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Abstract:
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Measures of fit such as assortments of R square's and deviance are functions of model parameters. Uncertainty about the parameters induces uncertainty about the fit measures. The common Bayesian practice is to integrate out the parameters. Stronger inference can be obtained by deriving the distribution of the fit measures from it the constituent parameters. Then the model fit can be estimated by the Bayes estimate of fit under a loss function and/or a posterior interval. Such an inference requires stochastic dominance of the measure of fit for the model over the measures of fit for all of its submodels. We provide algorithms for computing, posterior distributions of fit measures for a various statistical problems including linear regression, contingency table analysis, logit analysis, canonical correlation, and linear structural equations.
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