A Copula Model for Residual Dependency in DINA Model

Cognitive diagnosis models (CDMs) have been received the increasing attention by educational and psychological assessment. In practice, most CDMs are not robust to violations of local item independence. Many approaches have been proposed to deal with the local item dependence (LID), such as conditioning on other responses and additional random effects (Hansen In Hierarchical item response models for cognitive diagnosis. University of California, LA, 2013); however, these have some drawbacks, such as non-reproducibility of marginal probabilities and interpretation problem. (Braeken et al. In Psychometrika 72(3): 393–411 2007) introduced a new class of marginal models that makes use of copula functions to capture the residual dependence in item response models. In this paper, we applied the copula methodology to model the item dependencies in DINA model. It is shown that the proposed copula model could overcome some of the dependency problems in CDMs, and the estimated model parameters recovered well through simulations. Furthermore, we have extended the R package CDM to fit the proposed copula DINA model.