Abstract: Covariates play an important role in psychological and educational studies, which can be used as control variables or regulatory factors in modelling. A few studies involve covariates information in Cognitive diagnosis models (CDMs). However, these studies have some issues that need to be solved. First, the current covariate extension models cannot analyze these polytomous responses. Second, the category covariates included in these studies are only dichotomous variables (such as gender). It cannot handle multi-category covariate information, such as grade and family socioeconomic status.
This paper proposed the GPDM-C (The covariate extension of General polytomous diagnosis model) that incorporates both continuous and multi-category covariates in the polytomous response cognitive diagnosis framework. For simplicity, the saturated GPDM-C model was constrained as a reduced model, named the GPDINA-C model. MCMC algorithm was implemented in JAGS software to complete parameter estimation.
In order to evaluate the parameter estimation accuracy of the GPDINA-C model, showing the advantages of incorporatingcovariates in the polytomous responses model, three factors (item quality, test length, and covariates effect size) were considered in a simulation study. The results indicated that: (1) The MCMC algorithm can accurately estimate all GPDINA-C model parameters. (2) Both person parameters and structure parameters recovery of GPDINA-C outperform the recovery of GPDINA.
Finally, an empirical research is applied to examine the performance of the GPDINA-C model in practice. The results indicate that GPDINA-C hada smaller DIC value than the GPDINA model did, which manifests that the GPDINA-C had a better fit for this empirical data. Furthermore, the covariates parameters of the GPDINA-C can infer the influence of covariates on attribute mastery objectively.

Key words: cognitive diagnosis, covariates information, polytomous responses cognitive diagnosis model, MCMC