Model Diagnostics for Bayesian Networks

Bayesian networks are frequently used in educational assessments primarily for learning about students’ knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A number of aspects of model fit, those of usual interest to practitioners, are assessed using various diagnostic tools. This article suggests a direct data display for assessing overall fit, suggests several diagnostics for assessing item fit, suggests a graphical approach to examine if the model can explain the association among the items, and suggests a version of the Mantel–Haenszel statistic for assessing differential item functioning. Limited simulation studies and a real data application demonstrate the effectiveness of the suggested model diagnostics.