\name{generateStructure} \alias{generateStructure} \title{ Generate a Factor Structure Matrix.} \description{ The \code{generateStructure} function returns a \emph{mjc} factor structure matrix. The number of variables per major factor \emph{pmjc} is equal for each factor. The argument \emph{pmjc} must be divisible by \emph{nVar}. The arguments are strongly inspired from Zick and Velicer (1986, p. 435-436) methodology. } \usage{ generateStructure(var, mjc, pmjc, loadings, unique) } \arguments{ \item{var}{ numeric: number of variables} \item{mjc}{ numeric: number of major factors (factors with practical significance) } \item{pmjc}{ numeric: number of variables that load significantly on each major factor } \item{loadings}{ numeric: loadings on the significant variables on each major factor } \item{unique}{ numeric: loadings on the non significant variables on each major factor } } \value{ \item{values}{ numeric matrix: factor structure } } \seealso{ \code{\link{principalComponents}}, \code{\link{iterativePrincipalAxis}}, \code{\link{rRecovery}} } \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{ # ....................................................... # Example inspired from Zwick and Velicer (1986, table 2, p. 437) ## ................................................................... unique=0.2; loadings=0.5 zwick1 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings, unique=unique) zwick2 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings, unique=unique) zwick3 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings, unique=unique) zwick4 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings, unique=unique) sat=0.8 ## ................................................................... zwick5 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings, unique=unique) zwick6 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings, unique=unique) zwick7 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings, unique=unique) zwick8 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings, unique=unique) ## ................................................................... # nsubjects <- c(72, 144, 180, 360) # require(psych) # Produce an usual correlation matrix from a congeneric model nsubjects <- 72 mzwick5 <- sim.structure(fx=as.matrix(zwick5), n=nsubjects) mzwick5$r # Factor analysis: recovery of the factor structure iterativePrincipalAxis(mzwick5$model, nFactors=6, communalities="ginv")$loadings iterativePrincipalAxis(mzwick5$r , nFactors=6, communalities="ginv")$loadings factanal(covmat=mzwick5$model, factors=6) factanal(covmat=mzwick5$r , factors=6) # Number of components to retain eigenvalues <- eigen(mzwick5$r)$values aparallel <- parallel(var = length(eigenvalues), subject = nsubjects, rep = 30, quantile = 0.95, model="components")$eigen$qevpea results <- nScree(x = eigenvalues, aparallel = aparallel) results$Components plotnScree(results) # Number of factors to retain eigenvalues.fa <- eigen(corFA(mzwick5$r))$values aparallel.fa <- parallel(var = length(eigenvalues.fa), subject = nsubjects, rep = 30, quantile = 0.95, model="factors")$eigen$qevpea results.fa <- nScree(x = eigenvalues.fa, aparallel = aparallel.fa, model ="factors") results.fa\$Components plotnScree(results.fa) # ...................................................... } \keyword{ multivariate }