In educational measurement, cognitive diagnosis models have been developed to allow assessment of specific skills that are needed to perform tasks. Skill knowledge is characterized as present or absent and represented by a vector of binary indicators, or the skill set profile. After determining which skills are needed for each assessment item, a model is specified for the relationship between item responses and skill set profiles. Cognitive diagnosis models are often used for diagnosis, that is, for classifying students into the different skill set profiles. Generally, cognitive diagnosis models do not exploit student covariate information. However, investigating the effects of student covariates, such as gender, SES, or educational interventions, on skill knowledge mastery is important in education research, and covariate information may improve classification of students to skill set profiles. We extend a common cognitive diagnosis model, the DINA model, by modeling the relationship between the latent skill knowledge indicators and covariates. The probability of skill mastery is modeled as a logistic regression model, possibly with a student-level random intercept, giving a higher-order DINA model with a latent regression. Simulations show that parameter recovery is good for these models and that inclusion of covariates can improve skill diagnosis. When applying our methods to data from an online tutor, we obtain reasonable and interpretable parameter estimates that allow more detailed characterization of groups of students who differ in their predicted skill set profiles. Copyright Springer Science+Business Media New York 2013
