A Bayesian Sampling Approach to Regression Model Checking

A necessary step in any regression analysis is checking the fit of the model to the data. Graphical methods are often employed to allow visualization of features that the data should exhibit if the model was to hold. Judging whether such features are present or absent in any particular diagnostic plot can be problematic. In this article I take a Bayesian approach to aid in this task. The “unusualness” of some data with respect to a model can be assessed using the predictive distribution of the data under the model; an alternative is to use the posterior predictive distribution. Both approaches can be given a sampling interpretation that can then be utilized to enhance regression diagnostic plots such as marginal model plots.