Model selection posterior predictive model checking via limited-information indices for Bayesian diagnostic classification modeling

This study will advance knowledge in three ways: extend the knowledge of Bayesian model checking for diagnostic cognition, provide researchers with an alternative model selection procedure in Bayesian Diagnostic Classification Models, and provide a toolkit for Bayesian model comparisons for categorical responses. This project will formulate a novel Bayesian goodness-of-fit assessment based on limited-information tests, which can be easily extended to other frequently used models in social science fields such as Item Response Theory models and Latent Class Models with nominal responses. This research provides the criteria for Bayesian model checking, which can facilitate future research on Bayesian model comparison. The new approach could also facilitate the use of Bayesian DCMs with sparse data tables in a variety of testing scenarios such as large-scale assessment or adaptive testing. The functions built for this project will be available via the blatent package in R for other researchers to access.

Advances in the Bayesian model-data fit approach will have implications for a broad spectrum of applications. The decision makers of large-scale assessment programs can employ the method to build a more flexible theoretical structure that fits data better so that teachers could identify students’ mastery of different skills more accurately. Students then can be matched with learning resources they need to ensure their academic success in the classroom. In psychiatric evaluation, psychiatrists/ psychologists can learn patients’ presence/absence of disorders better with the help of better fitted Bayesian DCMs.