A Comparison of Joint and Stepwise Dynamic Cognitive Diagnostic Models

Abstract

To extend cognitive diagnostic models (CDMs) to longitudinal settings, stepwise approaches that integrate a CDM model with a latent transition model and covariates are widely used due to their flexibility. Previous research has shown that stepwise estimation can yield biased results, motivating classification-error correction as a means of improving inference over uncorrected stepwise procedures. In this study, we evaluate a unified Bayesian dynamic cognitive diagnostic model that jointly estimates measurement (item parameters, latent attribute profiles) and transition components (transition parameters) in longitudinal settings with covariates. We compare this joint approach with the bias-corrected stepwise latent transition CDM through a Monte Carlo study. Results demonstrate that joint modeling provides more accurate recovery of transition parameters, particularly under limited test length and sample size, underscoring its advantages for longitudinal diagnostic analysis and offering practical guidance for applied researchers.