nMreg.rd
\name{nMreg}
\alias{nMreg}

\title{ Multiple Regression Procedure to Determine the Number of Components/Factors}

\description{
This function computes the \eqn{\beta} indices, like their associated Student
\emph{t} and
probability (Zoski and Jurs, 1993, 1996, p. 445). These three values can be
used as three different
indices for determining the number of components/factors to retain.
}

\usage{
nMreg(x, cor=TRUE, model="components", details=TRUE, ...)
}

\arguments{
\item{x}{       numeric: a \code{vector} of eigenvalues, a \code{matrix} of
correlations or of covariances or a \code{data.frame} of data (eigenFrom)}
\item{cor}{     logical: if \code{TRUE} computes eigenvalues from a correlation
matrix, else from a covariance matrix}
\item{model}{   character: \code{"components"} or \code{"factors"} }
\item{details}{ logical: if \code{TRUE} also returns details about the computation for each eigenvalue.}
\item{...}{     variable: additionnal parameters to give to the \code{eigenComputes}
and \code{cor} or \code{cov} functions}
}

\value{
\item{nFactors}{ numeric: number of components/factors retained by the \emph{MREG} procedures. }
\item{details}{  numeric: matrix of the details for each indices.}
}

\details{
When the associated Student \emph{t} test is applied, the following hypothesis
is considered: \cr

\beta (\lambda_{k+1} \ldots \lambda_p), (k = 3, \ldots, p-3) = 0} \cr

}

\references{
Zoski, K. and Jurs, S. (1993). Using multiple regression to determine the
number of factors to retain in factor analysis. \emph{Multiple Linear Regression
Viewpoints, 20}(1), 5-9.

Zoski, K. and Jurs, S. (1996). An objective counterpart to the visual scree
test for factor analysis: the standard error scree test.
\emph{Educational and Psychological Measurement, 56}(3), 443-451.
}

\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/}
}

\seealso{
}

\examples{
## SIMPLE EXAMPLE OF A MREG ANALYSIS

data(dFactors)
eig      <- dFactors$Raiche$eigenvalues

results  <- nMreg(eig)
results

plotuScree(eig, main=paste(results$nFactors[1], ", ", results$nFactors[2], " or ",
results\$nFactors[3],
" factors retained by the MREG procedures",
sep=""))
}

\keyword{ multivariate }