nCng function

Cattell-Nelson-Gorsuch CNG Indices

This function computes the 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, ...)

Arguments

• x: numeric: a vector of eigenvalues, a matrix of correlations or of covariances or a data.frame of data
• cor: logical: if TRUE computes eigenvalues from a correlation matrix, else from a covariance matrix
• model: character: "components" or "factors"
• details: logical: if TRUE also returns detains about the computation for each eigenvalue.
• ...: variable: additionnal parameters to give to the eigenComputes function

Returns

• nFactors: numeric: number of factors retained by the CNG procedure. - details: numeric: matrix of the details for each index.

Details

Note that the 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 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). 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. 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. Multiple Linear Regression Viewpoints, 20(1), 5-9.

See Also

plotuScree, nScree, plotnScree, plotParallel

Author(s)

Gilles Raiche

Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca