\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 (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 } \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{ \code{\link{plotuScree}}, \code{\link{nScree}}, \code{\link{plotnScree}}, \code{\link{plotParallel}} } \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 }