nFactors (version 2.4.1.1)

nMreg: Multiple Regression Procedure to Determine the Number of Components/Factors

Description

This function computes the \(\beta\) 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, ...)

Value

nFactors

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

details

numeric: matrix of the details for each indices.

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 returns details about the computation for each eigenvalue.

...

variable: additionnal parameters to give to the eigenComputes and cor or cov functions

Author

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal

Details

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

(1) \(\qquad \qquad H_k: \beta (\lambda_1 \ldots \lambda_k) - \beta (\lambda_{k+1} \ldots \lambda_p), (k = 3, \ldots, p-3) = 0\)

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=""))