Composite marginal likelihood estimation of higher-order diagnostic classification models under high dimensionality

Area of Science:

• Psychometrics
• Statistical modeling
• Computational statistics

Background:

• Full-information maximum likelihood (FIML) is standard for diagnostic classification models (DCMs) but computationally inefficient for high-dimensional data.
• The scalability of DCMs is crucial for large-scale assessments, psychological testing, and longitudinal studies with many attributes.

Purpose of the Study:

• To introduce a Composite Marginal Likelihood estimation via Expectation-Maximization (CML-EM) algorithm as an efficient alternative for higher-order DCMs (HO-DCMs).
• To address the computational challenges of FIML in high-dimensional settings.

Main Methods:

• Proposed CML-EM algorithm for HO-DCMs, leveraging the partitioning of the full likelihood into low-dimensional subsets.
• Developed a subset-construction procedure for efficiency and feasibility.
• Introduced two methods for attribute classification.

Main Results:

• CML-EM demonstrated significant speed improvements over FIML in simulations.
• The method maintained accurate parameter recovery and acceptable classification performance.
• Empirical application confirmed practical utility in a high-dimensional personality assessment.

Conclusions:

• CML-EM offers a computationally efficient and accurate alternative for estimating HO-DCMs, particularly in high-dimensional applications.
• The proposed method enhances the scalability of DCMs for complex data structures.