How to Perform an Exploratory Factor Analysis of Ordinal Data using R

Factor analysis of ordinal data requires special attention because ordinal variables, while ranked, lack equidistant intervals between categories, violating assumptions of traditional factor analysis methods that rely on Pearson correlations and normality. Treating ordinal data as continuous can lead to misleading results, as the true structure of the data might not be accurately represented. To address these challenges, specialized approaches are necessary to model the underlying latent variables while respecting the ordinal nature of the data. In R, packages like psych and homals provide robust solutions. The psych package uses polychoric correlations to estimate relationships between ordinal variables, enabling accurate exploratory factor analysis (EFA) through methods such as minimum residual (minres) or maximum likelihood estimation. Meanwhile, the homals package employs nonlinear factor analysis, ideal for ordinal or nominal data, by transforming variables to optimize the fit in a lower-dimensional space. This method extracts meaningful latent factors while accommodating nonlinear relationships and provides joint plot visualization for interpretability. Both approaches address the unique challenges of ordinal data, ensuring valid and meaningful insights.

Factor analysis of ordinal data in R can be effectively performed using packages like psych and homals, each tailored for different analytical needs. The psych package leverages polychoric correlations to address the ordinal nature of data, enabling robust exploratory factor analysis (EFA) through techniques like minimum residual (minres) or maximum likelihood estimation. It ensures accurate modeling of the relationships among ordinal variables by considering the underlying continuous latent structure. In contrast, the homals package employs nonlinear factor analysis, ideal for ordinal or nominal data, by transforming variables to optimize the fit in a lower-dimensional space. This method extracts meaningful latent factors while accommodating nonlinear relationships, and it provides a joint plot visualization for interpretability. Both approaches offer complementary strengths, with psych excelling in latent trait analysis and homals providing flexibility for nonlinear structures.

The R codes used in this video are posted in the Comments.