An Extension of the DINA Model Using Covariates

Abstract

When students solve problems, their proficiency in a particular subject may influence how well they perform in a similar, but different area of study. For example, studies have shown that science ability may have an effect on the mastery of mathematics skills, which in turn may affect how examinees respond to mathematics items. From this view, it becomes natural to examine the relationship of performance on a particular area of study to the mastery of attributes on a related subject. To examine such an influence, this study proposes a covariate extension to the deterministic input noisy “and” gate (DINA) model by applying a latent class regression framework. The DINA model has been selected for the study as it is known for its parsimony, easy interpretation, and potential extension of the covariate framework to more complex cognitive diagnostic models. In this approach, covariates can be specified to affect items or attributes. Real-world data analysis using the fourth-grade Trends in International Mathematics and Science Study (TIMSS) data showed significant relationships between science ability and attributes in mathematics. Simulation study results showed stable recovery of parameters and latent classes for varying sample sizes. These findings suggest further applications of covariates in a cognitive diagnostic modeling framework that can aid the understanding of how various factors influence mastery of fine-grained attributes.