nSeScree {nFactors}R Documentation

Standard Error Scree and Coeffcient of Determination Procedures to Determine the Number of Components/Factors

Description

This function computes the seScree (S_{Y bullet X}) indices (Zoski and Jurs, 1996) and the coefficient of determination indices of Nelson (2005) R^2 for determining the number of components/factors to retain.

Usage

 nSeScree(x, cor=TRUE, model="components", details=TRUE, r2limen=0.75, ...)
 

Arguments

x numeric: eigenvalues.
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 return detains about the computation for each eigenvalue.
r2limen numeric: criterion value retained for the coefficient of determination indices.
... variable: additionnal parameters to give to the eigenComputes and cor or cov functions

Details

The Zoski and Jurs S_{Y bullet X} index is the standard error of the estimate (predicted) eigenvalues by the regression from the (k+1, ..., p) subsequent rank of the eigenvalues. The standard error is computed as:

(1) qquad qquad S_{Y bullet X} = sqrt{ frac{(λ_k - hat{λ}_k)^2} {p-2} }

A value of 1/p is choosen as the criteria to determine the number of components or factors to retain, p corresponding to the number of variables.

The Nelson R^2 index is simply the multiple regresion coefficient of determination for the k+1, ..., p eigenvalues. Note that Nelson didn't give formal prescription 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

nFactors numeric: number of components/factors retained by the seScree procedure.
details numeric: matrix of the details for each indices.

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

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.

Nelson, L. R. (2005). Some observations on the scree test, and on coefficient alpha. 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. 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. Educational and Psychological Measurement, 56(3), 443-451.

See Also

plotuScree, nScree, plotnScree, 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=""))
 

[Package nFactors version 2.3.1 Index]