Relative Accuracy of Two Modified Parallel Analysis Methods that Use the Proper Reference Distribution

Educational and Psychological Measurement
Samuel B GreenMarilyn S Thompson

Abstract

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The proper reference distribution of eigenvalues assesses the kth factor based on comparison datasets with k-1 underlying factors. Two methods that use the proper reference distribution are revised PA (R-PA) and the comparison data method (CDM). We compare the accuracies of these methods using Monte Carlo methods by manipulating the factor structure, factor loadings, factor correlations, and number of observations. In the 17 conditions in which CDM was more accurate than R-PA, both methods evidenced high accuracies (i.e.,>94.5%). In these conditions, CDM had slightly higher accuracies (mean difference of 1.6%). In contrast, in the remaining 25 conditions, R-PA evidenced higher accuracies (mean difference of 12.1%, and considerably higher for some conditions). We consider these findings in conjunction with previous research investigating PA methods and concluded that R-PA tends to offer somewh...Continue Reading

References

Jan 11, 2012·Psychometrika·Robert I Jennrich, Peter M Bentler
Sep 21, 2013·Multivariate Behavioral Research·Steven P Reise
Jul 1, 2008·Multivariate Behavioral Research·John Ruscio, Walter Kaczetow
Jan 1, 1988·Multivariate Behavioral Research·D Rindskopf, T Rose
Oct 1, 1992·Multivariate Behavioral Research·A Buja, N Eyuboglu
Feb 1, 2016·Educational and Psychological Measurement·Samuel B GreenRoy Levy

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Citations

Jan 15, 2019·Educational and Psychological Measurement·Yan XiaMarilyn S Thompson

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Methods Mentioned

BETA
PCAs
PCA

Software Mentioned

GenData
SAS
CDM
MT
PA
R

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