Bayesian Model Comparison and Model Checking

This chapter introduces various Bayesian statistics for hypothesis testing and model comparison and provides some statistical methods for assessment of the goodness of fit of the posited model and for model diagnosis. In Bayesian approach, the chapter considers the issue of hypothesis testing as model comparison, mainly because a hypothesis can be represented via a specific model. In addition to the Bayes factor, the chapter introduces several other Bayesian statistics for model comparison, namely the Bayesian information criterion (BIC), Akaike information criterion (AIC), deviance information criterion (DIC), and the Lv-measure, a criterion-based statistic. The chapter includes discussions related to path sampling and WinBUGS for computing this statistic and provides an application of the methodology to SEMs with fixed covariates. It gives some other methods for model comparison with an illustrative example. The chapter discusses methods for model checking and goodness of fit. Controlled Vocabulary Terms Akaike information criterion; Bayesian information criterion; covariate; deviance information criterion; sampling; WinBUGS