Using Diagnostic Classification Models to Validate Attribute Hierarchies and Evaluate Model Fit in Bayesian Networks

We investigate the relationship between Bayesian inference networks (BayesNets) and diagnostic classification models (DCMs). Specifically, we demonstrate and empirically examine the equivalency of parameterizations between BayesNets and DCMs. Then, we propose a model-comparison framework for testing the model fit of BayesNets, in which we show how BayesNets are nested within the saturated DCM structural models. Additionally, we show when attributes feature a linear hierarchy, the Hierarchical DCM is nested within both BayesNets and saturated DCMs. The usefulness of proposed framework and model-fit testing strategy was supported by the results of analyzing both simulated and empirical data.