A novel generalized model framework of diagnostic classification models for multiple-choice items

This study introduces a generalized model framework for multiple-choice diagnostic classification models (MC-DCMs) called the multiple-choice log-linear cognitive diagnostic model (MC-LCDM). The framework can represent various MC-DCMs as submodels through appropriate parameter constraints, analogous to the role of the LCDM and G-DINA models in dichotomous response DCMs. The MC-LCDM provides a unified perspective on existing models and aids in exploring new submodels. As with other generalized models, it can minimize the impact of model misspecification when sufficient sample sizes and computational resources are available. Simulation studies indicated that the submodels within the MC-LCDM framework accurately recovered true examinee and item parameter values, while an empirical study further demonstrated that including intercept parameters improved model fit and addressed previously observed diagnostic biases. These findings underscore the comprehensive and flexible nature of the MC-LCDM, thereby enhancing both theoretical understanding and practical applicability.