Using exploratory factor analysis to determine the dimensionality of discrete responses

Exploratory factor analysis (EFA) is commonly used to determine the dimensionality of continuous data. In a simulation study we investigate its usefulness with discrete data. We vary response scales (continuous, dichotomous, polytomous), factor loadings (medium, high), sample size (small, large), and factor structure (simple, complex). For each condition, we generate 1,000 data sets and apply EFA with 5 estimation methods (maximum likelihood [ML] of covariances, ML of polychoric correlations, robust ML, weighted least squares [WLS], and robust WLS) and 3 fit criteria (chi-square test, root mean square error of approximation, and root mean square residual). The various EFA procedures recover more factors when sample size is large, factor loadings are high, factor structure is simple, and response scales have more options. Robust WLS of polychoric correlations is the preferred method, as it is theoretically justified and shows fewer convergence problems than the other estimation methods.