##### https://github.com/cran/nFactors
Tip revision: 923d0cc
structureSim.rd
\name{structureSim}
\alias{structureSim}
\title{ Population or Simulated Sample Correlation Matrix from a Given Factor Structure Matrix}

\description{
The \code{structureSim} function returns a population and a sample correlation
matrices from a predefined congeneric factor structure.
}

\usage{
r2limen=0.75, all=FALSE)
}

\arguments{
\item{reppar}{    numeric:   number of replications for the parallel analysis}
\item{repsim}{    numeric:   number of replications of the matrix correlation
simulation}
\item{N}{         numeric:   number of subjects}
\item{quantile}{  numeric:   quantile for the parallel analysis}
\item{model}{     character: \code{"components"} or \code{"factors"} }
\item{adequacy}{  logical:   if \code{TRUE} prints the recovered population
matrix from the factor structure}
\item{details}{   logical:   if \code{TRUE} outputs details of the
\code{repsim} simulations }
\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)}
}

\value{
\item{values}{ the output depends of the logical value of details. If \code{FALSE},
returns only statistics about the eigenvalues: mean, median, quantile,
standard deviation, minimum and maximum. If \code{TRUE},
returns also details about the \code{repsim} simulations.
If \code{adequacy} = \code{TRUE} returns the recovered factor structure}
}

\seealso{
}

\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, table 2, p. 437)
## ...................................................................
nFactors  <- 3
unique    <- 0.2
nsubjects <- 180
repsim    <- 30
zwick     <- generateStructure(var=36, mjc=nFactors, pmjc=12,
unique=unique)
## ...................................................................

# Produce statistics about a replication of a parallel analysis on
# 30 sampled correlation matrices

repsim=repsim, N=nsubjects, quantile=0.5,
model="factors")

repsim=repsim, N=nsubjects, quantile=0.5, all=TRUE)

# Very long execution time that could be used only with model="components"
#                            repsim=repsim, N=nsubjects, quantile=0.5, all=TRUE)

par(mfrow=c(2,1))
plot(x=mzwick,    nFactors=nFactors, index=c(1:14), cex.axis=0.7, col="red")
plot(x=mzwick.fa, nFactors=nFactors, index=c(1:11), cex.axis=0.7, col="red")
par(mfrow=c(1,1))

par(mfrow=c(2,1))
boxplot(x=mzwick,    nFactors=3, cex.axis=0.8, vLine="blue", col="red")
boxplot(x=mzwick.fa, nFactors=3, cex.axis=0.8, vLine="blue", col="red",
xlab="Components")
par(mfrow=c(1,1))
# ......................................................
}
}

\keyword{ multivariate }