\name{studySim} \alias{studySim} \title{ Simulation Study from Given Factor Structure Matrices and Conditions} \description{ The \code{structureSim} function returns statistical results from simulations from predefined congeneric factor structures. The main ideas come from the methodology applied by Zwick and Velicer (1986). } \usage{ studySim(var, nFactors, pmjc, loadings, unique, N, repsim, reppar, stats=1, quantile=0.5, model="components", r2limen=0.75, all=FALSE, dir=NA, trace=TRUE) } \arguments{ \item{var}{ numeric: vector of the number of variables} \item{nFactors}{ numeric: vector of the number of components/factors} \item{pmjc}{ numeric: vector of the number of major loadings on each component/factor} \item{loadings}{ numeric: vector of the major loadings on each component/factor} \item{unique}{ numeric: vector of the unique loadings on each component/factor} \item{N}{ numeric: vector of the number of subjects/observations} \item{repsim}{ numeric: number of replications of the matrix correlation simulation} \item{reppar}{ numeric: number of replications for the parallel and permutation analysis} \item{stats}{ numeric: vector of the statistics to return: mean(1), median(2), sd(3), quantile(4), min(5), max(6)} \item{quantile}{ numeric: quantile for the parallel and permutation analysis} \item{model}{ character: \code{"components"} or \code{"factors"} } \item{r2limen}{ numeric: R2 limen value for the R2 Nelson index} \item{all}{ logical: if \code{TRUE} computes the Bentler and Yuan index (very long computing time to consider)} \item{dir}{ character: directory where to save output. Default to NA} \item{trace}{ logical: if \code{TRUE} outputs details of the status of the simulations} } \value{ \item{values}{ Returns selected statistics about the number of components/factors to retain: mean, median, quantile, standard deviation, minimum and maximum.} } \seealso{ \code{\link{generateStructure}}, \code{\link{structureSim}} } \references{ Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. \emph{Psychological Bulletin, 99}, 432-442. } \author{ Gilles Raiche \cr Centre sur les Applications des Modeles de Reponses aux Items (CAMRI) \cr Universite du Quebec a Montreal\cr \email{raiche.gilles@uqam.ca}, \url{http://www.er.uqam.ca/nobel/r17165/} } \examples{ \dontrun{ # .................................................................... # Example inspired from Zwick and Velicer (1986) # Very long computimg time # ................................................................... # 1. Initialisation # reppar <- 30 # repsim <- 5 # quantile <- 0.50 # 2. Simulations # X <- studySim(var=36,nFactors=3, pmjc=c(6,12), loadings=c(0.5,0.8), # unique=c(0,0.2), quantile=quantile, # N=c(72,180), repsim=repsim, reppar=reppar, # stats=c(1:6)) # 3. Results (first 10 results) # print(X[1:10,1:14],2) # names(X) # 4. Study of the error done in the determination of the number # of components/factors. A positive value is associated to over # determination. # results <- X[X$stats=="mean",] # residuals <- results[,c(11:25)] - X$nfactors # BY <- c("nsubjects","var","loadings") # round(aggregate(residuals, by=results[BY], mean),0) } } \keyword{ multivariate }