Explanatory Cognitive Diagnostic Models: Incorporating Latent and Observed Predictors

Large-scale educational testing data often contain vast amounts of variables associated with information pertaining to test takers, schools, or access to educational resources-information that can help explain relationships between test taker performance and their learning environment. This study examines approaches to incorporate latent and observed explanatory variables as predictors for cognitive diagnostic models (CDMs). Methods to specify and simultaneously estimate observed and latent variables (estimated using item response theory) as predictors affecting attribute mastery were examined. Real-world data analyses were conducted to demonstrate the application using large-scale international testing data. Simulation studies were conducted to examine the recovery and classification for simultaneously estimating multiple latent (using dichotomous and polytomous items as indicators for the latent construct) and observed predictors for varying sample sizes and number of attributes. Results showed stable parameter recovery and consistency in attribute classification. Implications for latent predictors and attribute specifications are discussed.