\name{nCng}
\alias{nCng}

\title{ Cattell-Nelson-Gorsuch CNG Indices}

\description{
This function computes the \emph{CNG} indices for the eigenvalues of a
correlation/covariance matrix (Gorsuch and Nelson, 1981; Nasser, 2002, p.
400; Zoski and Jurs, 1993, p. 6).
}

\usage{
nCng(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 }
\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 detains about the computation
for each eigenvalue.}
\item{...}{     variable: additionnal parameters to give to the \code{eigenComputes}
function}
}

\details{
Note that the \code{nCng} function is only valid when more than six eigenvalues
are used and that these are obtained in the context of a principal component
analysis. For a factor analysis, some eigenvalues could be negative and
the function will stop and give an error message.

The slope of all possible sets of three adjacent eigenvalues
are compared, so \emph{CNG} indices can be applied only when more than six eigenvalues
are used. The eigenvalue at which the greatest difference between two successive
slopes occurs is the indicator of the number of components/factors to retain.
}

\value{
\item{nFactors}{ numeric: number of factors retained by the CNG procedure. }
\item{details}{  numeric: matrix of the details for each index.}
}

\references{
Gorsuch, R. L. and Nelson, J. (1981). \emph{CNG scree test: an objective procedure
for determining the number of factors}. Presented at the annual meeting of
the Society for multivariate experimental psychology.

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.

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.
}

\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 CNG ANALYSIS

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

results  <- nCng(eig, details=TRUE)
results

plotuScree(eig, main=paste(results\$nFactors,
" factors retained by the CNG procedure",
sep=""))
}

\keyword{ multivariate }