% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/structureSim.r
\name{structureSim}
\alias{structureSim}
\title{Population or Simulated Sample Correlation Matrix from a Given Factor
Structure Matrix}
\usage{
structureSim(fload, reppar = 30, repsim = 100, N, quantile = 0.95,
  model = "components", adequacy = FALSE, details = TRUE,
  r2limen = 0.75, all = FALSE)
}
\arguments{
\item{fload}{matrix: loadings of the factor structure}

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

\dontrun{
# .......................................................
# Example inspired from Zwick and Velicer (1986, table 2, p. 437)
## ...................................................................
 nFactors  <- 3
 unique    <- 0.2
 loadings  <- 0.5
 nsubjects <- 180
 repsim    <- 30
 zwick     <- generateStructure(var=36, mjc=nFactors, pmjc=12,
                                loadings=loadings,
                                unique=unique)
## ...................................................................

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

 mzwick.fa <-  structureSim(fload=as.matrix(zwick), reppar=30,
                            repsim=repsim, N=nsubjects, quantile=0.5,
                            model="factors")

 mzwick    <-  structureSim(fload=as.matrix(zwick), reppar=30,
                            repsim=repsim, N=nsubjects, quantile=0.5, all=TRUE)

# Very long execution time that could be used only with model="components"
# mzwick    <-  structureSim(fload=as.matrix(zwick), reppar=30,
#                            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))
# ......................................................
 }

}
\references{
Raiche, G., Walls, T. A., Magis, D., Riopel, M. and Blais, J.-G. (2013). Non-graphical solutions
for Cattell's scree test. Methodology, 9(1), 23-29.

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.
}
\seealso{
\code{\link{principalComponents}},
\code{\link{iterativePrincipalAxis}}, \code{\link{rRecovery}}
}
\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}