https://github.com/cran/nFactors
Tip revision: 592b098fc786911733da1c1953e58c9d1c2e9517 authored by Gilles Raiche on 10 April 2010, 00:00:00 UTC
version 2.3.3
version 2.3.3
Tip revision: 592b098
nSeScree.rd
\name{nSeScree}
\alias{nSeScree}
\title{ Standard Error Scree and Coefficient of Determination Procedures to
Determine the Number of Components/Factors}
\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.
}
\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}
}
\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.
}
\value{
\item{nFactors}{ numeric: number of components/factors retained by the seScree procedure. }
\item{details}{ numeric: matrix of the details for each index.}
}
\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.
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.
}
\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 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=""))
}
\keyword{ multivariate }