for the missing values of an entire variable is done in the same manner as above, but inputing a \code{0} for the row instead of the row number. If priors are set for both the entire variable and an individual observation, the individual prior takes precedence. In addition to priors, Amelia allows for logical bounds on variables. The \code{bounds} argument should be a matrix with 3 columns, with each row referring to a logical bound on a variable. The first column should be the column number of the variable to be bounded, the second column should be the lower bounds for that variable, and the third column should be the upper bound for that variable. As Amelia enacts these bounds by resampling, particularly poor bounds will end up resampling forever. Amelia will stop resampling after \code{max.resample} attempts and simply set the imputation to the relevant bound. If each imputation is taking a long time to converge, you can increase the empirical prior, \code{empri}. This value has the effect of smoothing out the likelihood surface so that the EM algorithm can more easily find the maximum. It should be kept as low as possible and only used if needed. Amelia assumes the data is distributed multivariate normal. There are a number of variables that can break this assumption. Usually, though, a transformation can make any variable roughly continuous and unbounded. We have included a number of commonly needed transformations for data. Note that the data will not be transformed in the output datasets and the transformation is simply useful for climbing the likelihood. Amelia can run its imputations in parallel using the methods of the \pkg{parallel} package. The \code{parallel} argument names the parallel backend that Amelia should use. Users on Windows systems must use the \code{"snow"} option and users on Unix-like systems should use \code{"multicore"}. The \code{multicore} backend sets itself up automatically, but the \code{snow} backend requires more setup. You can pass a predefined cluster from the \code{parallel::makePSOCKcluster} function to the \code{cl} argument. Without this cluster, Amelia will attempt to create a reasonable default cluster and stop it once computation is complete. When using the parallel backend, users can set the number of CPUs to use with the \code{ncpus} argument. The defaults for these two arguments can be set with the options \code{"amelia.parallel"} and \code{"amelia.ncpus"}. Please refer to the Amelia manual for more information on the function or the options. } \section{Methods (by class)}{ \itemize{ \item \code{amelia}: Run additional imputations for Amelia output \item \code{molist}: Perform multiple overimputation from moPrep \item \code{default}: Run core Amelia algorithm }} \examples{ data(africa) a.out <- amelia(x = africa, cs = "country", ts = "year", logs = "gdp_pc") summary(a.out) plot(a.out) } \references{ Honaker, J., King, G., Blackwell, M. (2011). Amelia II: A Program for Missing Data. \emph{Journal of Statistical Software}, \bold{45(7)}, 1--47. URL http://www.jstatsoft.org/v45/i07/. } \seealso{ For imputation diagnostics, \code{\link{missmap}}, \code{\link{compare.density}}, \code{\link{overimpute}} and \code{\link{disperse}}. For time series plots, \code{\link{tscsPlot}}. Also: \code{\link{plot.amelia}}, \code{\link{write.amelia}}, and \code{\link{ameliabind}} } \author{ James Honaker Gary King Matt Blackwell } \keyword{models} Amelia/man/write.amelia.Rd0000644000176200001440000000502413277337645015107 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/write.amelia.R \name{write.amelia} \alias{write.amelia} \title{Write Amelia imputations to file} \usage{ write.amelia(obj, separate = TRUE, file.stem, extension = NULL, format = "csv", impvar = "imp", orig.data = TRUE, ...) } \arguments{ \item{obj}{an object of class "amelia"; typically output from the function \code{amelia}} \item{separate}{logical variable. If \code{TRUE} (default), the imputed datasets will be written to separate files, whose names come from the \code{file.stem} and \code{extension} arguments. If \code{FALSE}, the imputations are stacked and written as a single file.} \item{file.stem}{the leading part of the filename to save to output The imputation number and \code{extension} will be added to complete the filename. This can include a directory path.} \item{extension}{the extension of the filename. This is simply what follows \code{file.stem} and the imputation number.} \item{format}{one of the following output formats: \code{csv}, \code{dta} or \code{table}. See details.} \item{impvar}{the name of imputation number variable written to the stacked dataset when \code{separate} is \code{FALSE}.} \item{orig.data}{logical variable indicating whether the original, unimputed dataset should be included in the stacked dataset when \code{separate} is \code{FALSE}.} \item{\dots}{further arguments for the \code{write} functions.} } \description{ Writes the imptuted datasets to file from a run of \code{amelia} } \details{ \code{write.amelia} writes the imputed datasets to a file or a set of files using one of the following functions: \code{write.csv}, \code{write.dta}, or \code{write.table}. You can pass arguments to these functions from \code{write.amelia}. When \code{separate} is \code{TRUE}, each imputed dataset is written to its own file. If you were to set \code{file.stem} to \code{"outdata"} and the \code{extension} to \code{".csv"} , then the resulting filename of the written files will be \preformatted{ outdata1.csv outdata2.csv outdata3.csv ... } and so on. When \code{separate} is \code{FALSE}, the function adds a variable called \code{impvar} to each dataset which indicates the imputed dataset to which the row belongs. Then, each of the datasets are stacked together to create one dataset. If \code{orig.data} is \code{TRUE}, then the original, unimputed dataset is included at the top of the stack, with its imputation number set to 0. } \seealso{ \code{\link{write.csv}}, \code{\link{write.table}}, \code{\link{write.dta}} } Amelia/man/compare.density.Rd0000644000176200001440000000417113277337645015634 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diag.r \name{compare.density} \alias{compare.density} \title{Compare observed versus imputed densities} \usage{ compare.density(output, var, col = c("indianred", "dodgerblue"), scaled = FALSE, lwd = 1, main, xlab, ylab, legend = TRUE, frontend = FALSE, ...) } \arguments{ \item{output}{output from the function \code{amelia}.} \item{var}{column number or variable name of the variable to plot.} \item{col}{a vector of length 2 containing the color to plot the (1) imputed density and (2) the observed density.} \item{scaled}{a logical indicating if the two densities should be scaled to reflect the difference in number of units in each.} \item{lwd}{the line width of the density plots.} \item{main}{main title of the plot. The default is to title the plot using the variable name.} \item{xlab}{the label for the x-axis. The default is the name of the variable.} \item{ylab}{the label for the y-axis. The default is "Relative Density."} \item{legend}{a logical value indicating if a legend should be plotted.} \item{frontend}{a logical value used internally for the Amelia GUI.} \item{...}{further graphical parameters for the plot.} } \description{ Plots smoothed density plots of observed and imputed values from output from the \code{amelia} function. } \details{ This function first plots a density plot of the observed units for the variable \code{var} in \code{col[2]}. The the function plots a density plot of the mean or modal imputations for the missing units in \code{col[1]}. If a variable is marked "ordinal" or "nominal" with the \code{ords} or \code{noms} options in \code{amelia}, then the modal imputation will be used. If \code{legend} is \code{TRUE}, then a legend is plotted as well. } \examples{ data(africa) } \references{ Abayomi, K. and Gelman, A. and Levy, M. 2005 "Diagnostics for Multivariate Imputations," \emph{Applied Statistics}. 57,3: 273--291. } \seealso{ For more information on how densities are computed, \code{\link{density}}; Other imputation diagnostics are \code{\link{overimpute}}, \code{\link{disperse}}, and \code{\link{tscsPlot}}. } Amelia/man/mi.meld.Rd0000644000176200001440000000357113277337645014060 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diag.r \name{mi.meld} \alias{mi.meld} \title{Combine Multiple Results From Multiply Imputed Datasets} \usage{ mi.meld(q, se, byrow = TRUE) } \arguments{ \item{q}{A matrix or data frame of (k) quantities of interest (eg. coefficients, parameters, means) from (m) multiply imputed datasets. Default is to assume the matrix is m-by-k (see \code{byrow}), thus each row represents a set of results from one dataset, and each column represents the different values of a particular quantity of interest across the imputed datasets.} \item{se}{A matrix or data frame of standard errors that correspond to each of the elements of the quantities of interest in \code{q}. Should be the same dimensions as \code{q}.} \item{byrow}{logical. If \code{TRUE}, \code{q} and \code{se} are treated as though each row represents the set of results from one dataset (thus m-by-k). If \code{FALSE}, each column represents results from one dataset (thus k-by-m).} } \value{ \item{q.mi}{Average value of each quantity of interest across the m models} \item{se.mi}{Standard errors of each quantity of interest} } \description{ Combine sets of estimates (and their standard errors) generated from different multiply imputed datasets into one set of results. } \details{ Uses Rubin's rules for combining a set of results from multiply imputed datasets to reflect the average result, with standard errors that both average uncertainty across models and account for disagreement in the estimated values across the models. } \references{ Rubin, D. (1987). \emph{Multiple Imputation for Nonresponse in Surveys}. New York: Wiley. Honaker, J., King, G., Honaker, J. Joseph, A. Scheve K. (2001). Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation \emph{American Political Science Review}, \bold{95(1)}, 49--69. (p53) } Amelia/man/transform.amelia.Rd0000644000176200001440000000251313277337645015770 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/transform.amelia.R \name{transform.amelia} \alias{transform.amelia} \title{Transform imputed datasets from Amelia objects} \usage{ \method{transform}{amelia}(`_data`, ...) } \arguments{ \item{_data}{an object of class "amelia"; typically output from the function \code{amelia}.} \item{...}{further arguments of the form \code{tag = value}.} } \value{ An object of class \code{amelia} with its \code{imputations} and \code{missMatrix} values updated according to the transformations. In addition, each of the calls to \code{transform.amelia} are stored in } \description{ Updates the imputed datasets from an \code{amelia} output with the specified transformations. } \details{ The \code{\dots} arugments to \code{transform.amelia} are expressions of the form \code{tag = value}, where \code{tag} is the variable that is being updated or created and \code{value} is an expression that is a function of the variables in the imputed datasets. For instance, if you wanted to create an interaction of two imputed variables, you could have one argument be \code{intervar = var1 * var2}. This would either update the current variable \code{intervar} in the imputed data or append a new variable called \code{intervar} to the imputed datasets. } \seealso{ \code{\link{transform}} } Amelia/man/amelia.package.Rd0000755000176200001440000000253412064423557015345 0ustar liggesusers\name{amelia-package} \alias{amelia-package} \docType{package} \title{Amelia II: A Program for Missing Data} \description{Uses a bootstrap+EM algorithm to impute missing values from a dataset and produces multiple output datasets for analysis.} \details{ \tabular{ll}{ Package: \tab amelia\cr Type: \tab Package\cr Version: \tab 1.0\cr Date: \tab 2006-03-03\cr License: \tab See Manual\cr } You can use the package in one of two ways: either by invoking the \code{ameliagui()} command and running the program from a graphical interface or by loading in your data and then running the \code{amelia} function on the data. If you use the GUI in Windows, makes sure that you run R under a Single Window Interface (SDI) as it will try to grab focus from the GUI if you don't. } \author{ James Honaker, Matthew Blackwell, Gary King } \references{James Honaker, Gary King, Matthew Blackwell (2011). Amelia II: A Program for Missing Data. \emph{Journal of Statistical Software}, \bold{45(7)}, 1--47. URL http://www.jstatsoft.org/v45/i07/. King, Gary; James Honaker, Anne Joseph, and Kenneth Scheve. \"Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation\", \emph{American Political Science Review}, Vol. 95, No. 1 (March, 2001): Pp. 49-69. } \keyword{package} Amelia/man/moPrep.Rd0000644000176200001440000000727013566552200013760 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mo.R \name{moPrep} \alias{moPrep} \alias{moPrep.molist} \alias{moPrep.default} \title{Prepare Multiple Overimputation Settings} \usage{ moPrep(x, formula, subset, error.proportion, gold.standard = !missing(subset), error.sd) \method{moPrep}{molist}(x, formula, subset, error.proportion, gold.standard = FALSE, error.sd) \method{moPrep}{default}(x, formula, subset, error.proportion, gold.standard = !missing(subset), error.sd) } \arguments{ \item{x}{either a matrix, data.frame, or a object of class "molist" from a previous \code{moPrep} call. The first two derive the priors from the data given, and the third will derive the priors from the first \code{moPrep} call and add them to the already defined priors.} \item{formula}{a formula describing the nature of the measurement error for the variable. See "Details."} \item{subset}{an optional vector specifying a subset of observations which possess measurement error.} \item{error.proportion}{an optional vector specifying the fraction of the observed variance that is due to measurement error.} \item{gold.standard}{a logical value indicating if values with no measurement error should be used to estimate the measurement error variance.} \item{error.sd}{an optional vector specifying the standard error of the measurement error.} } \value{ An instance of the S3 class "molist" with the following objects: \itemize{ \item priors a four-column matrix of the multiple overimputation priors associated with the data. Each row of the matrix is \code{c(row,column, prior.mean, prior.sd)} \item overimp a two-column matrix of cells to be overimputed. Each row of the matrix is of the form \code{c(row, column)}, which indicate the row and column of the cell to be overimputed. \item data the object name of the matrix or data.frame to which priors refer. } Note that \code{priors} and \code{overimp} might contain results from multiple calls to \code{moPrep}, not just the most recent. } \description{ A function to generate priors for multiple overimputation of a variable measured with error. } \details{ This function generates priors for multiple overimputation of data measured with error. With the \code{formula} arugment, you can specify which variable has the error, what the mean of the latent data is, and if there are any other proxy measures of the mismeasured variable. The general syntax for the formula is: \code{errvar ~ mean | proxy}, where \code{errvar} is the mismeasured variable, \code{mean} is a formula for the mean of the latent variable (usually just \code{errvar} itself), and \code{proxy} is a another mismeasurement of the same latent variable. The proxies are used to estimate the variance of the measurement error. \code{subset} and \code{gold.standard} refer to the the rows of the data which are and are not measured with error. Gold-standard rows are used to estimate the variance of the measurement. error. \code{error.proportion} is used to estimate the variance of the measurement error by estimating the variance of the mismeasurement and taking the proportion assumed to be due to error. \code{error.sd} sets the standard error of the measurement error directly. } \section{Methods (by class)}{ \itemize{ \item \code{molist}: Alter existing moPrep output \item \code{default}: Default call to moPrep }} \examples{ data(africa) m.out <- moPrep(africa, trade ~ trade, error.proportion = 0.1) a.out <- amelia(m.out, ts = "year", cs = "country") plot(a.out) m.out <- moPrep(africa, trade ~ trade, error.sd = 1) a.out <- amelia(m.out, ts = "year", cs = "country") } \seealso{ \code{\link{amelia}} } Amelia/man/combine.output.Rd0000644000176200001440000000161413277337645015502 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/prep.r \name{combine.output} \alias{combine.output} \title{Combine Multiple Amelia Output Lists} \usage{ combine.output(...) } \arguments{ \item{...}{a list of Amelia output lists from runs of Amelia with the same arguments except the number of imputations.} } \description{ This function combines output lists from multiple runs of Amelia, where each run used the same arguments. The result is one list, formatted as if Amelia had been run once. } \details{ This function is useful for combining the output from Amelia runs that occurred at different times or in different sessions of R. It assumes that the arguments given to the runs of Amelia are the same except for \code{m}, the number of imputations, and it uses the arguments from the first output list as the arguments for the combined output list. } \keyword{utilities} Amelia/man/freetrade.Rd0000644000176200001440000000165312064423557014462 0ustar liggesusers\name{freetrade} \docType{data} \alias{freetrade} \title{Trade Policy and Democracy in 9 Asian States} \description{Economic and political data on nine developing countries in Asia from 1980 to 1999. This dataset includes 9 variables including year, country, average tariff rates, Polity IV score, total population, gross domestic product per capita, gross international reserves, a dummy variable for if the country had signed an IMF agreement in that year, a measure of financial openness, and a measure of US hegemony. These data were used in Milner and Kubota (2005).} \usage{freetrade} \format{A data frame with 10 variables and 171 observations.} \source{World Bank, World Trade Organization, Polity IV and others.} \references{Helen Milner and Keiko Kubota (2005), ``Why the move to free trade? Democracy and trade policy in the developing countries.'' \emph{International Organization}, Vol 59, Issue 1.} \keyword{datasets} Amelia/man/AmeliaView.Rd0000644000176200001440000000061313566552200014533 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ameliagui.r \name{AmeliaView} \alias{AmeliaView} \title{Interactive GUI for Amelia} \usage{ AmeliaView() } \description{ Brings up the AmeliaView graphical interface, which allows users to load datasets, manage options and run Amelia from a traditional windowed environment. } \details{ Requires the tcltk package. } Amelia/man/summary.amelia.Rd0000644000176200001440000000102413277337645015446 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.amelia.R \name{summary.amelia} \alias{summary.amelia} \title{Summary of an Amelia object} \usage{ \method{summary}{amelia}(object, ...) } \arguments{ \item{object}{an object of class \code{amelia}. Typically, an output from the function \code{amelia}.} \item{...}{further arguments.} } \description{ Returns summary information from the Amelia run along with missingles information. } \seealso{ \code{\link{amelia}}, \code{\link{plot.amelia}} } Amelia/man/disperse.Rd0000644000176200001440000000462113277434613014337 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diag.r \name{disperse} \alias{disperse} \title{Overdispersed starting values diagnostic for multiple imputation} \usage{ disperse(output, m = 5, dims = 1, p2s = 0, frontend = FALSE, ..., xlim = NULL, ylim = NULL) } \arguments{ \item{output}{output from the function \code{amelia}.} \item{m}{the number of EM chains to run from overdispersed starting values.} \item{dims}{the number of principle components of the parameters to display and assess convergence on (up to 2).} \item{p2s}{an integer that controls printing to screen. 0 (default) indicates no printing, 1 indicates normal screen output and 2 indicates diagnostic output.} \item{frontend}{a logical value used internally for the Amelia GUI.} \item{...}{further graphical parameters for the plot.} \item{xlim}{limits of the plot in the horizontal dimension.} \item{ylim}{limits of the plot in vertical dimension.} } \description{ A visual diagnostic of EM convergence from multiple overdispersed starting values for an output from \code{amelia}. } \details{ This function tracks the convergence of \code{m} EM chains which start from various overdispersed starting values. This plot should give some indication of the sensitivity of the EM algorithm to the choice of starting values in the imputation model in \code{output}. If all of the lines converge to the same point, then we can be confident that starting values are not affecting the EM algorithm. As the parameter space of the imputation model is of a high-dimension, this plot tracks how the first (and second if \code{dims} is 2) principle component(s) change over the iterations of the EM algorithm. Thus, the plot is a lower dimensional summary of the convergence and is subject to all the drawbacks inherent in said summaries. For \code{dims==1}, the function plots a horizontal line at the position where the first EM chain converges. Thus, we are checking that the other chains converge close to that horizontal line. For \code{dims==2}, the function draws a convex hull around the point of convergence for the first EM chain. The hull is scaled to be within the tolerance of the EM algorithm. Thus, we should check that the other chains end up in this hull. } \seealso{ Other imputation diagnostics are \code{\link{compare.density}}, \code{\link{disperse}}, and \code{\link{tscsPlot}} } Amelia/man/ameliagui.Rd0000644000176200001440000000061013566552200014442 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ameliagui.r \name{ameliagui} \alias{ameliagui} \alias{main.close} \title{Interactive GUI for Amelia} \usage{ AmeliaView() } \description{ Brings up the AmeliaView graphical interface, which allows users to load datasets, manage options and run Amelia from a traditional windowed environment. } \keyword{utilities} Amelia/man/ameliabind.Rd0000644000176200001440000000231213277337645014610 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/emb.r \name{ameliabind} \alias{ameliabind} \title{Combine multiple runs of Amelia} \usage{ ameliabind(...) } \arguments{ \item{...}{one or more objects of class \code{amelia} with the same arguments and created from the same data.} } \value{ An object of class \code{amelia}. } \description{ Combines multiple runs of \code{amelia} with the same arguments and data into one \code{amelia} object. } \details{ \code{ameliabind} will combine multiple runs of \code{amelia} into one object so that you can utilize diagnostics and modelling on all the imputations together. This function is useful for combining multiple runs of \code{amelia} run on parallel machines. Note that \code{ameliabind} only checks that they arguments and the missingness matrix are identical. Thus, it could be fooled by two datasets that are identical up to a transformation of one variable. } \examples{ data(africa) a1.out <- amelia(x = africa, cs = "country", ts = "year", logs = "gdp_pc") a2.out <- amelia(x = africa, cs = "country", ts = "year", logs = "gdp_pc") all.out <- ameliabind(a1.out, a2.out) summary(all.out) plot(all.out) } \seealso{ \code{\link{amelia}} } Amelia/man/missmap.Rd0000644000176200001440000000612413566633540014173 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/missmap.R \name{missmap} \alias{missmap} \title{Missingness Map} \usage{ missmap(obj, vars, legend = TRUE, col, main, y.cex = 0.8, x.cex = 0.8, y.labels, y.at, csvar = NULL, tsvar = NULL, rank.order = TRUE, margins = c(5, 5), gap.xaxis = 1, x.las = 2, ...) } \arguments{ \item{obj}{an object of class "amelia"; typically output from the function \code{amelia}, a matrix or a dataframe.} \item{vars}{a vector of column numbers or column names of the data to include in the plot. The default is to plot all variables.} \item{legend}{should a legend be drawn? (True or False)} \item{col}{a vector of length two where the first element specifies the color for missing cells and the second element specifies} \item{main}{main title of the plot. Defaults to "Missingness Map".} \item{y.cex}{expansion for the variables names on the x-axis.} \item{x.cex}{expansion for the unit names on the y-axis.} \item{y.labels}{a vector of row labels to print on the y-axis} \item{y.at}{a vector of the same length as \code{y.labels} with row nmumbers associated with the labels.} \item{csvar}{column number or name of the variable corresponding to the unit indicator. Only used when the \code{obj} is not of class \code{amelia}.} \item{tsvar}{column number or name of the variable corresponding to the time indicator. Only used when the \code{obj} is not of class \code{amelia}.} \item{rank.order}{a logical value. If \code{TRUE}, the default, then the order of the variables along the the x-axis is sorted by the percent missing (from highest to lowest). If \code{FALSE}, it is simply the order of the variables in the data.} \item{margins}{a vector of length two that specifies the bottom and left margins of the plot. Useful for when variable names or row names are long.} \item{gap.xaxis}{value to pass to the \code{gap.axis} argument of the \code{axis} function that plots the x-axis. See \code{\link{axis}} for more details. Ignored on R versions less than 4.0.0.} \item{x.las}{value of the \code{las} argument to pass to the \code{\link{axis}} function creating the x-axis.} \item{...}{further graphical arguments.} } \description{ Plots a missingness map showing where missingness occurs in the dataset passed to \code{amelia}. } \details{ \code{missmap} draws a map of the missingness in a dataset using the \code{image} function. The columns are reordered to put the most missing variable farthest to the left. The rows are reordered to a unit-period order if the \code{ts} and \code{cs} arguments were passed to \code{amelia}. If not, the rows are not reordered. The \code{y.labels} and \code{y.at} commands can be used to associate labels with rows in the data to identify them in the plot. The y-axis is internally inverted so that the first row of the data is associated with the top-most row of the missingness map. The values of \code{y.at} should refer to the rows of the data, not to any point on the plotting region. } \seealso{ \code{\link{compare.density}}, \code{\link{overimpute}}, \code{\link{tscsPlot}}, \code{\link{image}}, \code{\link{heatmap}} } Amelia/man/overimpute.Rd0000644000176200001440000000604513566552200014714 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diag.r \name{overimpute} \alias{overimpute} \title{Overimputation diagnostic plot} \usage{ overimpute(output, var, draws = 20, subset, legend = TRUE, xlab, ylab, main, frontend = FALSE, ...) } \arguments{ \item{output}{output from the function \code{amelia}.} \item{var}{column number or variable name of the variable to overimpute.} \item{draws}{the number of draws per imputed dataset to generate overimputations. Total number of simulations will \code{m * draws} where \code{m} is the number of imputations.} \item{subset}{an optional vector specifying a subset of observations to be used in the overimputation.} \item{legend}{a logical value indicating if a legend should be plotted.} \item{xlab}{the label for the x-axis. The default is "Observed Values."} \item{ylab}{the label for the y-axis. The default is "Imputed Values."} \item{main}{main title of the plot. The default is to smartly title the plot using the variable name.} \item{frontend}{a logical value used internally for the Amelia GUI.} \item{...}{further graphical parameters for the plot.} } \value{ A list that contains (1) the row in the original data (\code{row}), (2) the observed value of that observation (\code{orig}), (2) the mean of the overimputations (\code{mean.overimputed}), (3) the lower bound of the 95\% confidence interval of the overimputations (\code{lower.overimputed}), (4) the upper bound of the 95\% confidence interval of the overimputations (\code{upper.overimputed}), (5) the fraction of the variables that were missing for that observation in the original data (\code{prcntmiss}), and (6) a matrix of the raw overimputations, with observations in rows and the different draws in columns (\code{overimps}). } \description{ Treats each observed value as missing and imputes from the imputation model from \code{amelia} output. } \details{ This function temporarily treats each observed value in \code{var} as missing and imputes that value based on the imputation model of \code{output}. The dots are the mean imputation and the vertical lines are the 90\% percent confidence intervals for imputations of each observed value. The diagonal line is the \eqn{y=x} line. If all of the imputations were perfect, then our points would all fall on the line. A good imputation model would have about 90\% of the confidence intervals containing the truth; that is, about 90\% of the vertical lines should cross the diagonal. The color of the vertical lines displays the fraction of missing observations in the pattern of missingness for that observation. The legend codes this information. Obviously, the imputations will be much tighter if there are more observed covariates to use to impute that observation. The \code{subset} argument evaluates in the environment of the data. That is, it can but is not required to refer to variables in the data frame as if it were attached. } \seealso{ Other imputation diagnostics are \code{\link{compare.density}}, \code{\link{disperse}}, and \code{\link{tscsPlot}}. } Amelia/man/africa.Rd0000644000176200001440000000116013277166142013740 0ustar liggesusers\name{africa} \docType{data} \alias{africa} \title{Economic and Political Indictors in 6 African States} \description{Data on a few economic and political variables in six African States from 1972-1991. The variables are year, country name, Gross Domestic Product per capita, inflation, trade as a percentage of GDP, a measure of civil liberties and total population. The data is from the Africa Research Program. A few cells are missing.} \usage{africa} \format{A data frame with 7 variables and 120 observations.} \source{Africa Research Program \url{http://scholar.harvard.edu/rbates/data}} \keyword{datasets} Amelia/man/tscsPlot.Rd0000644000176200001440000000517113566552200014327 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diag.r \name{tscsPlot} \alias{tscsPlot} \title{Plot observed and imputed time-series for a single cross-section} \usage{ tscsPlot(output, var, cs, draws = 100, conf = 0.9, misscol = "red", obscol = "black", xlab, ylab, main, pch, ylim, xlim, frontend = FALSE, plotall = FALSE, nr, nc, pdfstub, ...) } \arguments{ \item{output}{output from the function \code{amelia}.} \item{var}{the column number or variable name of the variable to plot.} \item{cs}{the name (or level) of the cross-sectional unit to plot. Maybe a vector of names which will panel a window of plots} \item{draws}{the number of imputations on which to base the confidence intervals.} \item{conf}{the confidence level of the confidence intervals to plot for the imputated values.} \item{misscol}{the color of the imputed values and their confidence intervals.} \item{obscol}{the color of the points for observed units.} \item{xlab}{x axis label} \item{ylab}{y axis label} \item{main}{overall plot title} \item{pch}{point shapes for the plot.} \item{ylim}{y limits (y1, y2) of the plot.} \item{xlim}{x limits (x1, x2) of the plot.} \item{frontend}{a logical value for use with the \code{AmeliaView} GUI.} \item{plotall}{a logical value that provides a shortcut for ploting all unique values of the level. A shortcut for the \code{cs} argument, a TRUE value overwrites any \code{cs} argument.} \item{nr}{the number of rows of plots to use when ploting multiple cross-sectional units. The default value will try to minimize this value to create a roughly square representation, up to a value of four. If all plots do not fit on the window, a new window will be started.} \item{nc}{the number of columns of plots to use. See \code{nr}} \item{pdfstub}{a stub string used to write pdf copies of each window created by the plot. The default is not to write pdf output, but any string value will turn on pdf output to the local working directory. If the stub is \code{mystub}, then plots will be saved as \code{mystub1.pdf}, \code{mystub2.pdf}, etc.} \item{...}{further graphical parameters for the plot.} } \description{ Plots a time series for a given variable in a given cross-section and provides confidence intervals for the imputed values. } \details{ The \code{cs} argument should be a value from the variable set to the \code{cs} argument in the \code{amelia} function for this output. This function will not work if the \code{ts} and \code{cs} arguments were not set in the \code{amelia} function. If an observation has been overimputed, \code{tscsPlot} will plot both an observed and an imputed value. } Amelia/DESCRIPTION0000644000176200001440000000344113566771575013200 0ustar liggesusersPackage: Amelia Version: 1.7.6 Date: 2019-11-24 Title: A Program for Missing Data Author: James Honaker , Gary King , Matthew Blackwell Maintainer: Matthew Blackwell Depends: R (>= 3.0.2), Rcpp (>= 0.11) Imports: foreign, utils, grDevices, graphics, methods, stats LinkingTo: Rcpp (>= 0.11), RcppArmadillo Description: A tool that "multiply imputes" missing data in a single cross-section (such as a survey), from a time series (like variables collected for each year in a country), or from a time-series-cross-sectional data set (such as collected by years for each of several countries). Amelia II implements our bootstrapping-based algorithm that gives essentially the same answers as the standard IP or EMis approaches, is usually considerably faster than existing approaches and can handle many more variables. Unlike Amelia I and other statistically rigorous imputation software, it virtually never crashes (but please let us know if you find to the contrary!). The program also generalizes existing approaches by allowing for trends in time series across observations within a cross-sectional unit, as well as priors that allow experts to incorporate beliefs they have about the values of missing cells in their data. Amelia II also includes useful diagnostics of the fit of multiple imputation models. The program works from the R command line or via a graphical user interface that does not require users to know R. License: GPL (>= 2) URL: http://gking.harvard.edu/amelia Suggests: tcltk, Zelig RoxygenNote: 6.1.0 Encoding: UTF-8 LazyData: true NeedsCompilation: yes Packaged: 2019-11-25 04:04:45 UTC; mblackwell Repository: CRAN Date/Publication: 2019-11-25 15:30:05 UTC Amelia/build/0000755000176200001440000000000013566651335012556 5ustar liggesusersAmelia/build/vignette.rds0000644000176200001440000000034313566651335015115 0ustar liggesusersuQ @]KW? D !-ʒ l4havg͛y{@+tES@Ox.A. Y|eiYӣhQdc-SJR YύP=Ɨ~A8`F\yE2R1x^n~g"ǘr4_|{BBϟ\%5_7s6w 32) { stop("upper bounds not working") } Amelia/src/0000755000176200001440000000000013566651335012246 5ustar liggesusersAmelia/src/em.cpp0000644000176200001440000003771313566651335013366 0ustar liggesusers #include "em.h" #include using namespace Rcpp ; SEXP emcore(SEXP xs, SEXP AMr1s, SEXP os, SEXP ms, SEXP ivec, SEXP thetas, SEXP tols, SEXP emburns, SEXP p2ss, SEXP empris, SEXP autos, SEXP alls, SEXP prs){ //, SEXP p2ss, SEXP prs, SEXP empris, SEXP fends, SEXP alls, SEXP autos, SEXP emburns// NumericMatrix xr(xs); NumericMatrix thetar(thetas); NumericVector tol(tols); NumericMatrix AMr1r(AMr1s); NumericMatrix orr(os); NumericMatrix mr(ms); NumericVector ir(ivec); NumericVector emburn(emburns); NumericVector p2sr(p2ss); NumericVector emprir(empris); // NumericVector frontend(fends); NumericVector allthetas(alls); NumericVector autopri(autos); int p2s = p2sr(0), empri = emprir(0); int n = xr.nrow(), k = xr.ncol(); int const AMn = n; int npatt = orr.nrow(); int cvalue = 1; arma::mat x(xr.begin(), n, k, false); arma::mat thetaold(thetar.begin(), k + 1, k + 1, false); arma::mat AMr1(AMr1r.begin(), n, k, false); arma::mat obsmat(orr.begin(), npatt, k, false); arma::mat mismat(mr.begin(), npatt, k, false); arma::vec ii(ir.begin(), n, false); //Rcpp::Rcout << "Set up arma things. " << std::endl; // Bring out your priors. NumericMatrix prr; int npr, knr; arma::mat priors; if (!Rf_isNull(prs)) { prr = NumericMatrix(prs); npr = prr.nrow(); knr = prr.ncol(); priors = arma::mat(prr.begin(), npr, knr, false); } int count = 0; int is, isp; //int nparam = arma::accu(arma::find(arma::trimatu(thetaold))); arma::uvec upperpos = arma::find(arma::trimatu(arma::ones(k+1,k+1))); arma::mat xplay = arma::zeros(AMn,k); arma::mat hmcv(k,k); arma::mat imputations(2,k); arma::vec music(k); arma::mat thetanew(k+1, k+1); arma::mat theta(k+1, k+1); arma::vec sweeppos(k+1); arma::uvec mispos; arma::uvec thetaleft; arma::vec etest; arma::mat iterHist(1,3); arma::mat thetaHolder(upperpos.n_elem,1); thetaHolder.col(0) = thetaold.elem(upperpos); iterHist.zeros(); sweeppos.zeros(); hmcv.zeros(); music.zeros(); int st, ss, singFlag, monoFlag; if (arma::accu(mismat.row(0)) == 0) { st = 1; } else { st = 0; } // if (empri > 0) { arma::mat hold = empri * arma::eye(k,k); arma::mat simple(k,k); //} if (p2s > 0) Rcpp::Rcout << std::endl; //Rcpp::Rcout << "Starting loop. " << std::endl; while ( ( (cvalue > 0) | (count < emburn(0)) ) & ( (count < emburn(1)) | (emburn(1) < 1))) { count++; hmcv.zeros(k,k); music.zeros(k); xplay.zeros(AMn,k); if (p2s > 0) { if (count < 10) { Rcpp::Rcout << " " << count; } else { Rcpp::Rcout << " " << count; } if (count % 20 == 0) { Rcpp::Rcout << std::endl; } } if (st == 1) { xplay.rows(0,ii(1)-2) = x.rows(0,ii(1)-2); } if (Rf_isNull(prs)) { for (ss = st; ss < obsmat.n_rows; ss++) { is = ii(ss)-1; isp = ii(ss+1)-2; theta = thetaold; sweeppos.zeros(); sweeppos(arma::span(1,k)) = arma::trans(obsmat.row(ss)); sweep(theta, sweeppos); imputations.zeros(); imputations.set_size(isp - is, k); imputations = x.rows(is, isp) * theta(arma::span(1,k), arma::span(1,k)); imputations.each_row() += theta(0, arma::span(1,k)); imputations = AMr1.rows(is, isp) % imputations; xplay.rows(is, isp) = x.rows(is, isp) + imputations; mispos = arma::find(mismat.row(ss)); hmcv(mispos, mispos) += (1+ isp - is) * theta(mispos+1, mispos+1); } } else { for (ss = st; ss < obsmat.n_rows; ss++) { is = ii(ss)-1; isp = ii(ss+1)-2; theta = thetaold; sweeppos.zeros(); sweeppos(arma::span(1,k)) = arma::trans(obsmat.row(ss)); sweep(theta, sweeppos); imputations.zeros(); imputations.set_size(isp - is, k); imputations = x.rows(is, isp) * theta(arma::span(1,k), arma::span(1,k)); imputations.each_row() += theta(0, arma::span(1,k)); imputations = AMr1.rows(is, isp) % imputations; mispos = arma::find(mismat.row(ss)); arma::mat solveSigma = arma::inv(theta(mispos + 1, mispos + 1)); arma::mat diagLambda = arma::zeros(mispos.n_elem, mispos.n_elem); for (int p = 0; p <= isp-is; p++) { arma::uvec prRow = arma::find(priors.col(0) == p + is + 1); if (prRow.n_elem > 0) { arma::uvec pu(1); pu(0) = p; arma::mat thisPrior = priors.rows(prRow); arma::uvec theseCols = arma::conv_to::from(thisPrior.col(1)-1); arma::vec prHolder = arma::zeros(k); prHolder.elem(theseCols) = thisPrior.col(3); diagLambda.diag() = prHolder.elem(mispos); arma::mat wvar = arma::inv(diagLambda + solveSigma); prHolder.elem(theseCols) = thisPrior.col(2); arma::mat firstInner = solveSigma * arma::trans(imputations(pu, mispos)); arma::mat secondInner = prHolder.elem(mispos); arma::mat muMiss = wvar * (secondInner + firstInner); imputations(pu, mispos) = arma::trans(muMiss); hmcv(mispos, mispos) += wvar; } else { hmcv(mispos, mispos) += theta(mispos + 1, mispos + 1); } } xplay.rows(is, isp) = x.rows(is, isp) + imputations; } } hmcv += arma::trans(xplay) * xplay; music += arma::trans(arma::sum(xplay)); if (empri > 0) { simple = (music * arma::trans(music))/AMn; hmcv = (( (double)AMn/(AMn+empri+k+2)) * (hmcv - simple + hold)) + simple; } thetanew(0,0) = AMn; thetanew(0, arma::span(1,k)) = arma::trans(music); thetanew(arma::span(1,k), 0) = music; thetanew(arma::span(1,k), arma::span(1,k)) = hmcv; thetanew = thetanew/AMn; sweeppos.zeros(); sweeppos(0) = 1; sweep(thetanew, sweeppos); theta = arma::abs(thetanew - thetaold); thetaleft = arma::find(arma::trimatu(theta) > tol(0)); cvalue = thetaleft.n_elem; thetaold = thetanew; if (cvalue > iterHist(count-1,0) && count > 20) { monoFlag = 1; if (autopri(0) > 0) { if (arma::accu(iterHist(arma::span(count - 20, count - 1), 2)) > 3) { if (empri < (autopri(0) * (double)n)) { empri = empri + 0.01 * (double)n; } } } } else { monoFlag = 0; } etest = arma::eig_sym(thetaold(arma::span(1,k), arma::span(1,k))); if (arma::accu(etest <= 0)) { singFlag = 1; } else { singFlag = 0; } if (p2s > 1) { Rcpp::Rcout << "(" << cvalue << ")"; if (monoFlag == 1) { Rcpp::Rcout << "*"; } if (singFlag == 1) { Rcpp::Rcout << "!"; } } iterHist.resize(iterHist.n_rows+1, iterHist.n_cols); iterHist(count, 0) = cvalue; iterHist(count, 1) = monoFlag; iterHist(count, 2) = singFlag; if (allthetas(0) == 1) { thetaHolder.resize(thetaHolder.n_rows, thetaHolder.n_cols + 1); thetaHolder.col(count) = thetaold.elem(upperpos); } } iterHist.shed_row(0); if (p2s > 0) Rcpp::Rcout << std::endl; List z; if (allthetas(0) == 1) { thetaHolder.shed_row(0); z = List::create(Rcpp::Named("thetanew") = thetaHolder, Rcpp::Named("iter.hist") = iterHist); } else { z = List::create(Rcpp::Named("theta") = thetaold, Rcpp::Named("iter.hist") = iterHist); } return z ; } // void sweep(arma::mat& g, arma::vec m) { // int p = g.n_rows, h, j, i; // arma::uvec k = arma::find(m); // if (k.n_elem == p) { // g = -arma::inv(g); // } else { // for (h = 0; h < k.n_rows; h++) { // for (j = 0; j < p; j++) { // for (i = 0; i <= j; i++) { // if (i == k(h)) { // if (j == k(h)) { // g(i,j) = -1/g(i,j); // //Rcpp::Rcout << k(h) << ": " << "(i,j): (" <(k+1,k+1)))); arma::mat xplay = arma::zeros(AMn,k); arma::mat imputations(2,k); arma::mat theta(k+1, k+1); arma::mat junk(2,k); arma::mat Ci(k, k); arma::vec sweeppos(k+1); arma::uvec mispos; sweeppos.zeros(); int st, ss; if (arma::accu(mismat.row(0)) == 0) { st = 1; } else { st = 0; } if (st == 1) { xplay.rows(0,ii(1)-2) = x.rows(0,ii(1)-2); } if (Rf_isNull(prs)) { for (ss = st; ss < obsmat.n_rows; ss++) { is = ii(ss)-1; isp = ii(ss+1)-2; theta = thetaold; sweeppos.zeros(); sweeppos(arma::span(1,k)) = arma::trans(obsmat.row(ss)); sweep(theta, sweeppos); mispos = arma::find(mismat.row(ss)); Ci.zeros(k, k); Ci(mispos, mispos) = chol(theta(mispos+1, mispos + 1)); junk = Rcpp::rnorm((isp - is + 1)* k, 0, 1); junk.reshape(isp - is +1, k); junk = junk * Ci; imputations.zeros(); imputations.set_size(isp - is, k); imputations = x.rows(is, isp) * theta(arma::span(1,k), arma::span(1,k)); imputations.each_row() += theta(0, arma::span(1,k)); imputations = AMr1.rows(is, isp) % imputations; if (Rf_isNull(bdss)) { xplay.rows(is, isp) = x.rows(is, isp) + imputations + junk; } else { xplay.rows(is, isp) = resampler(x.rows(is, isp), Ci, imputations, mispos, bounds, maxsamples); } } } else { for (ss = st; ss < obsmat.n_rows; ss++) { is = ii(ss)-1; isp = ii(ss+1)-2; theta = thetaold; sweeppos.zeros(); sweeppos(arma::span(1,k)) = arma::trans(obsmat.row(ss)); sweep(theta, sweeppos); junk.zeros(isp - is + 1, k); junk = Rcpp::rnorm((isp - is + 1)* k, 0, 1); junk.reshape(isp - is +1, k); imputations.zeros(); imputations.set_size(isp - is, k); imputations = x.rows(is, isp) * theta(arma::span(1,k), arma::span(1,k)); imputations.each_row() += theta(0, arma::span(1,k)); imputations = AMr1.rows(is, isp) % imputations; mispos = arma::find(mismat.row(ss)); arma::mat solveSigma = arma::inv(theta(mispos + 1, mispos + 1)); arma::mat diagLambda = arma::zeros(mispos.n_elem, mispos.n_elem); for (int p = 0; p <= isp-is; p++) { arma::uvec prRow = arma::find(priors.col(0) == p + is + 1); Ci.zeros(k,k); if (prRow.n_elem > 0) { arma::uvec pu(1); pu(0) = p; arma::mat thisPrior = priors.rows(prRow); arma::uvec theseCols = arma::conv_to::from(thisPrior.col(1)-1); arma::vec prHolder = arma::zeros(k); prHolder.elem(theseCols) = thisPrior.col(3); diagLambda.diag() = prHolder.elem(mispos); arma::mat wvar = arma::inv(diagLambda + solveSigma); prHolder.elem(theseCols) = thisPrior.col(2); arma::mat muMiss = wvar * (prHolder.elem(mispos) + solveSigma * arma::trans(imputations(pu, mispos))); imputations(pu, mispos) = arma::trans(muMiss); Ci(mispos, mispos) = chol(wvar); } else { Ci(mispos, mispos) = chol(theta(mispos + 1, mispos + 1)); } junk.row(p) = junk.row(p) * Ci; if (Rf_isNull(bdss)) { xplay.row(is + p) = x.row(is + p) + imputations.row(p) + junk.row(p); } else { xplay.row(is + p) = resampler(x.row(is + p), Ci, imputations.row(p), mispos, bounds, maxsamples); } } } } return wrap(xplay); } arma::mat resampler(arma::mat x, arma::mat ci, arma::mat imps, arma::uvec mss, arma::mat bounds, int maxsample) { int nss = x.n_rows, k = x.n_cols; arma::mat ub(nss, k); arma::mat lb(nss, k); arma::umat utest; arma::umat ltest; ub.fill(arma::datum::inf); lb.fill(-arma::datum::inf); arma::mat xp = arma::zeros(nss, k); arma::mat junk = Rcpp::rnorm(nss * k, 0, 1); junk.reshape(nss, k); junk = junk * ci; int nb = 0, bdvar; for (int j = 0; j < bounds.n_rows; j++) { bdvar = (int) bounds(j,0) - 1; if (arma::accu(mss == bdvar)) { nb++; lb.col(bdvar) = arma::ones(nss) * bounds(j,1); ub.col(bdvar) = arma::ones(nss) * bounds(j,2); } } if (nb == 0) { return x + imps + junk; } //Rcpp::Rcout << ub << std::endl; int samp = 0; arma::colvec done = arma::zeros(nss); arma::colvec left = arma::ones(nss); arma::uvec finished; while ((arma::accu(left) > 0) & (samp < maxsample)) { samp++; utest = (imps + junk) > ub; ltest = (imps + junk) < lb; done += left % (arma::sum(utest + ltest, 1) == 0); finished = arma::find(left % (arma::sum(utest + ltest, 1) == 0)); left -= left % (arma::sum(utest + ltest, 1) == 0); ub.rows(finished).fill(arma::datum::inf); lb.rows(finished).fill(-arma::datum::inf); xp.rows(finished) = x.rows(finished) + imps.rows(finished) + junk.rows(finished); junk = Rcpp::rnorm(nss * k, 0, 1); junk.reshape(nss, k); junk = junk * ci; } if (arma::accu(left) > 0) { xp.rows(arma::find(left)) = x.rows(arma::find(left)) + imps.rows(arma::find(left)) + junk.rows(arma::find(left)); utest = (imps + junk) > ub; ltest = (imps + junk) < lb; arma::uvec ufails = arma::find(utest); arma::uvec lfails = arma::find(ltest); xp.elem(ufails) = ub.elem(ufails); xp.elem(lfails) = lb.elem(lfails); } return xp; } Amelia/src/init.c0000644000176200001440000000113413566651335013354 0ustar liggesusers#include #include #include // for NULL #include /* .Call calls */ extern SEXP ameliaImpute(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP emcore(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); static const R_CallMethodDef CallEntries[] = { {"ameliaImpute", (DL_FUNC) &ameliaImpute, 9}, {"emcore", (DL_FUNC) &emcore, 13}, {NULL, NULL, 0} }; void R_init_Amelia(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(dll, FALSE); } Amelia/src/em.h0000644000176200001440000000201713566651335013020 0ustar liggesusers#ifndef _Amelia_EMCORE_H #define _Amelia_EMCORE_H #include /* * note : RcppExport is an alias to `extern "C"` de ned by Rcpp. * * It gives C calling convention to the rcpp hello world function so that * it can be called from .Call in R. Otherwise, the C++ compiler mangles the * name of the function and .Call can't nd it. * * It is only useful to use RcppExport when the function is intended to be called * by .Call. See the thread http://thread.gmane.org/gmane.comp.lang.r.rcpp/649/focus=672 * on Rcpp-devel for a misuse of RcppExport */ RcppExport SEXP emcore(SEXP xs, SEXP AMr1s, SEXP os, SEXP ms, SEXP is, SEXP thetas, SEXP tols, SEXP emburn, SEXP p2ss, SEXP empris, SEXP autos, SEXP alls, SEXP prs) ; void sweep(arma::mat& g, arma::vec m); RcppExport SEXP ameliaImpute(SEXP xs, SEXP AMr1s, SEXP os, SEXP ms, SEXP ivec, SEXP thetas, SEXP prs, SEXP bdss, SEXP maxres); arma::mat resampler(arma::mat x, arma::mat ci, arma::mat imps, arma::uvec mss, arma::mat bounds, int maxsample); #endif Amelia/src/Makevars0000644000176200001440000000013613566651335013742 0ustar liggesusersPKG_LIBS = `$(R_HOME)/bin/Rscript -e "Rcpp:::LdFlags()"` $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) Amelia/src/Makevars.win0000644000176200001440000000030513566651335014534 0ustar liggesusers## Use the R HOME indirection to support installations of multiple R version PKG_LIBS = $(shell "${R_HOME}/bin${R_ARCH_BIN}/Rscript.exe" -e "Rcpp:::LdFlags()") $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) Amelia/vignettes/0000755000176200001440000000000013566651335013467 5ustar liggesusersAmelia/vignettes/numopts.png0000644000176200001440000003265112107457643015705 0ustar liggesusersPNG  IHDR 뽘 pHYs   OiCCPPhotoshop ICC profilexڝSgTS=BKKoR RB&*! 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Bb3LKpAy=z403# (--Eqq1z=Z[[ QQZZ+Wag Fގxܹsghoo0N $IBgggofǛQ)kfS)OGo+&ױh,XEYVƶYvE6MEujS0(o'-@ExԌY(~6tq|7M.C|0nL۵:X^D٧VaXi 744A"Bf+]hx.["zFMINgn /`V JpH-?8 z{NO!i8{lNgȦ$/ %4q $m2S8uUL 95>Umi#knl+L~ N:V?Vh$aիQZZgj?$&&bʕXz5f~f00:::3# 70f?~P`ܸqqbbb03$a͛q~]_~~C?+S !ׂOI!A`B(m!/Wfu xIENDB`Amelia/vignettes/index.shtml0000644000176200001440000001562712107457643015656 0ustar liggesusers Amelia Software Website

Authors: James Honaker, Gary King, Matthew Blackwell

Amelia II "multiply imputes" missing data in a single cross-section (such as a survey), from a time series (like variables collected for each year in a country), or from a time-series-cross-sectional data set (such as collected by years for each of several countries). Amelia II implements our bootstrapping-based algorithm that gives essentially the same answers as the standard IP or EMis approaches, is usually considerably faster than existing approaches and can handle many more variables. Unlike Amelia I and other statistically rigorous imputation software, it virtually never crashes (but please let us know if you find to the contrary!). The program also generalizes existing approaches by allowing for trends in time series across observations within a cross-sectional unit, as well as priors that allow experts to incorporate beliefs they have about the values of missing cells in their data. Amelia II also includes useful diagnostics of the fit of multiple imputation models. The program works from the R command line or via a graphical user interface that does not require users to know R.


Amelia is named after this famous missing person.

Multiple imputation involves imputing m values for each missing cell in your data matrix and creating m "completed" data sets. (Across these completed data sets, the observed values are the same, but the missing values are filled in with different imputations that reflect our uncertainty about the missing data.) After imputation, Amelia will then save the m data sets. You then apply whatever statistical method you would have used if there had been no missing values to each of the m data sets, and use a simple procedure to combine the results. Under normal circumstances, you only need to impute once and can then analyze the m imputed data sets as many times and for as many purposes as you wish. The advantage of Amelia is that it combines the comparative speed and ease-of-use of our algorithm with the power of multiple imputation, to let you focus on your substantive research questions rather than spending time developing complex application-specific models for nonresponse in each new data set. Unless the rate of missingness is exceptionally high, m=5 (the program default) will usually be adequate. Other methods of dealing with missing data, such as listwise deletion, mean substitution, or single imputation, are in common circumstances biased, inefficient, or both. When multiple imputation works properly, it fills in data in such a way as to not change any relationships in the data but which enables the inclusion of all the observed data in the partially missing rows.

Amelia II is a new program, and follows in the spirit with the same purpose as the first version of Amelia by James Honaker, Anne Joseph, Gary King, Kenneth Scheve, and Naunihal Singh.

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Ȩ$I$gהtegsU QfRaSSaX,SGr umyBVM Pk֮~ (g!6$cue8cBS>hA78Z?YV[qEKq[\L]О$b` ZŔEe&Wgbiy) H$٤!}6DIYm-jrl6C*=̩]D܄ A  Tp- (gzT*K۪\W Z{ن =y3*] %=s^Bާ (gks>g RLg ͧ[g Y@*2kls7@h4ղX]kYRa:KIF6P{&y}7l"}x(I`sz[ݧ'b@*Y@&6;g tlF..o1-KA#C5Q#.=]Q^_J뵥҃/*JsG4\8HF Gdj#sh@i -E_:MA9󙁖*pL;D3.4#O{ZB& ZgC3Jz   fc&v^O%92 lS)j AF\HcJT8lW6kJ*f.b=搟WFP| UcK6lP` H[gO6HfIbj$#3tz fNYAvSeJZE)q77r6n d[@A,U %ī7jK<ڤZܤ&j%.gI/iȯ\Fo fLgE O:/Q"Y-A9F>\VIb+I9ff^(o,FlC2FK V)pdžn/ 0APD!]3ć$PN5rTy~/OH ݶ+77rx^%͂jzSlY uHLfK2#+azX1z$*,vzA  k|eQ/'޾}֬YrpF2l!ʙ{R?F@|ˣ p /^;nj&\D/dړ/Ot\9p1МY?ح0 tӜ39)Oꫯ_C$Zg~"~3 sLS |ܕ`-oO*i|] | VVާmn>>S,[,$Zg>3Is~6ٓ{bh{ \ f0Va 4rHmIcbX-qMNg9鏽Ƭl/UR3P|d's9L5`9L4#|v]$Op`D0W&(,}$-x L͂JP Lt-q'eKK̭i׵3d7_ڒ$L{ qK/a9T+[a| [x'8 pYhNO^vLaGp8^#-xms56V >MIBH.nQdT,΢JdX,đ$⪀5QCD#g oQu ҥald lA9CA9v&m ,A:vG>>E9cw!ە[|'ىmn,7UrGَ.Y\xp_Mn\`',p\wjc6]-}QhP_ǝyvZ 5!S@%-Wgƕv[a޴k onnX'Ɲg䲴9[p;˓{rC(gWT6f* 0 D_"˥2[) 5O\i{QGe8#&/3| OnjfMkU{ڞKww8v02Hk:4v-Zg p-;Q h /C9@PJvv66s|hs/*iRmk=r tcBD #;fh's=3 B\[VZͤ?^۔]cN3 L_J !S'qtB8 hddT u,ʙ`R2A:ZYwvݘ]e h~cOPbəi4LtRb+N6fV(Xϯ\:WNRSۛl휹p BE0\rG1>Ud&ࡿ gZ4e<'S\ѿ` lx'bF *۲v{ b \ ޤ#P!o c;@odG܀QA/J9_j%8>頜!HpYaswW|P$h(rĸnҿ99<<#z5k?;;;]vҥk׮ݾ}j 'Ũ&H.M1R"(}1,o1 JTD >?8`XgK$>@hnnOOQaaǏ7n!>3ll*G$O!!5`Liefy13 |l˔q{'ldxZ2"L 9smεm> ,(C9CHI]h?nk0%Цӳ}v'};`A@dj#hb1mreFXrjsD20K\ AL*A @5@A #3APAPAPduv˟==0o> A$Jc g=,gA n,s]}j_¯w@8F9C&9>UWV:*Svm,hO∖^%M*lb. AC9C&:6~ee[]'/]_D6v8A F;@p- #7k6_ټl6{\oooXE7Z,_~l6 h34>I}YJJX, D}}}}}}.ҍ=ZPάVj ?,O IjEECF,/κ_~7nL&ƍwwP3&*ђ3f5ׇ} 52aһ',,|̘1ǏB,^D䬷,,,l̙{&Swww/Xz{{K[ǏQDc1}坜m޼jj1cƸ6~b6bXK)2DB;su$q Hș3 uT$M4kw1zQ(g E?,IENDB`Amelia/vignettes/amelia.bib0000644000176200001440000001134212107457643015372 0ustar liggesusers @STRING{ jasa = "Journal of the American Statistical Association"} @article{Efron94, author={Bradley Efron}, title={Missing data, imputation, and the bootstrap}, journal={Journal of the American Statistical Association}, volume={89}, year={1994}, pages={463-475}, month={June}, number={426} } @article{Lahlrl03, author={P. Lahlrl}, title={On the impact of boostrapping in survey sampling and small area estimation}, journal={Statistical Science}, volume= 18, year= 2003, pages={199-210}, number= 2 } @book{Rubin87, author={Donald B. Rubin}, title={Multiple imputation for nonresponse in surveys}, publisher={John Wiley \& Sons}, year={1987}, address={New York} } @article{Rubin94, author={Donald B. 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Democracy and trade policy in the developing countries}}, author = {Helen Milner and Keiko Kubota}, journal = {International Organization}, volume = {59}, number = {1}, pages = {107--143}, year = {2005} } @book{King89, author = {Gary King}, title = {Unifying political methodology: The likelihood theory of statistical inference}, publisher = {Michigan University Press}, year = 1989, address = {Ann Arbor} } @article{HonKin10, author = {James Honaker and Gary King}, title = {What to do about missing values in time series cross-section data}, journal = {American Journal of Political Science}, year = {2010}, volume = {54}, number = {2}, month = {April}, pages = {561--581}, note = {{http://gking.harvard.edu/files/abs/pr-abs.shtml}} } @article{KinHonJos01, author = {Gary King and James Honaker and Anne Joseph and Kenneth Scheve}, title = {Analyzing incomplete political science data: An alternative algorithm for multiple imputation}, journal = {American Political Science Review}, volume = 95, year = 2001, pages = {49--69}, month = {March}, number = 1 , note = {{http://gking.harvard.edu/files/abs/evil-abs.shtml}} } @article{KinTomWit00, author = {Gary King and Michael Tomz and Jason Wittenberg}, title = {Making the most of statistical analyses: Improving interpretation and presentation}, journal = {American Journal of Political Science}, volume = 44, year = 2000, pages = {341--355}, month = {April}, number = 2, note = {{http://gking.harvard.edu/files/abs/making-abs.shtml}} } @article{SchOls98, author={Joseph L. Schafer and Maren K. Olsen}, title={Multiple imputation for multivariate missing-data problems: A data analyst's perspective}, journal={Multivariate Behavioral Research}, volume={33}, year={1998}, pages={545-571}, number={4} } @article{DemLaiRub77, author={Arthur P. Dempster and N.M. Laird and D.B. Rubin}, title={Maximum likelihood estimation from incomplete data via the em algorithm}, journal={Journal of the Royal Statistical Society B}, volume={39}, year={1977}, pages={1-38} } @article{AbaGelLev08, author = {Kobi Abayomi and Andrew Gelman and Marc Levy}, title = {Diagnostics for multivariate imputations}, journal = {Applied Statistics}, volume = {57}, number = {3}, pages = {273--291}, year = {2008} } @misc{HonJosKin98, author = {James Honaker and Anne Joseph and Gary King and Kenneth Scheve and Naunihal Singh.}, title = {\pkg{AMELIA}: A program for missing data}, year = {1998-2002}, note = {http://gking.harvard.edu/amelia} } @Manual{R11, title = {\proglang{R}: A language and environment for statistical computing}, author = {{\proglang{R} Development Core Team}}, organization = {\proglang{R} Foundation for Statistical Computing}, address = {Vienna, Austria}, year = 2011, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org} }Amelia/vignettes/output-log.png0000644000176200001440000007676312107457643016333 0ustar liggesusersPNG  IHDR} pHYs   OiCCPPhotoshop ICC profilexڝSgTS=BKKoR RB&*! 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You may however distribute the LaTeX base system without %% such generated files. %% %% The list of all files belonging to the LaTeX base distribution is %% given in the file `manifest.txt'. See also `legal.txt' for additional %% information. %% %% The list of derived (unpacked) files belonging to the distribution %% and covered by LPPL is defined by the unpacking scripts (with %% extension .ins) which are part of the distribution. \ProvidesFile{utf8.def} [2004/02/09 v1.1b UTF-8 support for inputenc] \makeatletter \def\UTFviii@two@octets#1#2{\expandafter \UTFviii@defined\csname u8:#1\string#2\endcsname} \def\UTFviii@three@octets#1#2#3{\expandafter \UTFviii@defined\csname u8:#1\string#2\string#3\endcsname} \def\UTFviii@four@octets#1#2#3#4{\expandafter \UTFviii@defined\csname u8:#1\string#2\string#3\string#4\endcsname} \def\UTFviii@defined#1{% \ifx#1\relax \PackageError{inputenc}{Unicode char \string#1 not set up\space for use with LaTeX}\@eha \else\expandafter #1% \fi } \begingroup \catcode`\~13 \catcode`\"12 \def\UTFviii@loop{% \uccode`\~\count@ \uppercase\expandafter{\UTFviii@tmp}% \advance\count@\@ne \ifnum\count@<\@tempcnta \expandafter\UTFviii@loop \fi} \count@"C2 \@tempcnta"E0 \def\UTFviii@tmp{\xdef~{\noexpand\UTFviii@two@octets\string~}} \UTFviii@loop \count@"E0 \@tempcnta"F0 \def\UTFviii@tmp{\xdef~{\noexpand\UTFviii@three@octets\string~}} \UTFviii@loop \count@"F0 \@tempcnta"F4 \def\UTFviii@tmp{\xdef~{\noexpand\UTFviii@four@octets\string~}} \UTFviii@loop \endgroup \@inpenc@test \ifx\@begindocumenthook\@undefined \makeatother \endinput \fi \begingroup \catcode`\"=12 \catcode`\<=12 \catcode`\.=12 \catcode`\,=12 \catcode`\;=12 \catcode`\!=12 \catcode`\~=13 \gdef\DeclareUnicodeCharacter#1#2{% \count@"#1\relax \wlog{ \space\space defining Unicode char U+#1 (decimal \the\count@)}% \begingroup \parse@XML@charref \def\UTFviii@two@octets##1##2{\csname u8:##1\string##2\endcsname}% \def\UTFviii@three@octets##1##2##3{\csname u8:##1% \string##2\string##3\endcsname}% \def\UTFviii@four@octets##1##2##3##4{\csname u8:##1% \string##2\string##3\string##4\endcsname}% \expandafter\expandafter\expandafter \expandafter\expandafter\expandafter \expandafter \gdef\UTFviii@tmp{\IeC{#2}}% \endgroup } \gdef\parse@XML@charref{% \ifnum\count@<"A0\relax \PackageError{inputenc}{Cannot define Unicode char value < 00A0}\@eha \else\ifnum\count@<"800\relax \parse@UTFviii@a,% \parse@UTFviii@b C\UTFviii@two@octets.,% \else\ifnum\count@<"10000\relax \parse@UTFviii@a;% \parse@UTFviii@a,% \parse@UTFviii@b E\UTFviii@three@octets.{,;}% \else \parse@UTFviii@a;% \parse@UTFviii@a,% \parse@UTFviii@a!% \parse@UTFviii@b F\UTFviii@four@octets.{!,;}% \fi \fi \fi } \gdef\parse@UTFviii@a#1{% \@tempcnta\count@ \divide\count@ 64 \@tempcntb\count@ \multiply\count@ 64 \advance\@tempcnta-\count@ \advance\@tempcnta 128 \uccode`#1\@tempcnta \count@\@tempcntb} \gdef\parse@UTFviii@b#1#2#3#4{% \advance\count@ "#10\relax \uccode`#3\count@ \uppercase{\gdef\UTFviii@tmp{#2#3#4}}} \endgroup \@onlypreamble\DeclareUnicodeCharacter \@onlypreamble\parse@XML@charref \@onlypreamble\parse@UTFviii@a \@onlypreamble\parse@UTFviii@b \begingroup \def\cdp@elt#1#2#3#4{% \wlog{Now handling font encoding #1 ...}% \lowercase{% \InputIfFileExists{#1enc.dfu}} {\wlog{... processing UTF-8 mapping file for font encoding #1}}% {\wlog{... no UTF-8 mapping file for font encoding #1}}% } \cdp@list \endgroup \def\DeclareFontEncoding@#1#2#3{% \expandafter \ifx\csname T@#1\endcsname\relax \def\cdp@elt{\noexpand\cdp@elt}% \xdef\cdp@list{\cdp@list\cdp@elt{#1}% {\default@family}{\default@series}% {\default@shape}}% \expandafter\let\csname#1-cmd\endcsname\@changed@cmd \begingroup \wlog{Now handling font encoding #1 ...}% \lowercase{% \InputIfFileExists{#1enc.dfu}}% {\wlog{... processing UTF-8 mapping file for font encoding #1}}% {\wlog{... no UTF-8 mapping file for font encoding #1}}% \endgroup \else \@font@info{Redeclaring font encoding #1}% \fi \global\@namedef{T@#1}{#2}% \global\@namedef{M@#1}{\default@M#3}% \xdef\LastDeclaredEncoding{#1}% } \DeclareUnicodeCharacter{00A9}{\textcopyright} \DeclareUnicodeCharacter{00AA}{\textordfeminine} \DeclareUnicodeCharacter{00AE}{\textregistered} \DeclareUnicodeCharacter{00BA}{\textordmasculine} \DeclareUnicodeCharacter{02C6}{\textasciicircum} \DeclareUnicodeCharacter{02CA}{\textasciitilde} \DeclareUnicodeCharacter{200C}{\textcompwordmark} \DeclareUnicodeCharacter{2026}{\textellipsis} \DeclareUnicodeCharacter{2122}{\texttrademark} \DeclareUnicodeCharacter{2423}{\textvisiblespace} \endinput %% %% End of file `utf8.def'. 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Respondents do not answer every question, countries do not collect statistics every year, archives are incomplete, subjects drop out of panels. Most statistical analysis methods, however, assume the absence of missing data, and are only able to include observations for which every variable is measured. \AmeliaII\ allows users to impute (``fill in'' or rectangularize) incomplete data sets so that analyses which require complete observations can appropriately use all the information present in a dataset with missingness, and avoid the biases, inefficiencies, and incorrect uncertainty estimates that can result from dropping all partially observed observations from the analysis. \AmeliaII\ performs \emph{multiple imputation}, a general-purpose approach to data with missing values. Multiple imputation has been shown to reduce bias and increase efficiency compared to listwise deletion. Furthermore, ad-hoc methods of imputation, such as mean imputation, can lead to serious biases in variances and covariances. Unfortunately, creating multiple imputations can be a burdensome process due to the technical nature of algorithms involved. \Amelia\ provides users with a simple way to create and implement an imputation model, generate imputed datasets, and check its fit using diagnostics. The \AmeliaII\ program goes several significant steps beyond the capabilities of the first version of \Amelia\ \citep*{HonJosKin98}. For one, the bootstrap-based EMB algorithm included in \AmeliaII\ can impute many more variables, with many more observations, in much less time. The great simplicity and power of the EMB algorithm made it possible to write \AmeliaII\ so that it virtually never crashes --- which to our knowledge makes it unique among all existing multiple imputation software --- and is much faster than the alternatives too. \AmeliaII\ also has features to make valid and much more accurate imputations for cross-sectional, time-series, and time-series-cross-section data, and allows the incorporation of observation and data-matrix-cell level prior information. In addition to all of this, \AmeliaII\ provides many diagnostic functions that help users check the validity of their imputation model. This software implements the ideas developed in \citet*{HonKin10}. \section[What Amelia Does]{What \Amelia\ Does} \label{sec:what} Multiple imputation involves imputing $m$ values for each missing cell in your data matrix and creating $m$ ``completed'' data sets. Across these completed data sets, the observed values are the same, but the missing values are filled in with a distribution of imputations that reflect the uncertainty about the missing data. After imputation with \AmeliaII's EMB algorithm, you can apply whatever statistical method you would have used if there had been no missing values to each of the $m$ data sets, and use a simple procedure, described below, to combine the results\footnote{You can combine the results automatically by doing your data analyses within Zelig for R, or within Clarify for Stata; see \url{http://gking.harvard.edu/stats.shtml}.}. Under normal circumstances, you only need to impute once and can then analyze the $m$ imputed data sets as many times and for as many purposes as you wish. The advantage of \AmeliaII\ is that it combines the comparative speed and ease-of-use of our algorithm with the power of multiple imputation, to let you focus on your substantive research questions rather than spending time developing complex application-specific models for nonresponse in each new data set. Unless the rate of missingness is very high, $m = 5$ (the program default) is probably adequate. \subsection{Assumptions} The imputation model in \AmeliaII\ assumes that the complete data (that is, both observed and unobserved) are multivariate normal. If we denote the $(n \times k)$ dataset as $D$ (with observed part $D^{\obs}$ and unobserved part $D^{\mis}$), then this assumption is \begin{equation} \label{eq:norm} D \sim \mathcal{N}_k(\mu, \Sigma), \end{equation} which states that $D$ has a multivariate normal distribution with mean vector $\mu$ and covariance matrix $\Sigma$. The multivariate normal distribution is often a crude approximation to the true distribution of the data, yet there is evidence that this model works as well as other, more complicated models even in the face of categorical or mixed data \citep[see][]{Schafer97, SchOls98}. Furthermore, transformations of many types of variables can often make this normality assumption more plausible (see \ref{sec:trans} for more information on how to implement this in \Amelia). The essential problem of imputation is that we only observe $D^{\obs}$, not the entirety of $D$. In order to gain traction, we need to make the usual assumption in multiple imputation that the data are \emph{missing at random} (MAR). This assumption means that the pattern of missingness only depends on the observed data $D^{\obs}$, not the unobserved data $D^{\mis}$. Let $M$ to be the missingness matrix, with cells $m_{ij} = 1$ if $d_{ij} \in D^{\mis}$ and $m_{ij} = 0$ otherwise. Put simply, $M$ is a matrix that indicates whether or not a cell is missing in the data. With this, we can define the MAR assumption as \begin{equation} \label{eq:mar} p(M|D) = p(M|D^{\obs}). \end{equation} Note that MAR includes the case when missing values are created randomly by, say, coin flips, but it also includes many more sophisticated missingness models. When missingness is not dependent on the data at all, we say that the data are \emph{missing completely at random} (MCAR). \Amelia\ requires both the multivariate normality and the MAR assumption (or the simpler special case of MCAR). Note that the MAR assumption can be made more plausible by including additional variables in the dataset $D$ in the imputation dataset than just those eventually envisioned to be used in the analysis model. \subsection{Algorithm} In multiple imputation, we are concerned with the complete-data parameters, $\theta = (\mu, \Sigma)$. When writing down a model of the data, it is clear that our observed data is actually $D^{\obs}$ and $M$, the missingness matrix. Thus, the likelihood of our observed data is $p(D^{\obs}, M|\theta)$. Using the MAR assumption\footnote{There is an additional assumption hidden here that $M$ does not depend on the complete-data parameters.}, we can break this up, \begin{align} p(D^{\obs},M|\theta) = p(M|D^{\obs})p(D^{\obs}|\theta). \end{align} As we only care about inference on the complete data parameters, we can write the likelihood as \begin{align} L(\theta|D^{\obs}) &\propto p(D^{\obs}|\theta), \end{align} which we can rewrite using the law of iterated expectations as \begin{align} p(D^{\obs}|\theta) &= \int p(D|\theta) dD^{\mis}. \end{align} With this likelihood and a flat prior on $\theta$, we can see that the posterior is \begin{equation} p(\theta | D^{\obs}) \propto p(D^{\obs}|\theta) = \int p(D|\theta) dD^{\mis}. \end{equation} The main computational difficulty in the analysis of incomplete data is taking draws from this posterior. The EM algorithm \citep*{DemLaiRub77} is a simple computational approach to finding the mode of the posterior. Our EMB algorithm combines the classic EM algorithm with a bootstrap approach to take draws from this posterior. For each draw, we bootstrap the data to simulate estimation uncertainty and then run the EM algorithm to find the mode of the posterior for the bootstrapped data, which gives us fundamental uncertainty too (see \citet{HonKin10} for details of the EMB algorithm). Once we have draws of the posterior of the complete-data parameters, we make imputations by drawing values of $D^{\mis}$ from its distribution conditional on $D^{\obs}$ and the draws of $\theta$, which is a linear regression with parameters that can be calculated directly from $\theta$. \subsection{Analysis} In order to combine the results across $m$ data sets, first decide on the quantity of interest to compute, such as a univariate mean, regression coefficient, predicted probability, or first difference. Then, the easiest way is to draw $1/m$ simulations of $q$ from each of the $m$ data sets, combine them into one set of $m$ simulations, and then to use the standard simulation-based methods of interpretation common for single data sets \citep{KinTomWit00}. Alternatively, you can combine directly and use as the multiple imputation estimate of this parameter, $\bar{q}$, the average of the $m$ separate estimates, $q_j$ $(j=1,\dots,m)$: \begin{equation} \bar{q}=\frac{1}{m}\sum^{m}_{j=1}q_j. \end{equation} The variance of the point estimate is the average of the estimated variances from \emph{within} each completed data set, plus the sample variance in the point estimates \emph{across} the data sets (multiplied by a factor that corrects for the bias because $m<\infty$). Let $SE(q_j)^2$ denote the estimated variance (squared standard error) of $q_j$ from the data set $j$, and $S^{2}_{q}=\Sigma^{m}_{j=1}(q_j-\bar{q})^2/(m-1)$ be the sample variance across the $m$ point estimates. The standard error of the multiple imputation point estimate is the square root of \begin{equation} SE(q)^2=\frac{1}{m}\sum^{m}_{j=1}SE(q_j)^2+S^2_q(1+1/m). \end{equation} \begin{figure} \centering \begin{tikzpicture} [inner sep = 2.5mm, missdata/.style={rectangle, draw=red!50, fill=red!20, thick}, impdata/.style={rectangle, draw=blue!50, fill=blue!20, thick}, results/.style= {circle, draw=blue!50, fill=blue!20, thick}] \node (odata) at (3,3) [missdata] {}; \node [red!80,right] at (5.25,3) {incomplete data}; \node (boot1) at (1,1) [missdata] {} edge [<-, bend left=40] (odata); \node (boot2) at (2,1) [missdata] {} edge [<-, bend left=20] (odata); \node (boot3) at (3,1) [missdata] {} edge [<-] (odata); \node (boot4) at (4,1) [missdata] {} edge [<-, bend right=20] (odata); \node (boot5) at (5,1) [missdata] {} edge [<-, bend right=40] (odata); %% add "random question marks" \node[red!50!black] at (2.95,3.1) {\tiny ?}; \node[red!50!black] at (2.85,2.9) {\tiny ?}; \node[red!50!black] at (3.15,2.95) {\tiny ?}; \node[red!50!black] at (2.85,1.1) {\tiny ?}; \node[red!50!black] at (2.95,0.9) {\tiny ?}; \node[red!50!black] at (3.15,1.1) {\tiny ?}; \node[red!50!black] at (0.85,0.9) {\tiny ?}; \node[red!50!black] at (1.15,0.95) {\tiny ?}; \node[red!50!black] at (1.85,1.1) {\tiny ?}; \node[red!50!black] at (1.95,0.9) {\tiny ?}; \node[red!50!black] at (3.85,1.1) {\tiny ?}; \node[red!50!black] at (4.95,0.9) {\tiny ?}; \node[red!50!black] at (5.15,1.1) {\tiny ?}; \node [black!80,right] at (5.25,2) {bootstrap}; \node [red!80, right] at (5.25, 1) {bootstrapped data}; \node (imp1) at (1,0) [impdata] {} edge [<-] (boot1); \node (imp2) at (2,0) [impdata] {} edge [<-] (boot2); \node (imp3) at (3,0) [impdata] {} edge [<-] (boot3); \node (imp4) at (4,0) [impdata] {} edge [<-] (boot4); \node (imp5) at (5,0) [impdata] {} edge [<-] (boot5); \node [blue!80,right] at (5.25,0) {imputed datasets}; \node [black!80, right] at (5.25, 0.5) {EM}; \node (res1) at (1,-1) [results] {} edge [<-] (imp1); \node (res2) at (2,-1) [results] {} edge [<-] (imp2); \node (res3) at (3,-1) [results] {} edge [<-] (imp3); \node (res4) at (4,-1) [results] {} edge [<-] (imp4); \node (res5) at (5,-1) [results] {} edge [<-] (imp5); \node [black!80, right] at (5.25, -0.5) {analysis}; \node [blue!80, right] at (5.25, -1) {separate results}; \node[circle, draw=green!50!black!50, fill=green!20, thick] at (3,-3) {} edge [<-, bend right=40] (res5) edge [<-, bend left=40] (res1) edge [<-, bend right=20] (res4) edge [<-, bend left=20] (res2) edge [<-] (res3); \node [black!80, right] at (5.25, -2) {combination}; \node [green!80!black!80, right] at (5.25, -3) { final results}; \end{tikzpicture} \caption{A schematic of our approach to multiple imputation with the EMB algorithm. } \end{figure} \section[Versions of Amelia]{Versions of \Amelia\ } \label{sec:versions} Two versions of \AmeliaII\ are available, each with its own advantages and drawbacks, but both of which use the same underlying code and algorithms. First, \AmeliaII\ exists as a package for the \R\ statistical software package. Users can utilize their knowledge of the \R\ language to run \AmeliaII\ at the command line or to create scripts that will run \AmeliaII\ and preserve the commands for future use. Alternatively, you may prefer \AmeliaView, where an interactive Graphical User Interface (GUI) allows you to set options and run \Amelia\ without any knowledge of the \R\ programming language. Both versions of \AmeliaII\ are available on the Windows, Mac OS X, and Linux platforms and \AmeliaII\ for \R\ runs in any environment that \R\ can. All versions of \Amelia\ require the \R\ software, which is freely available at \url{http://www.r-project.org/}. Before installing \AmeliaII, you must have installed \R\ version 2.1.0 or higher, which is freely available at \url{http://www.r-project.org/}. \subsection{Installation and Updates from R} \label{sec:install} To install the \Amelia\ package on any platform, simply type the following at the \R\ command prompt, \begin{verbatim} > install.packages("Amelia") \end{verbatim} and \R\ will automatically install the package to your system from CRAN. If you wish to use the most current beta version of \Amelia\, feel free to install the test version, \begin{verbatim} > install.packages("Amelia", repos = "http://gking.harvard.edu") \end{verbatim} In order to keep your copy of \Amelia\ completely up to date, you should use the command \begin{verbatim} > update.packages() \end{verbatim} \subsection[Installation in Windows of AmeliaView as a Standalone Program]{Installation in Windows of \AmeliaView\ as a Standalone Program} \label{sec:win-install} To install a standalone version of \AmeliaView\ in the Windows environment, simply download the installer \texttt{setup.exe} from \url{http://gking.harvard.edu/amelia/} and run it. The installer will ask you to choose a location to install \AmeliaII. If you have installed \R\ with the default options, \AmeliaII\ will automatically find the location of \R. If the installer cannot find \R, it will ask you to locate the directory of the most current version of \R. Make sure you choose the directory name that includes the version number of \R\ (e.g. C:/Program Files/R/R-2.9.0) and contains a subdirectory named \texttt{bin}. The installer will also put shortcuts on your Desktop and Start Menu. Even users familiar with the \R\ language may find it useful to utilize \AmeliaView\ to set options on variables, change arguments, or run diagnostics. From the command line, \AmeliaView\ can be brought up with the call: \begin{verbatim} > library(Amelia) > AmeliaView() \end{verbatim} \subsection{Linux (local installation)} \label{sec:lin-install} Installing \Amelia\ on a Linux system is slightly more complicated due to user permissions. If you are running \R\ with root access, you can simply run the above installation procedure. If you do not have root access, you can install \Amelia\ to a local library. First, create a local directory to house the packages, \begin{verbatim} w4:mblackwell [~]: mkdir ~/myrlibrary \end{verbatim} and then, in an \R\ session, install the package directing \R\ to this location: \begin{verbatim} > install.packages("Amelia", lib = "~/myrlibrary") \end{verbatim} Once this is complete you need to edit or create your \R\ profile. Locate or create \texttt{\~/.Rprofile} in your home directory and add this line: \begin{verbatim} .libPath("~/myrlibrary") \end{verbatim} This will add your local library to the list of library paths that \R\ searches in when you load libraries. Linux users can use \AmeliaView\ in the same way as Windows users of \Amelia\ for \R. From the command line, \AmeliaView\ can be brought up with the call: \begin{verbatim} > AmeliaView() \end{verbatim} \section{A User's Guide} \label{sec:guide} \subsection{Data and Initial Results} We now demonstrate how to use \Amelia\ using data from \citet{MilKub05} which studies the effect of democracy on trade policy. For the purposes of this user's guide, we will use a subset restricted to nine developing countries in Asia from 1980 to 1999\footnote{We have artificially added some missingness to these data for presentational purposes. You can access the original data at \url{http://www.princeton.edu/~hmilner/Research.htm}}. This dataset includes 9 variables: year (\code{year}), country (\code{country}), average tariff rates (\code{tariff}), Polity IV score\footnote{The Polity score is a number between -10 and 10 indicating how democratic a country is. A fully autocratic country would be a -10 while a fully democratic country would be 1 10.} (\code{polity}), total population (\code{pop}), gross domestic product per capita (\code{gdp.pc}), gross international reserves (\code{intresmi}), a dummy variable signifying whether the country had signed an IMF agreement in that year (\code{signed}), a measure of financial openness (\code{fivop}), and a measure of US hegemony\footnote{This measure of US hegemony is the US imports and exports as a percent of the world total imports and exports.} (\code{usheg}). These variables correspond to the variables used in the analysis model of \citet{MilKub05} in table 2. <>= options("digits"=4) options("width"=70) options("show.signif.stars" = FALSE) set.seed(12345) @ We first load the \Amelia\ and the data: <>= require(Amelia) data(freetrade) @ We can check the summary statistics of the data to see that there is missingness on many of the variables: <<>= summary(freetrade) @ In the presence of missing data, most statistical packages use \emph{listwise deletion}, which removes any row that contains a missing value from the analysis. Using the base model of \citet{MilKub05} table 2, we run a simple linear model in \R, which uses listwise deletion: <>= summary(lm(tariff ~ polity + pop + gdp.pc + year + country, data = freetrade)) @ Note that 60 of the 171 original observations are deleted due to missingness. These observations, however, are partially observed, and contain valuable information about the relationships between those variables which are present in the partially completed observations. Multiple imputation will help us retrieve that information and make better, more efficient, inferences. \subsection{Multiple Imputation} When performing multiple imputation, the first step is to identify the variables to include in the imputation model. It is crucial to include at least as much information as will be used in the analysis model. That is, any variable that will be in the analysis model should also be in the imputation model. This includes any transformations or interactions of variables that will appear in the analysis model. In fact, it is often useful to add more information to the imputation model than will be present when the analysis is run. Since imputation is predictive, any variables that would increase predictive power should be included in the model, even if including them in the analysis model would produce bias in estimating a causal effect (such as for post-treatment variables) or collinearity would preclude determining which variable had a relationship with the dependent variable (such as including multiple alternate measures of GDP). In our case, we include all the variables in \code{freetrade} in the imputation model, even though our analysis model focuses on \code{polity}, \code{pop} and \code{gdp.pc}\footnote{Note that this specification does not utilize time or spatial data yet. The \texttt{ts} and \texttt{cs} arguments only have force when we also include \texttt{polytime} or \texttt{intercs}, discussed in section \ref{sec:tscs}}. To create multiple imputations in \Amelia, we can simply run <>= a.out <- amelia(freetrade, m = 5, ts = "year", cs = "country") a.out @ Note that our example dataset is deliberately small both in variables and in cross-sectional elements. Typical datasets may often have hundreds or possibly a couple thousand steps to the EM algorithm. Long chains should remind the analyst to consider whether transformations of the variables would more closely fit the multivariate normal assumptions of the model (correct but omitted transformations will shorten the number of steps and improve the fit of the imputations), but do not necessarily denote problems with the imputation model. The output gives some information about how the algorithm ran. Each of the imputed datasets is now in the list \code{a.out\$imputations}. Thus, we could plot a histogram of the \code{tariff} variable from the 3rd imputation, <>= hist(a.out$imputations[[3]]$tariff, col="grey", border="white") @ %$ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,1)))) @ \begin{figure} \begin{center} <>= <> @ \caption{Histogram of the \texttt{tariff} variable from the 3rd imputed dataset.} \label{fig:hist1} \end{center} \end{figure} \subsubsection{Saving imputed datasets} \label{sec:saving} If you need to save your imputed datasets, one direct method is to save the output list from \code{amelia}, \begin{verbatim} > save(a.out, file = "imputations.RData") \end{verbatim} As in the previous example, the \emph{i}th imputed datasets can be retrieved from this list as \code{a.out\$imputations[[i]]}. In addition, you can save each of the imputed datasets to its own file using the \code{write.amelia} command, \begin{verbatim} > write.amelia(obj=a.out, file.stem = "outdata") \end{verbatim} This will create one comma-separated value file for each imputed dataset in the following manner: \begin{verbatim} outdata1.csv outdata2.csv outdata3.csv outdata4.csv outdata5.csv \end{verbatim} The \code{write.amelia} function can also save files in tab-delimited and Stata (\code{.dta}) file formats. For instance, to save Stata files, simply change the \code{format} argument to \code{"dta"}, \begin{verbatim} > write.amelia(obj=a.out, file.stem = "outdata", format = "dta") \end{verbatim} Additionally, \code{write.amelia} can create a ``stacked'' version of the imputed dataset which stacks each imputed dataset on top of one another. This can be done by setting the \code{separate} argument to \code{FALSE}. The resulting matrix is of size $(N \cdot m) \times p$ if the original dataset is excluded (\code{orig.data = FALSE}) and of size $(N \cdot (m+1))\times p$ if it is included (\code{orig.data = TRUE}). The stacked dataset will include a variable (set with \code{impvar}) that indicates to which imputed dataset the observation belongs. See Section~\ref{sec:analysis} for a description of how to use this stacked dataset with the \code{mi} commands in Stata. \subsubsection[Combining Multiple Amelia Runs]{Combining Multiple \Amelia\ Runs} The EMB algorithm is what computer scientists call \emph{embarrassingly parallel}, meaning that it is simple to separate each imputation into parallel processes. With \Amelia\ it is simple to run subsets of the imputations on different machines and then combine them after the imputation for use in analysis model. This allows for a huge increase in the speed of the algorithm. Output lists from different \Amelia\ runs can be combined together into a new list. For instance, suppose that we wanted to add another ten imputed datasets to our earlier call to \code{amelia}. First, run the function to get these additional imputations, <<>>= a.out.more <- amelia(freetrade, m = 10, ts = "year", cs = "country", p2s=0) a.out.more @ then combine this output with our original output using the \code{ameliabind} function, <<>>= a.out.more <- ameliabind(a.out, a.out.more) a.out.more @ This function binds the two outputs into the same output so that you can pass the combined imputations easily to analysis models and diagnostics. Note that \code{a.out.more} now has a total of 15 imputations. A simple way to execute a parallel processing scheme with \Amelia\ would be to run \code{amelia} with \code{m} set to 1 on $m$ different machines or processors, save each output using the \code{save} function, load them all on the same \R\ session using \code{load} command and then combine them using \code{ameliabind}. In order to do this, however, make sure to name each of the outputs a different name so that they do not overwrite each other when loading into the same \R\ session. Also, some parallel environments will dump all generated files into a common directory, where they may overwrite each other. If it is convenient in a parallel environment to run a large number of \code{amelia} calls from a single piece of code, one useful way to avoid overwriting is to create the \code{file.stem} with a random suffix. For example: \begin{verbatim} > b<-round(runif(1,min=1111,max=9999)) > random.name<-paste("am",b,sep="") > amelia <- write.amelia(obj=a.out, file.stem = random.name) \end{verbatim} \subsubsection{Screen Output} Screen output can be adjusted with the ``print to screen'' argument, \code{p2s}. At a value of 0, no screen printing will occur. This may be useful in large jobs or simulations where a very large number of imputation models may be required. The default value of 1, lists each bootstrap, and displays the number of iterations required to reach convergence in that bootstrapped dataset. The value of 2 gives more thorough screen output, including, at each iteration, the number of parameters that have significantly changed since the last iteration. This may be useful when the EM chain length is very long, as it can provide an intuition for many parameters still need to converge in the EM chain, and a sense of the time remaining. However, it is worth noting that the last several parameters can often take a significant fraction of the total number of iterations to converge. Setting \code{p2s} to 2 will also generate information on how EM algorithm is behaving, such as a \code{!} when the current estimated complete data covariance matrix is not invertible and a \code{*} when the likelihood has not monotonically increased in that step. Having many of these two symbols in the screen output is an indication of a problematic imputation model\footnote{Problems of non-invertible matrices often mean that current guess for the covariance matrix is singular. This is a sign that there may be two highly correlated variables in the model. One way to resolve is to use a ridge prior (see \ref{sec:prior})}. An example of the output when \code{p2s} is 2 would be <>= amelia(freetrade, m = 1, ts = "year", cs = "country", p2s = 2) @ \subsection{Parallel Imputation Using Multicore CPUs} \label{sec:parallel} Each imputation in the above EMB algorithm is completely independent of any other imputation, a property called embarrassingly parallel. This type of approach can take advantage of the multiple -core infrastructure of modern CPUs. Each core in a multi-core processor can execute independent operations in parallel. \Amelia\ can utilize this parallel processing internally \emph{via} the \code{parallel} and the \code{ncpus} arguments. The \code{parallel} argument sets the parallel processing backend, either with \code{"multicore"} or \code{"snow"} (or \code{"no"} for no parallel processing). The \code{"multicore"} backend is not available on Windows systems, but tends to be quicker at parallel processing. On a Windows system, the \code{"snow"} backend provides parallel processing through a cluster of worker processes across the CPUs. You can set the default for this argument using the \code{"amelia.parallel"} option. This allows you to run Amelia in parallel as the default for an entire R session without setting arguments in the \code{amelia} call. For each of the parallel backends, \Amelia\ requires a number of CPUs to use in parallel. This can be set using the \code{ncpus} argument. It can be higher than the number of physical cores in the system if hyperthreading or other technologies are available. You can use the \code{parallel::detectCores} function to determine how many cores are available on your machine. The default for this argument can be set using the \code{"amelia.ncpus"} option. On Unix-alike systems (such as Mac OS X and Linux distributions), the \code{"multicore"} backend automatically sets up and stops the parallel workers by forking the process. On Windows, the \code{"snow"} backend requires more attention. \Amelia\ will attempt to create a parallel cluster of worker processes (since Windows systems cannot fork a process) and will stop this cluster after the imputations are complete. Alternatively, \Amelia\ also has a \code{cl} argument, which accepts a predefined cluster made using the \code{parallel::makePSOCKcluster}. For more information about parallel processing in R, see the documentation for the \pkg{parallel} package that ships along with R. \subsection{Imputation-improving Transformations} \label{sec:trans} Social science data commonly includes variables that fail to fit to a multivariate normal distribution. Indeed, numerous models have been introduced specifically to deal with the problems they present. As it turns out, much evidence in the literature (discussed in \citealt{KinHonJos01}) indicates that the multivariate normal model used in \Amelia\ usually works well for the imputation stage even when discrete or non-normal variables are included and when the analysis stage involves these limited dependent variable models. Nevertheless, \Amelia\ includes some limited capacity to deal directly with ordinal and nominal variables and to modify variables that require other transformations. In general nominal and log transform variables should be declared to \Amelia, whereas ordinal (including dichotomous) variables often need not be, as described below. (For harder cases, see \citep{Schafer97}, for specialized MCMC-based imputation models for discrete variables.)\nocite{KinHonJos01} Although these transformations are taken internally on these variables to better fit the data to the multivariate normal assumptions of the imputation model, all the imputations that are created will be returned in the original untransformed form of the data. If the user has already performed transformations on their data (such as by taking a log or square root prior to feeding the data to \code{amelia}) these do not need to be declared, as that would result in the transformation occurring \emph{doubly} in the imputation model. The fully imputed data sets that are returned will always be in the form of the original data that is passed to the \code{amelia} routine. \subsubsection{Ordinal} \label{sec:ord} In much statistical research, researchers treat independent ordinal (including dichotomous) variables as if they were really continuous. If the analysis model to be employed is of this type, then nothing extra is required of the of the imputation model. Users are advised to allow \Amelia\ to impute non-integer values for any missing data, and to use these non-integer values in their analysis. Sometimes this makes sense, and sometimes this defies intuition. One particular imputation of 2.35 for a missing value on a seven point scale carries the intuition that the respondent is between a 2 and a 3 and most probably would have responded 2 had the data been observed. This is easier to accept than an imputation of 0.79 for a dichotomous variable where a zero represents a male and a one represents a female respondent. However, in both cases the non-integer imputations carry more information about the underlying distribution than would be carried if we were to force the imputations to be integers. Thus whenever the analysis model permits, missing ordinal observations should be allowed to take on continuously valued imputations. In the \code{freetrade} data, one such ordinal variable is \code{polity} which ranges from -10 (full autocracy) to 10 (full democracy). If we tabulate this variable from one of the imputed datasets, <>= table(a.out$imputations[[3]]$polity) @ %$ we can see that there is one imputation between -4 and -3 and one imputation between 6 and 7. Again, the interpretation of these values is rather straightforward even if they are not strictly in the coding of the original Polity data. Often, however, analysis models require some variables to be strictly ordinal, as for example, when the dependent variable will be modeled in a logistical or Poisson regression. Imputations for variables set as ordinal are created by taking the continuously valued imputation and using an appropriately scaled version of this as the probability of success in a binomial distribution. The draw from this binomial distribution is then translated back into one of the ordinal categories. For our data we can simply add \code{polity} to the \code{ords} argument: <>= a.out1 <- amelia(freetrade, m = 5, ts = "year", cs = "country", ords = "polity", p2s = 0) table(a.out1$imputations[[3]]$polity) @ Now, we can see that all of the imputations fall into one of the original polity categories. \subsubsection{Nominal} \label{sec:nom} Nominal variables\footnote{Dichotomous (two category) variables are a special case of nominal variables. For these variables, the nominal and ordinal methods of transformation in \Amelia\ agree.} must be treated quite differently than ordinal variables. Any multinomial variables in the data set (such as religion coded 1 for Catholic, 2 for Jewish, and 3 for Protestant) must be specified to \Amelia. In our \code{freetrade} dataset, we have \code{signed} which is 1 if a country signed an IMF agreement in that year and 0 if it did not. Of course, our first imputation did not limit the imputations to these two categories <<>>= table(a.out1$imputations[[3]]$signed) @ In order to fix this for a $ p$-category multinomial variable,\Amelia\ will determine $ p$ (as long as your data contain at least one value in each category), and substitute $ p-1$ binary variables to specify each possible category. These new $ p-1$ variables will be treated as the other variables in the multivariate normal imputation method chosen, and receive continuous imputations. These continuously valued imputations will then be appropriately scaled into probabilities for each of the $ p$ possible categories, and one of these categories will be drawn, where upon the original $ p$-category multinomial variable will be reconstructed and returned to the user. Thus all imputations will be appropriately multinomial. For our data we can simply add \code{signed} to the \code{noms} argument: <>= a.out2 <- amelia(freetrade, m = 5, ts = "year", cs = "country", noms = "signed", p2s = 0) table(a.out2$imputations[[3]]$signed) @ Note that \Amelia\ can only fit imputations into categories that exist in the original data. Thus, if there was a third category of signed, say 2, that corresponded to a different kind of IMF agreement, but it never occurred in the original data, \Amelia\ could not match imputations to it. Since \Amelia\ properly treats a $ p$-category multinomial variable as $ p-1$ variables, one should understand the number of parameters that are quickly accumulating if many multinomial variables are being used. If the square of the number of real and constructed variables is large relative to the number of observations, it is useful to use a ridge prior as in section \ref{sec:prior}. \subsubsection{Natural Log} \label{sec:log} If one of your variables is heavily skewed or has outliers that may alter the imputation in an unwanted way, you can use a natural logarithm transformation of that variable in order to normalize its distribution. This transformed distribution helps \Amelia\ to avoid imputing values that depend too heavily on outlying data points. Log transformations are common in expenditure and economic variables where we have strong beliefs that the marginal relationship between two variables decreases as we move across the range. For instance, figure \ref{fig:logshist} show the \code{tariff} variable clearly has positive (or, right) skew while its natural log transformation has a roughly normal distribution. <>= hist(freetrade$tariff, col="grey", border="white") hist(log(freetrade$tariff), col="grey", border="white") @ %$ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,2)))) @ \begin{figure} \begin{center} <>= <> @ \caption{Histogram of \texttt{tariff} and \texttt{log(tariff)}.} \label{fig:logshist} \end{center} \end{figure} <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,1)))) @ \subsubsection{Square Root} \label{sec:sqrt} Event count data is often heavily skewed and has nonlinear relationships with other variables. One common transformation to tailor the linear model to count data is to take the square roots of the counts. This is a transformation that can be set as an option in \Amelia. \subsubsection{Logistic} \label{sec:lgstc} Proportional data is sharply bounded between 0 and 1. A logistic transformation is one possible option in \Amelia\ to make the distribution symmetric and relatively unbounded. \subsection{Identification Variables} \label{sec:idvars} Datasets often contain identification variables, such as country names, respondent numbers, or other identification numbers, codes or abbreviations. Sometimes these are text and sometimes these are numeric. Often it is not appropriate to include these variables in the imputation model, but it is useful to have them remain in the imputed datasets (However, there are models that would include the ID variables in the imputation model, such as fixed effects model for data with repeated observations of the same countries). Identification variables which are not to be included in the imputation model can be identified with the argument \code{idvars}. These variables will not be used in the imputation model, but will be kept in the imputed datasets. If the \code{year} and \code{country} contained no information except labels, we could omit them from the imputation: <>= amelia(freetrade, idvars = c("year", "country")) @ Note that Amelia will return with an error if your dataset contains a factor or character variable that is not marked as a nominal or identification variable. Thus, if we were to omit the factor \code{country} from the \code{cs} or \code{idvars} arguments, we would receive an error: <<>>= a.out2 <- amelia(freetrade, idvars = c("year")) @ In order to conserve memory, it is wise to remove unnecessary variables from a data set before loading it into \Amelia. The only variables you should include in your data when running \Amelia\ are variables you will use in the analysis stage and those variables that will help in the imputation model. While it may be tempting to simply mark unneeded variables as IDs, it only serves to waste memory and slow down the imputation procedure. \subsection{Time Series, or Time Series Cross Sectional Data} \label{sec:tscs} Many variables that are recorded over time within a cross-sectional unit are observed to vary smoothly over time. In such cases, knowing the observed values of observations close in time to any missing value may enormously aid the imputation of that value. However, the exact pattern may vary over time within any cross-section. There may be periods of growth, stability, or decline; in each of which the observed values would be used in a different fashion to impute missing values. Also, these patterns may vary enormously across different cross-sections, or may exist in some and not others. \Amelia\ can build a general model of patterns within variables across time by creating a sequence of polynomials of the time index. If, for example, tariffs vary smoothly over time, then we make the modeling assumption that there exists some polynomial that describes the economy in cross-sectional unit $i$ at time $t$ as: \begin{equation} \textrm{tariff}_{ti} = \beta_0 + \beta_1 t + \beta_1 t^2 + \beta_1 t^3 \ldots \end{equation} And thus if we include enough higher order terms of time then the pattern between observed values of the tariff rate can be estimated. \Amelia\ will create polynomials of time up to the user defined $k$-th order, ($k\leq3$). We can implement this with the \code{ts} and \code{polytime} arguments. If we thought that a second-order polynomial would help predict we could run <>= a.out2 <- amelia(freetrade, ts = "year", cs = "country", polytime = 2) @ With this input, \Amelia\ will add covariates to the model that correspond to time and its polynomials. These covariates will help better predict the missing values. If cross-sectional units are specified these polynomials can be interacted with the cross-section unit to allow the patterns over time to vary between cross-sectional units. Unless you strongly believe all units have the same patterns over time in all variables (including the same constant term), this is a reasonable setting. When $k$ is set to 0, this interaction simply results in a model of \emph{fixed effects} where every unit has a uniquely estimated constant term. \Amelia\ does not smooth the observed data, and only uses this functional form, or one you choose, with all the other variables in the analysis and the uncertainty of the prediction, to impute the missing values. In order to impute with trends specific to each cross-sectional unit, we can set \code{intercs} to \code{TRUE}: <>= a.out.time <- amelia(freetrade, ts = "year", cs = "country", polytime = 2, intercs = TRUE, p2s = 2) @ Note that attempting to use \code{polytime} without the \code{ts} argument, or \code{intercs} without the \code{cs} argument will result in an error. Using the \code{tscsPlot} function (discussed below), we can see in figure \ref{fig:tcomp} that we have a much better prediction about the missing values when incorporating time than when we omit it: <>= tscsPlot(a.out, cs = "Malaysia", main = "Malaysia (no time settings)", var = "tariff", ylim = c(-10, 60)) tscsPlot(a.out.time, cs = "Malaysia", main = "Malaysia (with time settings)", var = "tariff", ylim = c(-10, 60)) @ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,2)))) @ \begin{figure} \begin{center} <

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4<ÉyԄ8@r%FRx- F_݄ae?| ֋Y :^3)k 6\q3h97ѾZ eh콚g4QOl՗ gz! ^ZtvwvpVrW'Qp!;8>vX.C;">et(kR/6m)ѥ4,n5^~S\Evי7sU4\FLY%vA3X^cxqUqÿ6Wz˦)Cl&[MJ2,h -rl .E\z䈄18 Y xaڲW*{L)u2~៯r4)?/x5}mݽ7)/]"M>fD׼Ã?:}5€;B~OHH@bX]^< sZi^%)EP8%ö튡sP/V}Zn5V#[-zv:k"ysU*jYRM}x9ǝ_\ 2"vO}FAE2ѺYrdixn!<$(_2es ݅>|aw\rU 2,#Nݔ^Ė8YulWNBQ]bc7&M@WZ5qfT KN'_w8& kL"+U+36)By AWªQoJ:'\ endstream endobj 457 0 obj << /Length 2019 /Filter /FlateDecode >> stream xڕYD}Ep\>*@*RH)\XOgeوp̭-I30wT \ %A㷐gV+#||WYMr8pbG` ~U@wGD pkTKZb zJTHE)oX-W[aIedsA #T]`Kk=F}év 9jxFHʹ~^KZVlGq8ָC͌i ):#^<_2܊^/rRFg\oKګʑ1DVbcc&@"+ս5{{J q#n&IU֢mVYDW8i>AI(k%ѩ 1*f}B@~?)@XҾFYd/Q+tv=^Aq2l9tq]V\Y8Vc;V6LVRP'k'y:B:/JplV[pRYɺПXv/xK8[eOd%1FnUPrRH*= qOC|DU6tؗR1$OJW ǙϿ0@{^Phx/s<["m1 ʅTWeh_w2<#ɡSEב6`BD 1qwѰ*/Wkqn?>B'0tlNv g&:F8KI6%;x0ܹ&9憆}?z"%Ilc!sWx4r iʗ'^4 IȂ33uq- ہ>V-֧DK.>Ufh'1 e]ǵֹDCY1^VU-U{G76/N0Qa`OQ*=kpU^7 'qM3O.iʿ]䣒x\E11vKNdxqٖA~6XXD,#}Qܰ`95 @5h(lnl)1y#?8U<=9ciMݫqiC(]2j|Kcv3kb ÿղq+t 76GS:Y_uTW ֻBn ܭ%i}2$x>p$Dr1CC*m>Xo-E?02 Fe2,$:=9E1Y%p39E1rUs2p?oy endstream endobj 448 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (./amelia-timecompare.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 459 0 R /BBox [0 0 720 432] /Resources << /ProcSet [ /PDF /Text ] /Font << /F1 460 0 R/F2 461 0 R/F3 462 0 R>> /ExtGState << >>/ColorSpace << /sRGB 463 0 R >>>> /Length 1504 /Filter /FlateDecode >> stream xYMo7 ϯq}"RM)znm.5ߗh3Y=3IDI sV|~߅R4FWңEx%_7J)1Z/&z+~t%u m >v@Y_ G ?8-{;[_LN<|)H_2qKQPp|4(qFF5#Ah@z?>mӻuSJ#͘9a;>Ap-՜{/-C^4At얠R*;C%rNQ9D q׍`v yʓ["SNr|RRNnFN*d]*e'̩%wO=j/PItO{h8މm{5أF {3`?`~0PC1-\ 97rxVhOjZzF.Ii[f}E 78SvTZ  W`HUm_#{^noV?(oFyv]u+ܙрJ53@@~/tth<>:p=#1gJˍm\jB)Ƙ6 5H]=;-M=\DuGyQ?rNS3ӑpzZ}<+$Vnn.?Jln|>;"-<:wzFx#r )9PzVOgbdf q1-W19&Ud fR]nc^diW>O+iw5aq^z6Tcs^-h? jqRo2œkqwKnpgy+)Ikt|Pw UZ ~Ss$i!Ad]ww "8<3Ѷ="N?58M(!)7=4t=!Il)kz4e| W#$=ml/' p?u?֚?8MNHlL\DZD-.V6=n;z-n~qwLv-qzwfw[5߄;ܢ[nmC ̀'/,+/pDrؒHU P`2}ysi.D˘,P̑+G2cL@1y+mT3FtUI(M \qtt[ũ;B8y`8yV'hܕV̭ Z3 ݽ*ZiF ZV'hqz@xODbN}ܳ*[iF Z<\+xϜ}R2= t6ޏ endstream endobj 465 0 obj << /Alternate /DeviceRGB /N 3 /Length 2596 /Filter /FlateDecode >> stream xwTSϽ7PkhRH H.*1 J"6DTpDQ2(C"QDqpId߼y͛~kg}ֺLX Xňg` lpBF|،l *?Y"1P\8=W%Oɘ4M0J"Y2Vs,[|e92<se'9`2&ctI@o|N6(.sSdl-c(2-yH_/XZ.$&\SM07#1ؙYrfYym";8980m-m(]v^DW~ emi]P`/u}q|^R,g+\Kk)/C_|Rax8t1C^7nfzDp 柇u$/ED˦L L[B@ٹЖX!@~(* {d+} G͋љς}WL$cGD2QZ4 E@@A(q`1D `'u46ptc48.`R0) @Rt CXCP%CBH@Rf[(t CQhz#0 Zl`O828.p|O×X ?:0FBx$ !i@ڐH[EE1PL ⢖V6QP>U(j MFkt,:.FW8c1L&ӎ9ƌaX: rbl1 {{{;}#tp8_\8"Ey.,X%%Gщ1-9ҀKl.oo/O$&'=JvMޞxǥ{=Vs\x ‰N柜>ucKz=s/ol|ϝ?y ^d]ps~:;/;]7|WpQoH!ɻVsnYs}ҽ~4] =>=:`;cܱ'?e~!ańD#G&}'/?^xI֓?+\wx20;5\ӯ_etWf^Qs-mw3+?~O~ endstream endobj 468 0 obj << /Length 2776 /Filter /FlateDecode >> stream xڥn=_!Z,gx_4EȢ>4})ZV]R~}ufHQ>Ȝ˙3gΜ8Ylot?daL\]/:&]UY,m&[>_"qn?`nE8zyGDB3= D߷iHM 1u3:FW,Kh+ΐQ ,]6T]!+wOԙAZIM(ȎG;fRkh!X&Mj+YVVxywD7Utp2Ǚ~=/mI3 hhg\{^p%bG' N;7`".m9sj'X`#[2QA,Ø[bIgA s;;  z Rԟs9ܧd^;qp1(')s:> qb~^ ;NhG- T{ˣ#B#.#Fг4:*!;X7ܰulzc 4F06SQմ*ug ef iD(II}z^G(_dnF Plj5_-4x\6-ee`[+(@KjhA\ Ev) ۪2ԶJ Lmy?I:¿8pr+ +9O[8i> 09+s|׷I<'S~M,(RY~Н)kIb \DFdAf{8$5lct=?i"6CYѓ9Z)/BiDU&cy۱#Mɲ!Sn1X39fcA!O6AtH2ݢnxd/9q| ݤ7̐cBąmu éh{DbfE⟱l4qlu .E dcj++3 \u>{ݑ;Y>Hb_ّ3TqkDe$r(@ >2A?2^.Q8$J/MGJW $ > B ;r>ܙ`/Ynx\jcqkhü{f=NָFɌk*1.tT4jPM*D899 y)=Th%a_QؼmURc3fֿ̖8X$ Z?ʡϣLҫ/Rs,G-58l\+Zy !)c z֚@y> stream xXkFB 2=o+%p^ʕ^_[Y ~4})mmB Vlh%ѷW_-&lfM^ȗ޸dջ߯L6#`HSNwYg;=W@۫֔޻>*Klvlg#ѵGܢ]i(8t)J;}FI{͂{}s?:{Tk8Ppv0N;p d ), d3ec!z53y"!$قBy$ ٜx !FQaz|p!)-)U(gx}%;bJDwkD;xGɿ(gR!Pb*t?~ʘYi/u+ s3(`'$HRّ2QN|YN>--^h3,^r6_(페$㺅|xh()ҳN gڈ &eʺ," kڜ8K] Y@ uh⟨m9QH > /ExtGState << >>/ColorSpace << /sRGB 483 0 R >>>> /Length 1507 /Filter /FlateDecode >> stream xXKo7 ϯ>D5AS@ ^'#[ޤYK13z3^#8LrDRI} [ 2ki@G1Jbs%_F|TJU|B|GwI(qFn;`{^fu-P6KHS_8-8;[6o&ǞijZJ&VcN2L dg#@@_16[VzJS0 OMdn jK ){ GyB}-Aev)*;>s9(qC%b:8gu%;[|^jodZ5Z/݌j\]ͩ'=ԄiO,kiM{h8މmy5ȣF yaN,#c*Z1~ ,Gts@cޯ>U()4]jAd4H9`{q#9lڏ^ Gܤ3J7W HUm<ˇǹ%(wΕḶրJ53@tuut<5nI[aM@Y3[k!ΰVBNwNcL[LZ$9}WN y]^['?D6[䲢%x#4p^<+$NO~/RWͷObuS <ܬH8 !@.N.7'7׽'BfS r'&I۸Elk4xwJG CEQ RaWSI jHhpҠȏwwGU^0,RRǢg?m '(@~QsYCӐOk:j^Cu>' ym{~a qƨ~jrgnuw)j,=D0!\~&͟}c"E,E,/X[XѶĺE,XN 0㑉,b{1go1 `Bwl ^6,@`gd_Xp Pz}8z yOP5*P56ht@UUc`F *)P4F@q/j3Qj7j;j7?L΅ (g1-EP#> stream xwTSϽ7PkhRH H.*1 J"6DTpDQ2(C"QDqpId߼y͛~kg}ֺLX Xňg` lpBF|،l *?Y"1P\8=W%Oɘ4M0J"Y2Vs,[|e92<se'9`2&ctI@o|N6(.sSdl-c(2-yH_/XZ.$&\SM07#1ؙYrfYym";8980m-m(]v^DW~ emi]P`/u}q|^R,g+\Kk)/C_|Rax8t1C^7nfzDp 柇u$/ED˦L L[B@ٹЖX!@~(* {d+} G͋љς}WL$cGD2QZ4 E@@A(q`1D `'u46ptc48.`R0) @Rt CXCP%CBH@Rf[(t CQhz#0 Zl`O828.p|O×X ?:0FBx$ !i@ڐH[EE1PL ⢖V6QP>U(j MFkt,:.FW8c1L&ӎ9ƌaX: rbl1 {{{;}#tp8_\8"Ey.,X%%Gщ1-9ҀKl.oo/O$&'=JvMޞxǥ{=Vs\x ‰N柜>ucKz=s/ol|ϝ?y ^d]ps~:;/;]7|WpQoH!ɻVsnYs}ҽ~4] =>=:`;cܱ'?e~!ańD#G&}'/?^xI֓?+\wx20;5\ӯ_etWf^Qs-mw3+?~O~ endstream endobj 488 0 obj << /Length 2172 /Filter /FlateDecode >> stream xڥYIoFWERp@ 4@ҦC@Kc$R߷BRP$ߛQZ$^$fջ4Y7E.;hqU2oC4Q\U]C>zet#|-utoF=_sXUt?Kd׆Wii=W7xkoHxµ;7He3ēnsD TqQ4y^yyGv{IxA?q\A"v[]w.)f3{$ARd30r6exFL%ۂŢPDxL8@XJVUIDϮ}O<\PjLYUe8t{̳QOunDn+&9:BEtd{sbCgIƮ*RҨZ_Oޑ}`]`eum}[v:GWz)_Ԋ,'A)dhq>&EmE5SHmLX1Oګ4chgߵGxCʤJ)]ಜmULDŽ;Jqާ~ƞhUA.6rޭ!e{Ͼ‚Cц,cbr4v|RSSOȭ:-BB7V]Js bF4_d?螕q{>zjSW)gJ[õT]XIoeWցfíG%//ݙ,Y6ᇱYҿJ,󱵑CϬp+9a(w2% PUb4RmZ7i0VONsw\qݥ+\E<~~湭~s"4jR%`̎% ԟн(4{S'uU\`\YE}]ё{@ +NImEmG4c6\\OWt^;-7=6~BH2[n2c42y7 ) 8NeqtM4JBr/eC>ٴG4o4ͅ8FMcᘒ73 36(Of.]Q ͵2jjόUȿ;^?al׳j:\~ &"aR{H]IIYҨ0|`~AwLHޙﲀq^ ,?w@~Q֊Ƌtkh\{U^o$ >4kq'sP?Di2jBy>h1 Rq!ee=y(j$xiR%gF2+4En :iL |>e_^Lr?O (hN#D6#yJ.^S=/;KELvr? 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ZLZю@; Z.~V؃qg;^h.ЍvQ--uh>-ƈg~,b@Ә2[ك14hMht0BxtAcLcycEc Q06N:C[#=N1M 0vi ܲcq;u)p m5i0VD[%= f􌫤s ~WHςy2s<5e `:en]"]n- (+ER`M+hʤzUq4=R?:iR MY4[5vTdj34 d TX4j1u2Gp(@ j0P y+CkIB+h{sz5*'hIۈJuY7B/p>@" t " =c`p`pNs/4|N&.3`\]]qUARtiAp)0 n8pl)p\ugV 􋰭(f 0@-= oEs(|kA4u6h=3kfD@47 rcEl>U$V@} 7-Zkm~O7кUnZw׉\w.a39]X=̺[6ԥfRV򀹯Tʂ\wa.,esϾ~@3fcd)0;jK'ͽ4ipgA3muU%`J.*d˖ XА骹?=P[`gMe p{YۨT#o+y_HG +֘P+IkFJ1RR<֛uNv6KcVom?m6u5ۍ#R|O1Wm6:ülq])ۏJA-Cfժ/>CfrN(jʮUE-V9Ө*QfVnm/*e?*m3uXXguZ!E{-BVQ+|'z{ܨ9 8gU5c::[v ؛%]UIIpq¡!9tȘpJ{'njdѓ`SM8%l/ppDI&A O*/ULE endstream endobj startxref 661369 %%EOF Amelia/inst/doc/amelia.Rnw0000644000176200001440000031765513347513057015135 0ustar liggesusers\documentclass[12pt,letterpaper]{article} \usepackage[T1]{fontenc} \usepackage{Rd} \usepackage{Sweave} \usepackage{upquote} % === for bad lm output === % this wasn't working with rbuild %% so i took out the signficance stars %\usepackage[utf8]{inputenc} %\usepackage{Rd/Rd} %\usepackage{Rd/Sweave} %\usepackage{Rd/upquote} \SweaveOpts{width=70} % === graphic packages === \usepackage{graphicx} \usepackage{epstopdf} \DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png} % === bibliography package === \usepackage{natbib} % === margin and formatting === \usepackage{setspace} \usepackage{fullpage} \usepackage{caption} % === math packages === \usepackage[reqno]{amsmath} \usepackage{amsthm} \usepackage{amssymb,enumerate} \newtheorem{Com} {Comment} \newtheorem{prop}{Proposition} \newtheorem{thm}{Theorem} % === dcolumn package === \usepackage{dcolumn} \newcolumntype{.}{D{.}{.}{-1}} \newcolumntype{d}[1]{D{.}{.}{#1}} % === additional packages === \usepackage{url} \setcounter{tocdepth}{4} \usepackage{tikz} %\VignetteIndexEntry{Amelia II: A Package for Missing Data} %\VignetteDepends{Zelig} %\VignetteKeyWords{} %\VignettePackage{Amelia} \usepackage{color} \usepackage[pdftex, bookmarksopen=true, bookmarksnumbered=true, pdfstartview=FitH, breaklinks=true, urlbordercolor={0 1 0}, citebordercolor={0 0 1}]{hyperref} \newcommand{\obs}{{\text{obs}}} \newcommand{\mis}{{\text{mis}}} %\newcommand{\Amelia}{\texttt{Amelia}} \renewcommand{\R}{\textsf{R}} \newcommand{\Amelia}{\ensuremath{\mathbb A}melia} \newcommand{\AmeliaII}{\ensuremath{\mathbb A}melia~\ensuremath{\mathbb{II}}} \newcommand{\AmeliaView}{\ensuremath{\mathbb A}melia\ensuremath{\mathbb{V}}iew} \newcommand{\adjparbox}[2]{\parbox{#1}{\vspace{.35em}#2\vspace{.35em}}} \usepackage{vmargin} \topmargin=0in \title{${\mathbb{AMELIA~II}}$: A Program for Missing Data} % rbuild: replace 'Version ' '\\' Version \author{James Honaker, Gary King, and Matthew Blackwell} \begin{document} <>= ameliaVersion <- packageVersion("Amelia") @ \date{Version \Sexpr{ameliaVersion}\\ \today} \maketitle \tableofcontents \newpage \section{Introduction} \label{sec:intro} Missing data is a ubiquitous problem in social science data. Respondents do not answer every question, countries do not collect statistics every year, archives are incomplete, subjects drop out of panels. Most statistical analysis methods, however, assume the absence of missing data, and are only able to include observations for which every variable is measured. \AmeliaII\ allows users to impute (``fill in'' or rectangularize) incomplete data sets so that analyses which require complete observations can appropriately use all the information present in a dataset with missingness, and avoid the biases, inefficiencies, and incorrect uncertainty estimates that can result from dropping all partially observed observations from the analysis. \AmeliaII\ performs \emph{multiple imputation}, a general-purpose approach to data with missing values. Multiple imputation has been shown to reduce bias and increase efficiency compared to listwise deletion. Furthermore, ad-hoc methods of imputation, such as mean imputation, can lead to serious biases in variances and covariances. Unfortunately, creating multiple imputations can be a burdensome process due to the technical nature of algorithms involved. \Amelia\ provides users with a simple way to create and implement an imputation model, generate imputed datasets, and check its fit using diagnostics. The \AmeliaII\ program goes several significant steps beyond the capabilities of the first version of \Amelia\ \citep*{HonJosKin98}. For one, the bootstrap-based EMB algorithm included in \AmeliaII\ can impute many more variables, with many more observations, in much less time. The great simplicity and power of the EMB algorithm made it possible to write \AmeliaII\ so that it virtually never crashes --- which to our knowledge makes it unique among all existing multiple imputation software --- and is much faster than the alternatives too. \AmeliaII\ also has features to make valid and much more accurate imputations for cross-sectional, time-series, and time-series-cross-section data, and allows the incorporation of observation and data-matrix-cell level prior information. In addition to all of this, \AmeliaII\ provides many diagnostic functions that help users check the validity of their imputation model. This software implements the ideas developed in \citet*{HonKin10}. \section[What Amelia Does]{What \Amelia\ Does} \label{sec:what} Multiple imputation involves imputing $m$ values for each missing cell in your data matrix and creating $m$ ``completed'' data sets. Across these completed data sets, the observed values are the same, but the missing values are filled in with a distribution of imputations that reflect the uncertainty about the missing data. After imputation with \AmeliaII's EMB algorithm, you can apply whatever statistical method you would have used if there had been no missing values to each of the $m$ data sets, and use a simple procedure, described below, to combine the results\footnote{You can combine the results automatically by doing your data analyses within Zelig for R, or within Clarify for Stata; see \url{http://gking.harvard.edu/stats.shtml}.}. Under normal circumstances, you only need to impute once and can then analyze the $m$ imputed data sets as many times and for as many purposes as you wish. The advantage of \AmeliaII\ is that it combines the comparative speed and ease-of-use of our algorithm with the power of multiple imputation, to let you focus on your substantive research questions rather than spending time developing complex application-specific models for nonresponse in each new data set. Unless the rate of missingness is very high, $m = 5$ (the program default) is probably adequate. \subsection{Assumptions} The imputation model in \AmeliaII\ assumes that the complete data (that is, both observed and unobserved) are multivariate normal. If we denote the $(n \times k)$ dataset as $D$ (with observed part $D^{\obs}$ and unobserved part $D^{\mis}$), then this assumption is \begin{equation} \label{eq:norm} D \sim \mathcal{N}_k(\mu, \Sigma), \end{equation} which states that $D$ has a multivariate normal distribution with mean vector $\mu$ and covariance matrix $\Sigma$. The multivariate normal distribution is often a crude approximation to the true distribution of the data, yet there is evidence that this model works as well as other, more complicated models even in the face of categorical or mixed data \citep[see][]{Schafer97, SchOls98}. Furthermore, transformations of many types of variables can often make this normality assumption more plausible (see \ref{sec:trans} for more information on how to implement this in \Amelia). The essential problem of imputation is that we only observe $D^{\obs}$, not the entirety of $D$. In order to gain traction, we need to make the usual assumption in multiple imputation that the data are \emph{missing at random} (MAR). This assumption means that the pattern of missingness only depends on the observed data $D^{\obs}$, not the unobserved data $D^{\mis}$. Let $M$ to be the missingness matrix, with cells $m_{ij} = 1$ if $d_{ij} \in D^{\mis}$ and $m_{ij} = 0$ otherwise. Put simply, $M$ is a matrix that indicates whether or not a cell is missing in the data. With this, we can define the MAR assumption as \begin{equation} \label{eq:mar} p(M|D) = p(M|D^{\obs}). \end{equation} Note that MAR includes the case when missing values are created randomly by, say, coin flips, but it also includes many more sophisticated missingness models. When missingness is not dependent on the data at all, we say that the data are \emph{missing completely at random} (MCAR). \Amelia\ requires both the multivariate normality and the MAR assumption (or the simpler special case of MCAR). Note that the MAR assumption can be made more plausible by including additional variables in the dataset $D$ in the imputation dataset than just those eventually envisioned to be used in the analysis model. \subsection{Algorithm} In multiple imputation, we are concerned with the complete-data parameters, $\theta = (\mu, \Sigma)$. When writing down a model of the data, it is clear that our observed data is actually $D^{\obs}$ and $M$, the missingness matrix. Thus, the likelihood of our observed data is $p(D^{\obs}, M|\theta)$. Using the MAR assumption\footnote{There is an additional assumption hidden here that $M$ does not depend on the complete-data parameters.}, we can break this up, \begin{align} p(D^{\obs},M|\theta) = p(M|D^{\obs})p(D^{\obs}|\theta). \end{align} As we only care about inference on the complete data parameters, we can write the likelihood as \begin{align} L(\theta|D^{\obs}) &\propto p(D^{\obs}|\theta), \end{align} which we can rewrite using the law of iterated expectations as \begin{align} p(D^{\obs}|\theta) &= \int p(D|\theta) dD^{\mis}. \end{align} With this likelihood and a flat prior on $\theta$, we can see that the posterior is \begin{equation} p(\theta | D^{\obs}) \propto p(D^{\obs}|\theta) = \int p(D|\theta) dD^{\mis}. \end{equation} The main computational difficulty in the analysis of incomplete data is taking draws from this posterior. The EM algorithm \citep*{DemLaiRub77} is a simple computational approach to finding the mode of the posterior. Our EMB algorithm combines the classic EM algorithm with a bootstrap approach to take draws from this posterior. For each draw, we bootstrap the data to simulate estimation uncertainty and then run the EM algorithm to find the mode of the posterior for the bootstrapped data, which gives us fundamental uncertainty too (see \citet{HonKin10} for details of the EMB algorithm). Once we have draws of the posterior of the complete-data parameters, we make imputations by drawing values of $D^{\mis}$ from its distribution conditional on $D^{\obs}$ and the draws of $\theta$, which is a linear regression with parameters that can be calculated directly from $\theta$. \subsection{Analysis} In order to combine the results across $m$ data sets, first decide on the quantity of interest to compute, such as a univariate mean, regression coefficient, predicted probability, or first difference. Then, the easiest way is to draw $1/m$ simulations of $q$ from each of the $m$ data sets, combine them into one set of $m$ simulations, and then to use the standard simulation-based methods of interpretation common for single data sets \citep{KinTomWit00}. Alternatively, you can combine directly and use as the multiple imputation estimate of this parameter, $\bar{q}$, the average of the $m$ separate estimates, $q_j$ $(j=1,\dots,m)$: \begin{equation} \bar{q}=\frac{1}{m}\sum^{m}_{j=1}q_j. \end{equation} The variance of the point estimate is the average of the estimated variances from \emph{within} each completed data set, plus the sample variance in the point estimates \emph{across} the data sets (multiplied by a factor that corrects for the bias because $m<\infty$). Let $SE(q_j)^2$ denote the estimated variance (squared standard error) of $q_j$ from the data set $j$, and $S^{2}_{q}=\Sigma^{m}_{j=1}(q_j-\bar{q})^2/(m-1)$ be the sample variance across the $m$ point estimates. The standard error of the multiple imputation point estimate is the square root of \begin{equation} SE(q)^2=\frac{1}{m}\sum^{m}_{j=1}SE(q_j)^2+S^2_q(1+1/m). \end{equation} \begin{figure} \centering \begin{tikzpicture} [inner sep = 2.5mm, missdata/.style={rectangle, draw=red!50, fill=red!20, thick}, impdata/.style={rectangle, draw=blue!50, fill=blue!20, thick}, results/.style= {circle, draw=blue!50, fill=blue!20, thick}] \node (odata) at (3,3) [missdata] {}; \node [red!80,right] at (5.25,3) {incomplete data}; \node (boot1) at (1,1) [missdata] {} edge [<-, bend left=40] (odata); \node (boot2) at (2,1) [missdata] {} edge [<-, bend left=20] (odata); \node (boot3) at (3,1) [missdata] {} edge [<-] (odata); \node (boot4) at (4,1) [missdata] {} edge [<-, bend right=20] (odata); \node (boot5) at (5,1) [missdata] {} edge [<-, bend right=40] (odata); %% add "random question marks" \node[red!50!black] at (2.95,3.1) {\tiny ?}; \node[red!50!black] at (2.85,2.9) {\tiny ?}; \node[red!50!black] at (3.15,2.95) {\tiny ?}; \node[red!50!black] at (2.85,1.1) {\tiny ?}; \node[red!50!black] at (2.95,0.9) {\tiny ?}; \node[red!50!black] at (3.15,1.1) {\tiny ?}; \node[red!50!black] at (0.85,0.9) {\tiny ?}; \node[red!50!black] at (1.15,0.95) {\tiny ?}; \node[red!50!black] at (1.85,1.1) {\tiny ?}; \node[red!50!black] at (1.95,0.9) {\tiny ?}; \node[red!50!black] at (3.85,1.1) {\tiny ?}; \node[red!50!black] at (4.95,0.9) {\tiny ?}; \node[red!50!black] at (5.15,1.1) {\tiny ?}; \node [black!80,right] at (5.25,2) {bootstrap}; \node [red!80, right] at (5.25, 1) {bootstrapped data}; \node (imp1) at (1,0) [impdata] {} edge [<-] (boot1); \node (imp2) at (2,0) [impdata] {} edge [<-] (boot2); \node (imp3) at (3,0) [impdata] {} edge [<-] (boot3); \node (imp4) at (4,0) [impdata] {} edge [<-] (boot4); \node (imp5) at (5,0) [impdata] {} edge [<-] (boot5); \node [blue!80,right] at (5.25,0) {imputed datasets}; \node [black!80, right] at (5.25, 0.5) {EM}; \node (res1) at (1,-1) [results] {} edge [<-] (imp1); \node (res2) at (2,-1) [results] {} edge [<-] (imp2); \node (res3) at (3,-1) [results] {} edge [<-] (imp3); \node (res4) at (4,-1) [results] {} edge [<-] (imp4); \node (res5) at (5,-1) [results] {} edge [<-] (imp5); \node [black!80, right] at (5.25, -0.5) {analysis}; \node [blue!80, right] at (5.25, -1) {separate results}; \node[circle, draw=green!50!black!50, fill=green!20, thick] at (3,-3) {} edge [<-, bend right=40] (res5) edge [<-, bend left=40] (res1) edge [<-, bend right=20] (res4) edge [<-, bend left=20] (res2) edge [<-] (res3); \node [black!80, right] at (5.25, -2) {combination}; \node [green!80!black!80, right] at (5.25, -3) { final results}; \end{tikzpicture} \caption{A schematic of our approach to multiple imputation with the EMB algorithm. } \end{figure} \section[Versions of Amelia]{Versions of \Amelia\ } \label{sec:versions} Two versions of \AmeliaII\ are available, each with its own advantages and drawbacks, but both of which use the same underlying code and algorithms. First, \AmeliaII\ exists as a package for the \R\ statistical software package. Users can utilize their knowledge of the \R\ language to run \AmeliaII\ at the command line or to create scripts that will run \AmeliaII\ and preserve the commands for future use. Alternatively, you may prefer \AmeliaView, where an interactive Graphical User Interface (GUI) allows you to set options and run \Amelia\ without any knowledge of the \R\ programming language. Both versions of \AmeliaII\ are available on the Windows, Mac OS X, and Linux platforms and \AmeliaII\ for \R\ runs in any environment that \R\ can. All versions of \Amelia\ require the \R\ software, which is freely available at \url{http://www.r-project.org/}. Before installing \AmeliaII, you must have installed \R\ version 2.1.0 or higher, which is freely available at \url{http://www.r-project.org/}. \subsection{Installation and Updates from R} \label{sec:install} To install the \Amelia\ package on any platform, simply type the following at the \R\ command prompt, \begin{verbatim} > install.packages("Amelia") \end{verbatim} and \R\ will automatically install the package to your system from CRAN. If you wish to use the most current beta version of \Amelia\, feel free to install the test version, \begin{verbatim} > install.packages("Amelia", repos = "http://gking.harvard.edu") \end{verbatim} In order to keep your copy of \Amelia\ completely up to date, you should use the command \begin{verbatim} > update.packages() \end{verbatim} \subsection[Installation in Windows of AmeliaView as a Standalone Program]{Installation in Windows of \AmeliaView\ as a Standalone Program} \label{sec:win-install} To install a standalone version of \AmeliaView\ in the Windows environment, simply download the installer \texttt{setup.exe} from \url{http://gking.harvard.edu/amelia/} and run it. The installer will ask you to choose a location to install \AmeliaII. If you have installed \R\ with the default options, \AmeliaII\ will automatically find the location of \R. If the installer cannot find \R, it will ask you to locate the directory of the most current version of \R. Make sure you choose the directory name that includes the version number of \R\ (e.g. C:/Program Files/R/R-2.9.0) and contains a subdirectory named \texttt{bin}. The installer will also put shortcuts on your Desktop and Start Menu. Even users familiar with the \R\ language may find it useful to utilize \AmeliaView\ to set options on variables, change arguments, or run diagnostics. From the command line, \AmeliaView\ can be brought up with the call: \begin{verbatim} > library(Amelia) > AmeliaView() \end{verbatim} \subsection{Linux (local installation)} \label{sec:lin-install} Installing \Amelia\ on a Linux system is slightly more complicated due to user permissions. If you are running \R\ with root access, you can simply run the above installation procedure. If you do not have root access, you can install \Amelia\ to a local library. First, create a local directory to house the packages, \begin{verbatim} w4:mblackwell [~]: mkdir ~/myrlibrary \end{verbatim} and then, in an \R\ session, install the package directing \R\ to this location: \begin{verbatim} > install.packages("Amelia", lib = "~/myrlibrary") \end{verbatim} Once this is complete you need to edit or create your \R\ profile. Locate or create \texttt{\~/.Rprofile} in your home directory and add this line: \begin{verbatim} .libPath("~/myrlibrary") \end{verbatim} This will add your local library to the list of library paths that \R\ searches in when you load libraries. Linux users can use \AmeliaView\ in the same way as Windows users of \Amelia\ for \R. From the command line, \AmeliaView\ can be brought up with the call: \begin{verbatim} > AmeliaView() \end{verbatim} \section{A User's Guide} \label{sec:guide} \subsection{Data and Initial Results} We now demonstrate how to use \Amelia\ using data from \citet{MilKub05} which studies the effect of democracy on trade policy. For the purposes of this user's guide, we will use a subset restricted to nine developing countries in Asia from 1980 to 1999\footnote{We have artificially added some missingness to these data for presentational purposes. You can access the original data at \url{http://www.princeton.edu/~hmilner/Research.htm}}. This dataset includes 9 variables: year (\code{year}), country (\code{country}), average tariff rates (\code{tariff}), Polity IV score\footnote{The Polity score is a number between -10 and 10 indicating how democratic a country is. A fully autocratic country would be a -10 while a fully democratic country would be 1 10.} (\code{polity}), total population (\code{pop}), gross domestic product per capita (\code{gdp.pc}), gross international reserves (\code{intresmi}), a dummy variable signifying whether the country had signed an IMF agreement in that year (\code{signed}), a measure of financial openness (\code{fivop}), and a measure of US hegemony\footnote{This measure of US hegemony is the US imports and exports as a percent of the world total imports and exports.} (\code{usheg}). These variables correspond to the variables used in the analysis model of \citet{MilKub05} in table 2. <>= options("digits"=4) options("width"=70) options("show.signif.stars" = FALSE) set.seed(12345) @ We first load the \Amelia\ and the data: <>= require(Amelia) data(freetrade) @ We can check the summary statistics of the data to see that there is missingness on many of the variables: <<>= summary(freetrade) @ In the presence of missing data, most statistical packages use \emph{listwise deletion}, which removes any row that contains a missing value from the analysis. Using the base model of \citet{MilKub05} table 2, we run a simple linear model in \R, which uses listwise deletion: <>= summary(lm(tariff ~ polity + pop + gdp.pc + year + country, data = freetrade)) @ Note that 60 of the 171 original observations are deleted due to missingness. These observations, however, are partially observed, and contain valuable information about the relationships between those variables which are present in the partially completed observations. Multiple imputation will help us retrieve that information and make better, more efficient, inferences. \subsection{Multiple Imputation} When performing multiple imputation, the first step is to identify the variables to include in the imputation model. It is crucial to include at least as much information as will be used in the analysis model. That is, any variable that will be in the analysis model should also be in the imputation model. This includes any transformations or interactions of variables that will appear in the analysis model. In fact, it is often useful to add more information to the imputation model than will be present when the analysis is run. Since imputation is predictive, any variables that would increase predictive power should be included in the model, even if including them in the analysis model would produce bias in estimating a causal effect (such as for post-treatment variables) or collinearity would preclude determining which variable had a relationship with the dependent variable (such as including multiple alternate measures of GDP). In our case, we include all the variables in \code{freetrade} in the imputation model, even though our analysis model focuses on \code{polity}, \code{pop} and \code{gdp.pc}\footnote{Note that this specification does not utilize time or spatial data yet. The \texttt{ts} and \texttt{cs} arguments only have force when we also include \texttt{polytime} or \texttt{intercs}, discussed in section \ref{sec:tscs}}. To create multiple imputations in \Amelia, we can simply run <>= a.out <- amelia(freetrade, m = 5, ts = "year", cs = "country") a.out @ Note that our example dataset is deliberately small both in variables and in cross-sectional elements. Typical datasets may often have hundreds or possibly a couple thousand steps to the EM algorithm. Long chains should remind the analyst to consider whether transformations of the variables would more closely fit the multivariate normal assumptions of the model (correct but omitted transformations will shorten the number of steps and improve the fit of the imputations), but do not necessarily denote problems with the imputation model. The output gives some information about how the algorithm ran. Each of the imputed datasets is now in the list \code{a.out\$imputations}. Thus, we could plot a histogram of the \code{tariff} variable from the 3rd imputation, <>= hist(a.out$imputations[[3]]$tariff, col="grey", border="white") @ %$ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,1)))) @ \begin{figure} \begin{center} <>= <> @ \caption{Histogram of the \texttt{tariff} variable from the 3rd imputed dataset.} \label{fig:hist1} \end{center} \end{figure} \subsubsection{Saving imputed datasets} \label{sec:saving} If you need to save your imputed datasets, one direct method is to save the output list from \code{amelia}, \begin{verbatim} > save(a.out, file = "imputations.RData") \end{verbatim} As in the previous example, the \emph{i}th imputed datasets can be retrieved from this list as \code{a.out\$imputations[[i]]}. In addition, you can save each of the imputed datasets to its own file using the \code{write.amelia} command, \begin{verbatim} > write.amelia(obj=a.out, file.stem = "outdata") \end{verbatim} This will create one comma-separated value file for each imputed dataset in the following manner: \begin{verbatim} outdata1.csv outdata2.csv outdata3.csv outdata4.csv outdata5.csv \end{verbatim} The \code{write.amelia} function can also save files in tab-delimited and Stata (\code{.dta}) file formats. For instance, to save Stata files, simply change the \code{format} argument to \code{"dta"}, \begin{verbatim} > write.amelia(obj=a.out, file.stem = "outdata", format = "dta") \end{verbatim} Additionally, \code{write.amelia} can create a ``stacked'' version of the imputed dataset which stacks each imputed dataset on top of one another. This can be done by setting the \code{separate} argument to \code{FALSE}. The resulting matrix is of size $(N \cdot m) \times p$ if the original dataset is excluded (\code{orig.data = FALSE}) and of size $(N \cdot (m+1))\times p$ if it is included (\code{orig.data = TRUE}). The stacked dataset will include a variable (set with \code{impvar}) that indicates to which imputed dataset the observation belongs. See Section~\ref{sec:analysis} for a description of how to use this stacked dataset with the \code{mi} commands in Stata. \subsubsection[Combining Multiple Amelia Runs]{Combining Multiple \Amelia\ Runs} The EMB algorithm is what computer scientists call \emph{embarrassingly parallel}, meaning that it is simple to separate each imputation into parallel processes. With \Amelia\ it is simple to run subsets of the imputations on different machines and then combine them after the imputation for use in analysis model. This allows for a huge increase in the speed of the algorithm. Output lists from different \Amelia\ runs can be combined together into a new list. For instance, suppose that we wanted to add another ten imputed datasets to our earlier call to \code{amelia}. First, run the function to get these additional imputations, <<>>= a.out.more <- amelia(freetrade, m = 10, ts = "year", cs = "country", p2s=0) a.out.more @ then combine this output with our original output using the \code{ameliabind} function, <<>>= a.out.more <- ameliabind(a.out, a.out.more) a.out.more @ This function binds the two outputs into the same output so that you can pass the combined imputations easily to analysis models and diagnostics. Note that \code{a.out.more} now has a total of 15 imputations. A simple way to execute a parallel processing scheme with \Amelia\ would be to run \code{amelia} with \code{m} set to 1 on $m$ different machines or processors, save each output using the \code{save} function, load them all on the same \R\ session using \code{load} command and then combine them using \code{ameliabind}. In order to do this, however, make sure to name each of the outputs a different name so that they do not overwrite each other when loading into the same \R\ session. Also, some parallel environments will dump all generated files into a common directory, where they may overwrite each other. If it is convenient in a parallel environment to run a large number of \code{amelia} calls from a single piece of code, one useful way to avoid overwriting is to create the \code{file.stem} with a random suffix. For example: \begin{verbatim} > b<-round(runif(1,min=1111,max=9999)) > random.name<-paste("am",b,sep="") > amelia <- write.amelia(obj=a.out, file.stem = random.name) \end{verbatim} \subsubsection{Screen Output} Screen output can be adjusted with the ``print to screen'' argument, \code{p2s}. At a value of 0, no screen printing will occur. This may be useful in large jobs or simulations where a very large number of imputation models may be required. The default value of 1, lists each bootstrap, and displays the number of iterations required to reach convergence in that bootstrapped dataset. The value of 2 gives more thorough screen output, including, at each iteration, the number of parameters that have significantly changed since the last iteration. This may be useful when the EM chain length is very long, as it can provide an intuition for many parameters still need to converge in the EM chain, and a sense of the time remaining. However, it is worth noting that the last several parameters can often take a significant fraction of the total number of iterations to converge. Setting \code{p2s} to 2 will also generate information on how EM algorithm is behaving, such as a \code{!} when the current estimated complete data covariance matrix is not invertible and a \code{*} when the likelihood has not monotonically increased in that step. Having many of these two symbols in the screen output is an indication of a problematic imputation model\footnote{Problems of non-invertible matrices often mean that current guess for the covariance matrix is singular. This is a sign that there may be two highly correlated variables in the model. One way to resolve is to use a ridge prior (see \ref{sec:prior})}. An example of the output when \code{p2s} is 2 would be <>= amelia(freetrade, m = 1, ts = "year", cs = "country", p2s = 2) @ \subsection{Parallel Imputation Using Multicore CPUs} \label{sec:parallel} Each imputation in the above EMB algorithm is completely independent of any other imputation, a property called embarrassingly parallel. This type of approach can take advantage of the multiple -core infrastructure of modern CPUs. Each core in a multi-core processor can execute independent operations in parallel. \Amelia\ can utilize this parallel processing internally \emph{via} the \code{parallel} and the \code{ncpus} arguments. The \code{parallel} argument sets the parallel processing backend, either with \code{"multicore"} or \code{"snow"} (or \code{"no"} for no parallel processing). The \code{"multicore"} backend is not available on Windows systems, but tends to be quicker at parallel processing. On a Windows system, the \code{"snow"} backend provides parallel processing through a cluster of worker processes across the CPUs. You can set the default for this argument using the \code{"amelia.parallel"} option. This allows you to run Amelia in parallel as the default for an entire R session without setting arguments in the \code{amelia} call. For each of the parallel backends, \Amelia\ requires a number of CPUs to use in parallel. This can be set using the \code{ncpus} argument. It can be higher than the number of physical cores in the system if hyperthreading or other technologies are available. You can use the \code{parallel::detectCores} function to determine how many cores are available on your machine. The default for this argument can be set using the \code{"amelia.ncpus"} option. On Unix-alike systems (such as Mac OS X and Linux distributions), the \code{"multicore"} backend automatically sets up and stops the parallel workers by forking the process. On Windows, the \code{"snow"} backend requires more attention. \Amelia\ will attempt to create a parallel cluster of worker processes (since Windows systems cannot fork a process) and will stop this cluster after the imputations are complete. Alternatively, \Amelia\ also has a \code{cl} argument, which accepts a predefined cluster made using the \code{parallel::makePSOCKcluster}. For more information about parallel processing in R, see the documentation for the \pkg{parallel} package that ships along with R. \subsection{Imputation-improving Transformations} \label{sec:trans} Social science data commonly includes variables that fail to fit to a multivariate normal distribution. Indeed, numerous models have been introduced specifically to deal with the problems they present. As it turns out, much evidence in the literature (discussed in \citealt{KinHonJos01}) indicates that the multivariate normal model used in \Amelia\ usually works well for the imputation stage even when discrete or non-normal variables are included and when the analysis stage involves these limited dependent variable models. Nevertheless, \Amelia\ includes some limited capacity to deal directly with ordinal and nominal variables and to modify variables that require other transformations. In general nominal and log transform variables should be declared to \Amelia, whereas ordinal (including dichotomous) variables often need not be, as described below. (For harder cases, see \citep{Schafer97}, for specialized MCMC-based imputation models for discrete variables.)\nocite{KinHonJos01} Although these transformations are taken internally on these variables to better fit the data to the multivariate normal assumptions of the imputation model, all the imputations that are created will be returned in the original untransformed form of the data. If the user has already performed transformations on their data (such as by taking a log or square root prior to feeding the data to \code{amelia}) these do not need to be declared, as that would result in the transformation occurring \emph{doubly} in the imputation model. The fully imputed data sets that are returned will always be in the form of the original data that is passed to the \code{amelia} routine. \subsubsection{Ordinal} \label{sec:ord} In much statistical research, researchers treat independent ordinal (including dichotomous) variables as if they were really continuous. If the analysis model to be employed is of this type, then nothing extra is required of the of the imputation model. Users are advised to allow \Amelia\ to impute non-integer values for any missing data, and to use these non-integer values in their analysis. Sometimes this makes sense, and sometimes this defies intuition. One particular imputation of 2.35 for a missing value on a seven point scale carries the intuition that the respondent is between a 2 and a 3 and most probably would have responded 2 had the data been observed. This is easier to accept than an imputation of 0.79 for a dichotomous variable where a zero represents a male and a one represents a female respondent. However, in both cases the non-integer imputations carry more information about the underlying distribution than would be carried if we were to force the imputations to be integers. Thus whenever the analysis model permits, missing ordinal observations should be allowed to take on continuously valued imputations. In the \code{freetrade} data, one such ordinal variable is \code{polity} which ranges from -10 (full autocracy) to 10 (full democracy). If we tabulate this variable from one of the imputed datasets, <>= table(a.out$imputations[[3]]$polity) @ %$ we can see that there is one imputation between -4 and -3 and one imputation between 6 and 7. Again, the interpretation of these values is rather straightforward even if they are not strictly in the coding of the original Polity data. Often, however, analysis models require some variables to be strictly ordinal, as for example, when the dependent variable will be modeled in a logistical or Poisson regression. Imputations for variables set as ordinal are created by taking the continuously valued imputation and using an appropriately scaled version of this as the probability of success in a binomial distribution. The draw from this binomial distribution is then translated back into one of the ordinal categories. For our data we can simply add \code{polity} to the \code{ords} argument: <>= a.out1 <- amelia(freetrade, m = 5, ts = "year", cs = "country", ords = "polity", p2s = 0) table(a.out1$imputations[[3]]$polity) @ Now, we can see that all of the imputations fall into one of the original polity categories. \subsubsection{Nominal} \label{sec:nom} Nominal variables\footnote{Dichotomous (two category) variables are a special case of nominal variables. For these variables, the nominal and ordinal methods of transformation in \Amelia\ agree.} must be treated quite differently than ordinal variables. Any multinomial variables in the data set (such as religion coded 1 for Catholic, 2 for Jewish, and 3 for Protestant) must be specified to \Amelia. In our \code{freetrade} dataset, we have \code{signed} which is 1 if a country signed an IMF agreement in that year and 0 if it did not. Of course, our first imputation did not limit the imputations to these two categories <<>>= table(a.out1$imputations[[3]]$signed) @ In order to fix this for a $ p$-category multinomial variable,\Amelia\ will determine $ p$ (as long as your data contain at least one value in each category), and substitute $ p-1$ binary variables to specify each possible category. These new $ p-1$ variables will be treated as the other variables in the multivariate normal imputation method chosen, and receive continuous imputations. These continuously valued imputations will then be appropriately scaled into probabilities for each of the $ p$ possible categories, and one of these categories will be drawn, where upon the original $ p$-category multinomial variable will be reconstructed and returned to the user. Thus all imputations will be appropriately multinomial. For our data we can simply add \code{signed} to the \code{noms} argument: <>= a.out2 <- amelia(freetrade, m = 5, ts = "year", cs = "country", noms = "signed", p2s = 0) table(a.out2$imputations[[3]]$signed) @ Note that \Amelia\ can only fit imputations into categories that exist in the original data. Thus, if there was a third category of signed, say 2, that corresponded to a different kind of IMF agreement, but it never occurred in the original data, \Amelia\ could not match imputations to it. Since \Amelia\ properly treats a $ p$-category multinomial variable as $ p-1$ variables, one should understand the number of parameters that are quickly accumulating if many multinomial variables are being used. If the square of the number of real and constructed variables is large relative to the number of observations, it is useful to use a ridge prior as in section \ref{sec:prior}. \subsubsection{Natural Log} \label{sec:log} If one of your variables is heavily skewed or has outliers that may alter the imputation in an unwanted way, you can use a natural logarithm transformation of that variable in order to normalize its distribution. This transformed distribution helps \Amelia\ to avoid imputing values that depend too heavily on outlying data points. Log transformations are common in expenditure and economic variables where we have strong beliefs that the marginal relationship between two variables decreases as we move across the range. For instance, figure \ref{fig:logshist} show the \code{tariff} variable clearly has positive (or, right) skew while its natural log transformation has a roughly normal distribution. <>= hist(freetrade$tariff, col="grey", border="white") hist(log(freetrade$tariff), col="grey", border="white") @ %$ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,2)))) @ \begin{figure} \begin{center} <>= <> @ \caption{Histogram of \texttt{tariff} and \texttt{log(tariff)}.} \label{fig:logshist} \end{center} \end{figure} <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,1)))) @ \subsubsection{Square Root} \label{sec:sqrt} Event count data is often heavily skewed and has nonlinear relationships with other variables. One common transformation to tailor the linear model to count data is to take the square roots of the counts. This is a transformation that can be set as an option in \Amelia. \subsubsection{Logistic} \label{sec:lgstc} Proportional data is sharply bounded between 0 and 1. A logistic transformation is one possible option in \Amelia\ to make the distribution symmetric and relatively unbounded. \subsection{Identification Variables} \label{sec:idvars} Datasets often contain identification variables, such as country names, respondent numbers, or other identification numbers, codes or abbreviations. Sometimes these are text and sometimes these are numeric. Often it is not appropriate to include these variables in the imputation model, but it is useful to have them remain in the imputed datasets (However, there are models that would include the ID variables in the imputation model, such as fixed effects model for data with repeated observations of the same countries). Identification variables which are not to be included in the imputation model can be identified with the argument \code{idvars}. These variables will not be used in the imputation model, but will be kept in the imputed datasets. If the \code{year} and \code{country} contained no information except labels, we could omit them from the imputation: <>= amelia(freetrade, idvars = c("year", "country")) @ Note that Amelia will return with an error if your dataset contains a factor or character variable that is not marked as a nominal or identification variable. Thus, if we were to omit the factor \code{country} from the \code{cs} or \code{idvars} arguments, we would receive an error: <<>>= a.out2 <- amelia(freetrade, idvars = c("year")) @ In order to conserve memory, it is wise to remove unnecessary variables from a data set before loading it into \Amelia. The only variables you should include in your data when running \Amelia\ are variables you will use in the analysis stage and those variables that will help in the imputation model. While it may be tempting to simply mark unneeded variables as IDs, it only serves to waste memory and slow down the imputation procedure. \subsection{Time Series, or Time Series Cross Sectional Data} \label{sec:tscs} Many variables that are recorded over time within a cross-sectional unit are observed to vary smoothly over time. In such cases, knowing the observed values of observations close in time to any missing value may enormously aid the imputation of that value. However, the exact pattern may vary over time within any cross-section. There may be periods of growth, stability, or decline; in each of which the observed values would be used in a different fashion to impute missing values. Also, these patterns may vary enormously across different cross-sections, or may exist in some and not others. \Amelia\ can build a general model of patterns within variables across time by creating a sequence of polynomials of the time index. If, for example, tariffs vary smoothly over time, then we make the modeling assumption that there exists some polynomial that describes the economy in cross-sectional unit $i$ at time $t$ as: \begin{equation} \textrm{tariff}_{ti} = \beta_0 + \beta_1 t + \beta_1 t^2 + \beta_1 t^3 \ldots \end{equation} And thus if we include enough higher order terms of time then the pattern between observed values of the tariff rate can be estimated. \Amelia\ will create polynomials of time up to the user defined $k$-th order, ($k\leq3$). We can implement this with the \code{ts} and \code{polytime} arguments. If we thought that a second-order polynomial would help predict we could run <>= a.out2 <- amelia(freetrade, ts = "year", cs = "country", polytime = 2) @ With this input, \Amelia\ will add covariates to the model that correspond to time and its polynomials. These covariates will help better predict the missing values. If cross-sectional units are specified these polynomials can be interacted with the cross-section unit to allow the patterns over time to vary between cross-sectional units. Unless you strongly believe all units have the same patterns over time in all variables (including the same constant term), this is a reasonable setting. When $k$ is set to 0, this interaction simply results in a model of \emph{fixed effects} where every unit has a uniquely estimated constant term. \Amelia\ does not smooth the observed data, and only uses this functional form, or one you choose, with all the other variables in the analysis and the uncertainty of the prediction, to impute the missing values. In order to impute with trends specific to each cross-sectional unit, we can set \code{intercs} to \code{TRUE}: <>= a.out.time <- amelia(freetrade, ts = "year", cs = "country", polytime = 2, intercs = TRUE, p2s = 2) @ Note that attempting to use \code{polytime} without the \code{ts} argument, or \code{intercs} without the \code{cs} argument will result in an error. Using the \code{tscsPlot} function (discussed below), we can see in figure \ref{fig:tcomp} that we have a much better prediction about the missing values when incorporating time than when we omit it: <>= tscsPlot(a.out, cs = "Malaysia", main = "Malaysia (no time settings)", var = "tariff", ylim = c(-10, 60)) tscsPlot(a.out.time, cs = "Malaysia", main = "Malaysia (with time settings)", var = "tariff", ylim = c(-10, 60)) @ <>= options(SweaveHooks = list(fig = function() par(mfrow=c(1,2)))) @ \begin{figure} \begin{center} <