% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/nSeScree.r
\name{nSeScree}
\alias{nSeScree}
\title{Standard Error Scree and Coefficient of Determination Procedures to
Determine the Number of Components/Factors}
\usage{
nSeScree(x, cor = TRUE, model = "components", details = TRUE,
  r2limen = 0.75, ...)
}
\arguments{
\item{x}{numeric: eigenvalues.}

\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{r2limen}{numeric: criterion value retained for the coefficient of
determination indices.}

\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 seScree procedure. } \item{details}{ numeric: matrix of the details for
each index.}
}
\description{
This function computes the \emph{seScree} (\eqn{S_{Y \bullet X}}) indices
(Zoski and Jurs, 1996) and the coefficient of determination indices of
Nelson (2005) \eqn{R^2} for determining the number of components/factors to
retain.
}
\details{
The Zoski and Jurs \eqn{S_{Y \bullet X}} index is the standard error of the
estimate (predicted) eigenvalues by the regression from the \eqn{(k+1,
\ldots, p)} subsequent ranks of the eigenvalues. The standard error is
computed as:

(1) \eqn{\qquad \qquad S_{Y \bullet X} = \sqrt{ \frac{(\lambda_k -
\hat{\lambda}_k)^2} {p-2} } } \cr

A value of \eqn{1/p} is choosen as the criteria to determine the number of
components or factors to retain, \emph{p} corresponding to the number of
variables.

The Nelson \eqn{R^2} index is simply the multiple regresion coefficient of
determination for the \eqn{k+1, \ldots, p} eigenvalues.  Note that Nelson
didn't give formal prescriptions for the criteria for this index. He only
suggested that a value of 0.75 or more must be considered. More is to be
done to explore adequate values.
}
\examples{

## SIMPLE EXAMPLE OF SESCREE AND R2 ANALYSIS

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

 results  <- nSeScree(eig)
 results

 plotuScree(eig, main=paste(results$nFactors[1], " or ", results$nFactors[2],
                            " factors retained by the sescree and R2 procedures",
                            sep=""))

}
\references{
Nasser, F. (2002). The performance of regression-based
variations of the visual scree for determining the number of common factors.
\emph{Educational and Psychological Measurement, 62(3)}, 397-419.

Nelson, L. R. (2005). Some observations on the scree test, and on
coefficient alpha. \emph{Thai Journal of Educational Research and
Measurement, 3(1)}, 1-17.

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.

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 visuel scree
test for factor analysis: the standard error scree. \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}