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

Although full-information maximum likelihood (FIML) estimation is widely used for diagnostic classification models (DCMs), its computational efficiency deteriorates sharply in high-dimensional settings. This scalability challenge is increasingly critical as DCMs are applied to large-scale assessments, psychological testing and longitudinal studies involving many attributes. We propose a composite marginal likelihood (CML) estimation approach via expectation-maximization (EM) algorithm (CML-EM) for higher-order DCMs (HO-DCMs) as an alternative. The central premise is that, because response probabilities depend only on the attributes specified by the Q-matrix and because of the conditional independence assumption of HO-DCMs, the full likelihood can be partitioned into low-dimensional subsets of items and attributes. This reduces both attribute and response spaces in the E-step to that of each subset, resulting in substantial computational gains that become more pronounced with larger sample sizes and numbers of attributes. We also introduce a subset-construction procedure that ensures both efficiency and feasibility of CML-EM and present two methods for attribute classification. Simulation results demonstrate that CML-EM is significantly faster than FIML while maintaining accurate parameter recovery and acceptable classification performance. The practical utility of the method is further illustrated through an empirical application to a high-dimensional personality assessment.