Parallel Analysis with Categorical Variables: Impact of Category Probability Proportions on Dimensionality Assessment Accuracy

Parallel analysis (PA) is regarded as one of the most accurate methods to determine the number of factors underlying a set of variables. Commonly, PA is performed on the basis of the variables' product-moment correlation matrix. To improve dimensionality assessments for dichotomous or ordered categorical variables, it has been proposed to replace product-moment correlations with more appropriate coefficients, such as tetrachoric or polychoric correlations. While similar modifications have proven useful for various factor analytic approaches, PA results were not consistently improved. The present article outlines a main reason for this result. Specifically, it explains the dependency of PA results on differing proportions of category probabilities when using tetrachoric or polychoric correlations and shows how to adjust for it by generating appropriate reference eigenvalues. The accuracy of dimensionality assessments of PA accounting for category probability proportions versus not accounting for them is investigated using simulation studies. The results show that the category probability adjusted approach distinctly improves dimensionality assessments. (PsycINFO Database Record (c) 2019 APA, all rights reserved).