Factor Analysis of Ordinal Data and the Number of Response Categories

Abstract

Compared to the test factor model underlying factor analysis of continuous data, exploratory item factor analysis of ordinal data has received little attention. We investigated the effect of the number and distribution of response categories on several exploratory item factor analysis outcomes including congruence coefficients and bias between the original and reproduced correlation matrices among others. Data were simulated for various conditions including: simplicity of factor structure (simple/complex), factor correlations (uncorrelated, minimally correlated, moderately correlated), sample size (60, 150, 300, 750), number of response categories (2, 3, 4, 5, 6, 7), and shape of response distribution (uniform, symmetrical, skewed). We used several criteria to investigate fit including RMSE, bias, etc. We conducted MANOVA followed by univariate ANOVAs and found that sample size had the most impact on the congruence coefficient and explained 45% of the variance. Relatedly, factor structure explained 32% of the variance in bias in correlations between the two matrices. The most impact for the number and shape of response categories was found on RMSE. Implications for practice, limitations, and directions for future research were discussed.