% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/nMreg.r
\name{nMreg}
\alias{nMreg}
\title{Multiple Regression Procedure to Determine the Number of Components/Factors}
\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.}
}
\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.
}
\details{
When the associated Student \emph{t} test is applied, the following
hypothesis is considered: \cr

(1) \eqn{\qquad \qquad H_k: \beta (\lambda_1 \ldots \lambda_k) - \beta
(\lambda_{k+1} \ldots \lambda_p), (k = 3, \ldots, p-3) = 0} \cr
}
\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=""))

}
\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.
}
\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}