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Abstract:
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Statistical inferences based on a single model are criticized for ignoring model uncertainty and overselling faith in model results. Accounting for model uncertainty with Bayesian model averaging (BMA) makes explanatory inference challenging and it may be unclear how a resulting posterior variance captures model uncertainty. An understanding of changes in posterior variances of partial regression coefficients across approaches will help inform choices about when to use BMA. Within the context of all subsets regression, we investigate three strategies: full model averaging, using the entire model set with posterior model probabilities (PMP) as weights; model averaging over a subset of models that include a particular covariate of interest, using re-normalized PMP; and making inference from one model with the largest PMP. For each strategy, we consider different correlations among covariates and signal-to-noise ratios in the data-generating model, and whether or not the data-generating model is in the model set. Counterintuitively, the posterior variance for a model-averaged partial regression coefficient is not always larger when considering more models.
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