New estimation methods for diagnostic classification models

This paper introduces a new class of estimators for cognitive diagnosis models (CDMs) based on the Cressie-Read family of $\varphi$ -divergences. Focusing on the loglinear CDM (LCDM), for which joint maximum likelihood estimation (JMLE) has been shown to be consistent, we propose a joint minimum divergence estimation (JMDE) framework. We establish the consistency of the proposed estimator and derive its asymptotic distribution. Simulation studies are used to compare the finite-sample performance of JMDE and JMLE under ideal conditions and increasingly challenging settings, including different forms of data contamination-such as random response perturbations and structured model misspecification-and varying levels of model complexity. The results indicate that JMDE provides enhanced robustness and improved stability in finite samples under contaminated scenarios. The approach is empirically illustrated, highlighting its practical behavior in applied settings.