Endogeneity-Aware Cognitive Diagnostic Model for Multidomain Ordinal Assessments

Multidomain assessment batteries generate ordinal item responses that are often summarized through latent attribute profiles. Conventional cognitive diagnostic models (CDMs) provide interpretable measurement models for such profiles, but they typically do not represent directed dependence among latent attributes from distinct domains. We propose an endogeneity-aware cognitive diagnostic model (EACDM) for multivariate ordinal assessments. The model combines a block-structured diagnostic measurement component, in which item groups are linked to domain-specific binary attributes through a block-diagonal Q-matrix, with a logistic structural component, in which one attribute block is regressed on another block and subject-level covariates while accounting for latent classification uncertainty. This formulation yields a parsimonious framework for studying endogenous relationships among diagnostic attributes without collapsing domain-specific measurement structure. We establish identifiability conditions for the Q-matrix, effective loadings, latent-profile probabilities, and structural coefficients, and develop a Markov chain Monte Carlo algorithm for joint estimation of the measurement and structural components. Simulation studies demonstrate accurate recovery of item parameters, latent structures, and structural coefficients for the proposed EACDM, whereas conventional CDMs can fail to recover the ground truth when endogeneity is present. We apply the proposed method to Parkinson's disease data to examine how non-motor latent traits relate to motor impairment profiles.