% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/nCng.r
\name{nCng}
\alias{nCng}
\title{Cattell-Nelson-Gorsuch CNG Indices}
\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}
}
\value{
\item{nFactors}{ numeric: number of factors retained by the CNG
procedure. } \item{details}{ numeric: matrix of the details for each index.}
}
\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).
}
\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.
}
\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=""))

}
\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.
}
\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}