nMreg {nFactors}R Documentation

Multiple Regression Procedure to Determine the Number of Components/Factors

Description

This function computes the β indices, like their associated Student t and probability (Zoski and Jurs, 1993, 1996, p. 445). These three values can be used as three different indices for determining the number of components/factors to retain.

Usage

 nMreg(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 (eigenFrom)
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 eigenvalues.
... variable: additionnal parameters to give to the eigenComputes and cor or cov functions

Details

When the associated Student t test is applied, the following hypothesis is considered:

(1) qquad qquad H_k: β (λ_1 ... λ_k) - β (λ_{k+1} ... λ_p), (k = 3, ..., p-3) = 0

Value

nFactors numeric: number of components/factors retained by the MREG procedures.
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

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 visual scree test for factor analysis: the standard error scree test. Educational and Psychological Measurement, 56(3), 443-451.

See Also

plotuScree, nScree, plotnScree, plotParallel

Examples

## SIMPLE EXAMPLE OF A MREG ANALYSIS

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

 results  <- nMreg(eig)
 results

 plotuScree(eig, main=paste(results$nFactors[1], ", ",
                            results$nFactors[2], " or ",
                            results$nFactors[3],
                            " factors retained by the MREG procedures",
                            sep=""))
 

[Package nFactors version 2.3.1 Index]