\name{eigenBootParallel} \alias{eigenBootParallel} \title{ Bootstrapping of the Eigenvalues From a Data Frame} \description{ The \code{eigenBootParallel} function samples observations from a \code{data.frame} to produce correlation or covariance matrices from which eigenvalues are computed. The function returns statistics about these bootstrapped eigenvalues. Their means or their quantile could be used later to replace the eigenvalues inputted to a parallel analysis. The \code{eigenBootParallel} can also compute random eigenvalues from empirical data by column permutation (Buja and Eyuboglu, 1992). } \usage{ eigenBootParallel(x, quantile=0.95, nboot=30, option="permutation", cor=TRUE, model="components", ...) } \arguments{ \item{x}{ data.frame: data from which a correlation matrix will be obtained} \item{quantile}{ numeric: eigenvalues quantile to be reported } \item{nboot}{ numeric: number of bootstrap samples } \item{option}{ character: \code{"permutation"} or \code{"bootstrap"}} \item{cor}{ logical: if \code{TRUE} computes eigenvalues from a correlation matrix, else from a covariance matrix (\code{eigenComputes})} \item{model}{ character: bootstraps from a principal component analysis (\code{"components"}) or from a factor analysis (\code{"factors"}) } \item{...}{ variable: additionnal parameters to give to the \code{cor} or \code{cov} functions} } \value{ \item{values}{ data.frame: mean, median, quantile, standard deviation, minimum and maximum of bootstrapped eigenvalues } } \seealso{ \code{\link{principalComponents}}, \code{\link{iterativePrincipalAxis}}, \code{\link{rRecovery}} } \references{ Buja, A. and Eyuboglu, N. (1992). Remarks on parallel analysis. \emph{Multivariate Behavioral Research, 27}(4), 509-540. 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 from the iris data eigenvalues <- eigenComputes(x=iris[,-5]) # Permutation parallel analysis distribution aparallel <- eigenBootParallel(x=iris[,-5], quantile=0.95)$quantile # Number of components to retain results <- nScree(x = eigenvalues, aparallel = aparallel) results$Components plotnScree(results) # ...................................................... # ...................................................... # Bootstrap distributions study of the eigenvalues from iris data # with different correlation methods eigenBootParallel(x=iris[,-5],quantile=0.05, option="bootstrap",method="pearson") eigenBootParallel(x=iris[,-5],quantile=0.05, option="bootstrap",method="spearman") eigenBootParallel(x=iris[,-5],quantile=0.05, option="bootstrap",method="kendall") } \keyword{ multivariate }