The EM Algorithm and Its Variants in Cognitive Diagnostic Models: Comparing Their Propensity for Boundaries, Extremes, Convergence, and Suboptimal Solutions

Choosing suitable estimation methods for cognitive diagnostic models (CDMs) is critical. However, practitioners often face issues like non-convergence, boundary estimates, extreme values, and unstable suboptimal solutions, which affect the accuracy and reliability of parameter estimates. In this study, we compared expectation–maximization (EM), Bayesian modal estimation (BM), their monotonic constraint variants (EMM and BMM), and variational Bayes (VB) methods. A simulation study was conducted, manipulating factors such as sample size (50, 200, 1000), test length (15, 30), item quality (high, low), and attribute distribution (uniform and multivariate normal). The performance was assessed based on the empirical frequency of each issue, the recovery accuracy of the parameters, and the sensitivity to algorithm initialization. The results, analyzed using the generalized deterministic inputs noisy “and” gate model, reveal three main findings. First, an insufficient sample size was identified as a key factor in problems related to parameter estimation. Second, methods that incorporate prior information (BM and VB) exhibited fewer cases of non-convergence and extreme estimates than EM. Third, the sensitivity analysis showed that the stability of solutions was affected by the choice of initial values, emphasizing the need for proper initialization to reduce the risk of becoming trapped in local suboptimal solutions. This systematic comparison demonstrates that no single estimator is universally superior, and the choice depends on practical constraints. Our findings offer evidence-based guidance for selecting context-sensitive methods, thereby improving the validity of CDMs in real-world applications.