A Two-Step Estimation Approach of Latent Class-Item Response Theory Models in the Presence of DIF and Multidimensionality

Estimation of Latent class item response theory (LC-IRT) models is typically performed using full-information maximum likelihood, which may be computationally demanding, susceptible to convergence problems, and subject to interpretational confounding. We propose a two-step estimation approach for unidimensional and multidimensional LC-IRT models with covariates and differential item functioning (DIF). In the first step, the measurement model is estimated, including direct covariate effects on item responses when DIF is part of the final measurement specification. In the second step, covariate effects on latent class membership are estimated while treating the measurement parameters as fixed. We evaluate the two-step estimator through simulation studies and identify the conditions under which it yields low bias, particularly when measurement quality and entropy are adequate. We then apply the proposed approach to data on student performance in statistics.