Covariate-Adjusted Generalized Factor Analysis with Application to Testing Fairness

Music City Center 

Latent variable models are popularly used to measure latent factors from large-scale assessment data. Beyond understanding latent factors, the covariate effect on responses controlling for latent factors is also of great scientific interest and has wide applications, such as evaluating testing fairness, where the covariate effect reflects whether a test question is biased toward certain individual characteristics (e.g., gender), controlling for their latent abilities. However, the large sample sizes and high dimensional responses pose challenges to developing efficient methods and drawing valid inferences. Moreover, to accommodate the discrete responses, nonlinear factor models are often assumed, adding further complexity. To address these challenges, we consider a covariate-adjusted generalized factor model and develop novel and interpretable conditions to address the identifiability issue. Based on the identifiability conditions, we propose a joint maximum likelihood estimation method and establish estimation consistency and asymptotic normality results for the covariate effects. Furthermore, we derive estimation and inference results for latent factors and factor loadings.

Generalized factor model

Covariate adjustment

Large-scale testing 

Section on Statistical Learning and Data Science