Comparing Bayesian Regularized Methods in Q -Matrix Inference Within the Partially Confirmatory Cognitive Diagnosis Modeling Framework

Various Bayesian regularization methods have been incorporated into cognitive diagnosis models to enhance Q-matrix inference. The purpose of implementing regularization is to identify significant parameters while penalizing insignificant ones toward zero, thereby reducing model complexity and promoting a sparser solution. In this study, we aim to: (a) formulate the partially confirmatory cognitive diagnosis modeling (PCCDM) framework under different link functions (probit and logit); (b) compare Bayesian regularization methods for Q-matrix inference within the PCCDM framework; and (c) evaluate the effectiveness of the cut-off-based approach and the Wald-test-based approach for determining the significance of q-entries. The investigation of penalty included spike-and-slab and Least Absolute Shrinkage and Selection Operator. Implemented by Markov chain Monte Carlo estimation using Gibbs sampler, the results were demonstrated from both simulated and real data.