% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/parallel.R
\name{parallel}
\alias{parallel}
\title{Parallel Analysis of a Correlation or Covariance Matrix}
\usage{
parallel(subject = 100, var = 10, rep = 100, cent = 0.05,
  quantile = cent, model = "components", sd = diag(1, var), ...)
}
\arguments{
\item{subject}{numeric: nmber of subjects (default is 100)}

\item{var}{numeric: number of variables (default is 10)}

\item{rep}{numeric: number of replications of the correlation matrix
(default is 100)}

\item{cent}{depreciated numeric (use quantile instead): quantile of the
distribution on which the decision is made (default is 0.05)}

\item{quantile}{numeric: quantile of the distribution on which the decision
is made (default is 0.05)}

\item{model}{character: \code{"components"} or \code{"factors"}}

\item{sd}{numeric: vector of standard deviations of the simulated variables
(for a parallel analysis on a covariance matrix)}

\item{...}{variable: other parameters for the \code{"mvrnorm"}, \code{corr}
or \code{cov} functions}
}
\value{
\item{eigen}{ Data frame consisting of the mean and the quantile of
the eigenvalues distribution } \item{eigen$mevpea}{ Mean of the eigenvalues
distribution} \item{eigen$sevpea}{ Standard deviation of the eigenvalues
distribution} \item{eigen$qevpea}{ quantile of the eigenvalues distribution}
\item{eigen$sqevpea}{ Standard error of the quantile of the eigenvalues
distribution} \item{subject}{ Number of subjects} \item{variables}{ Number
of variables} \item{centile}{ Selected quantile} Otherwise, returns a
summary of the parallel analysis.
}
\description{
This function gives the distribution of the eigenvalues of correlation or a
covariance matrices of random uncorrelated standardized normal variables.
The mean and a selected quantile of this distribution are returned.
}
\details{
Note that if the decision is based on a quantile value rather than on the
mean, care must be taken with the number of replications (\code{rep}). In
fact, the smaller the quantile (\code{cent}), the bigger the number of
necessary replications.
}
\examples{

## SIMPLE EXAMPLE OF A PARALLEL ANALYSIS
## OF A CORRELATION MATRIX WITH ITS PLOT
 data(dFactors)
 eig      <- dFactors$Raiche$eigenvalues
 subject  <- dFactors$Raiche$nsubjects
 var      <- length(eig)
 rep      <- 100
 quantile <- 0.95
 results  <- parallel(subject, var, rep, quantile)

 results

## IF THE DECISION IS BASED ON THE CENTILE USE qevpea INSTEAD
## OF mevpea ON THE FIRST LINE OF THE FOLLOWING CALL
 plotuScree(x    = eig,
            main = "Parallel Analysis"
            )

 lines(1:var,
       results$eigen$qevpea,
       type="b",
       col="green"
       )


## ANOTHER SOLUTION IS SIMPLY TO
 plotParallel(results)

}
\references{
Drasgow, F. and Lissak, R. (1983) Modified parallel analysis: a
procedure for examining the latent dimensionality of dichotomously scored
item responses. \emph{Journal of Applied Psychology, 68}(3), 363-373.

Hoyle, R. H. and Duvall, J. L. (2004). Determining the number of factors in
exploratory and confirmatory factor analysis.  In D. Kaplan (Ed.): \emph{The
Sage handbook of quantitative methodology for the social sciences}. Thousand
Oaks, CA: Sage.

Horn, J. L. (1965). A rationale and test of the number of factors in factor
analysis. \emph{Psychometrika, 30}, 179-185.
}
\seealso{
\code{\link{plotuScree}}, \code{\link{nScree}},
\code{\link{plotnScree}}, \code{\link{plotParallel}}
}
\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}
}
\keyword{multivariate}