PARALLEL {EFA.dimensions}

Parallel analysis of eigenvalues (random data only)

Description

Generates eigenvalues and corresponding percentile values for random data sets with specified numbers of variables and cases.

Usage

PARALLEL(Nvars, Ncases, Ndatasets=100, extraction='PCA', percentile='95',
         corkind='pearson', verbose=TRUE, factormodel)

Arguments

Nvars

The number of variables.

Ncases

The number of cases.

Ndatasets

An integer indicating the # of random data sets for parallel analyses.

extraction

The factor extraction method. The options are: 'PAF' for principal axis / common factor analysis; 'PCA' for principal components analysis. 'image' for image analysis.

percentile

An integer indicating the percentile from the distribution of parallel analysis random eigenvalues. Suggested value: 95

corkind

The kind of correlation matrix to be used for the random data. The options are 'pearson', 'kendall', and 'spearman'.

verbose

Should detailed results be displayed in console? TRUE (default) or FALSE

factormodel

(Deprecated.) Use 'extraction' instead.

Details

This procedure for determining the number of components or factors involves comparing the eigenvalues derived from an actual data set to the eigenvalues derived from the random data. In Horn's original description of this procedure, the mean eigenvalues from the random data served as the comparison baseline, whereas the more common current practice is to use the eigenvalues that correspond to the desired percentile (typically the 95th) of the distribution of random data eigenvalues. Factors or components are retained as long as the ith eigenvalue from the actual data is greater than the ith eigenvalue from the random data. This function produces only random data eigenvalues and it does not take real data as input. See the RAWPAR function in this package for parallel analyses that also involve real data.

The PARALLEL function permits users to specify PCA or PAF or image as the factor extraction method. Principal components eigenvalues are often used to determine the number of common factors. This is the default in most statistical software packages, and it is the primary practice in the literature. It is also the method used by many factor analysis experts, including Cattell, who often examined principal components eigenvalues in his scree plots to determine the number of common factors. Principal components eigenvalues are based on all of the variance in correlation matrices, including both the variance that is shared among variables and the variances that are unique to the variables. In contrast, principal axis eigenvalues are based solely on the shared variance among the variables. The procedures are qualitatively different. Some therefore claim that the eigenvalues from one extraction method should not be used to determine the number of factors for another extraction method. The PAF option in the extraction argument for the PARALLEL function was included solely for research purposes. It is best to use PCA as the extraction method for regular data analyses.

Value

Random data eigenvalues

Author(s)

Brian P. O'Connor

References

Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.

O'Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. Behavior Research Methods, Instrumentation, and Computers, 32, 396-402.

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.

Examples

PARALLEL(Nvars=15, Ncases=250, Ndatasets=100, extraction='PCA', percentile=95,
         corkind='pearson', verbose=TRUE)