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Tip revision: 923d0cc1f43c36debbea1f1fb06e4de448065380 authored by Gilles Raiche on 31 August 2019, 09:11:55 UTC
Tip revision: 923d0cc

\title{ Cattell-Nelson-Gorsuch CNG Indices}

  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).

 nCng(x, cor=TRUE, model="components", details=TRUE, ...)

  \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}
  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.

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

    Gilles Raiche \cr
    Centre sur les Applications des Modeles de Reponses aux Items (CAMRI) \cr
    Universite du Quebec a Montreal\cr
    \email{}, \url{}



 eig      <- dFactors$Raiche$eigenvalues

 results  <- nCng(eig, details=TRUE)
 plotuScree(eig, main=paste(results$nFactors,
                            " factors retained by the CNG procedure",

\keyword{ multivariate }

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