Polytomous Exploratory Factor Analysis

Whenever your items have three or more ordered response categories (e.g., a 5-point Likert scale). Standard EFA on Pearson correlations treats ordinal scores as continuous, which attenuates correlations and distorts the recovered factor structure. Polytomous EFA using polychoric correlations models the data correctly.

Weighted least squares with mean and variance adjustment (WLSMV, also called robust WLS) is generally recommended because it is distribution-free and performs well even when item distributions are asymmetric. Maximum likelihood is an alternative if the bivariate normality assumption is plausible, but it is more sensitive to distributional violations.

Polychoric correlations are estimated pairwise and require sufficient cell counts at each response-category combination. A minimum of roughly 200 cases is commonly cited, with larger samples (300–500+) strongly preferred, especially when items have many categories or extreme response distributions.

No. Binary (yes/no, correct/incorrect) items require tetrachoric correlations, which are a special case of the polychoric model with exactly two categories. Most software distinguishes between the two; select the appropriate option for your data type.

Both model the relationship between latent traits and ordered categorical responses, and both assume an underlying continuous latent variable. Polytomous EFA is exploratory and does not constrain the number of factors or the item parameters; IRT (e.g., the graded response model) is confirmatory and provides richer item-level diagnostics. They are complementary: polytomous EFA can guide the dimensionality assessment that precedes IRT calibration.