Multiple Sets of Initial Values Method for MLE‐EM and Its Variants in Cognitive Diagnosis Models

Abstract Cognitive diagnosis models (CDMs) are widely used to assess individuals’ latent characteristics, offering detailed diagnostic insights for tailored instructional development. Maximum likelihood estimation using the expectation‐maximization algorithm (MLE‐EM) or its variants, such as the EM algorithm with monotonic constraints and Bayes modal estimation, typically uses a single set of initial values (SIV). The MLE‐EM method is sensitive to initial values, especially when dealing with non‐convex likelihood functions. This sensitivity implies that different initial values may converge to different local maximum likelihood solutions, but SIV does not guarantee a satisfactory local optimum. Thus, we introduced the multiple sets of initial values (MIV) method to reduce sensitivity to the choice of initial values. We compared MIV and SIV in terms of convergence, log‐likelihood values of the converged solutions, parameter recovery, and time consumption under varying conditions of item quality, sample size, attribute correlation, number of initial sets, and convergence settings. The results showed that MIV outperformed SIV in terms of convergence. Applying the MIV method increased the probability of obtaining solutions with higher log‐likelihood values. We provide a detailed discussion of this outcome under small sample conditions in which MIV performed worse than SIV.