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.
Jin et al. (Wed,) studied this question.