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

Samuel Green1, Yuning Xu1, Marilyn S Thompson1

  • 1Arizona State University, Tempe, AZ, USA.

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Revised Parallel Analysis (R-PA) generally offers stronger results than the Comparison Data Method (CDM) for determining the number of factors in exploratory factor analysis, though both methods show high accuracy.

Keywords:
exploratory factor analysisparallel analysispsychometrics

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Area of Science:

  • Psychometrics
  • Statistical Analysis
  • Exploratory Factor Analysis

Background:

  • Traditional Parallel Analysis (PA) uses an incorrect reference distribution for assessing eigenvalues in exploratory factor analysis.
  • Accurate factor determination requires comparing sample data to a proper reference distribution.
  • Revised PA (R-PA) and Comparison Data Method (CDM) utilize appropriate reference distributions.

Purpose of the Study:

  • To compare the accuracy of R-PA and CDM in determining the number of factors.
  • To evaluate these methods under various conditions including factor structure, loadings, correlations, and sample size.

Main Methods:

  • Monte Carlo simulations were employed to assess the performance of R-PA and CDM.
  • Method accuracies were manipulated by varying key parameters of the factor analysis model.
  • Eigenvalue comparison was central to assessing the number of factors.

Main Results:

  • Both R-PA and CDM demonstrated high accuracy (>94.5%) in conditions where CDM outperformed R-PA.
  • CDM showed slightly higher accuracy (1.6% difference) in 17 simulated conditions.
  • R-PA exhibited significantly higher accuracy (12.1% difference) in the remaining 25 conditions.

Conclusions:

  • R-PA generally provides more robust results for determining the number of factors compared to CDM.
  • Further research is needed to fully understand the performance of these methods.
  • Future studies should explore effect size statistics to complement hypothesis testing in R-PA and CDM.