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The EM Algorithm and Its Variants in Cognitive Diagnostic Models: Comparing Their Propensity for Boundaries,
Yue Zhao1, Tao Xin1, Yanlou Liu2
1Collaborative Innovation Center of Assessment for Basic Education Quality, Beijing Normal University, Beijing, China.
Applied Psychological Measurement
|June 25, 2026
Summary
Choosing the right estimation method for cognitive diagnostic models (CDMs) is crucial. Bayesian modal estimation (BM) and variational Bayes (VB) methods show better performance than expectation-maximization (EM) by reducing estimation issues, especially with smaller sample sizes.
Area of Science:
- Psychometrics
- Educational Measurement
- Statistical Modeling
Background:
- Cognitive Diagnostic Models (CDMs) are essential for understanding student mastery of specific skills.
- Parameter estimation in CDMs can suffer from convergence issues, boundary estimates, and unstable solutions.
- Selecting appropriate estimation methods is critical for accurate and reliable CDM results.
Purpose of the Study:
- To compare the performance of different estimation methods for CDMs.
- To identify factors influencing estimation problems in CDMs.
- To provide guidance on selecting optimal estimation methods for practical applications.
Main Methods:
- A simulation study compared Expectation-Maximization (EM), Bayesian Modal Estimation (BM), their monotonic variants (EMM, BMM), and Variational Bayes (VB).
- Factors manipulated included sample size, test length, item quality, and attribute distribution.
- Performance was evaluated by issue frequency, parameter recovery accuracy, and sensitivity to initialization.
Main Results:
- Insufficient sample size was a primary driver of parameter estimation problems.
- Bayesian methods (BM, VB) demonstrated fewer non-convergence and extreme estimate issues compared to EM.
- Algorithm initialization significantly impacted solution stability, highlighting the need for careful value selection.
Conclusions:
- No single estimation method is universally superior for CDMs; selection depends on specific constraints.
- Bayesian approaches offer advantages in stability and convergence over EM, particularly with limited data.
- Evidence-based guidance is provided for choosing context-sensitive estimation methods to enhance CDM validity.
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