Bayesian Penalization for Explanatory Cognitive Diagnostic Model: A Covariate DINA with the Lasso Prior

Diagnostic assessment data obtained from online learning platforms for schools are typically accompanied by student background variables and item responses. To leverage such information for cognitive diagnosis, the present study examines the applicability of the lasso prior for variable selection in a deterministic input, noisy-and-gate (DINA) model with attribute-level explanatory variables. We compared the covariate DINA model with and without the lasso prior using a real-world data analysis and a simulation study. In the real-world data analysis, which used a school-sized sample collected from an online learning platform, we found that the lasso prior selected only relatively large effects without substantially affecting the diagnostic classification and item parameter estimation. In the simulation study, we found that the lasso prior did not degrade the accuracy of the diagnostic classification or parameter estimation. Finally, we discuss the situations in which the lasso prior can be useful and appropriate with the covariate DINA model, its limitation, and the scope for future research.