Bayesian penalization for explanatory cognitive diagnostic models: covariate DINA model and covariate LCDM with the lasso prior

Abstract

AbstractDiagnostic 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 explanatory cognitive diagnostic models (ECDMs) with attribute-level explanatory variables. We proposed the covariate log-linear cognitive diagnostic model (LCDM) and covariate deterministic input, noisy, and gate (DINA) model and compared the models 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 with the ECDMs.