% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/generateStructure.r
\name{generateStructure}
\alias{generateStructure}
\title{Generate a Factor Structure Matrix}
\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{
values  numeric matrix: factor structure
}
\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.
}
\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   <- psych::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)
# ......................................................


}
\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}
\cr \cr David Magis \cr Departement de mathematiques \cr Universite de Liege
\cr \email{David.Magis@ulg.ac.be}
}
\keyword{multivariate}