Model-averaged Wald confidence intervals

The process of model averaging has become increasingly popular as a method for performing inference in the presence of model uncertainty. In the frequentist setting, a model-averaged estimate of a parameter is calculated as the weighted sum of single-model estimates, often using weights derived from an information criterion such as AIC or BIC. A standard method for calculating a model-averaged confidence interval is to use a Wald interval centered around the model-averaged estimate. We propose a new method for construction of a model-averaged Wald confidence interval, based on the idea of model averaging tail areas of the sampling distributions of the single-model estimates. We use simulation to compare the performance of the new method and existing methods, in terms of coverage rate and interval width. The new method consistently outperforms existing methods in terms of coverage, often for little increase in the interval width. We also consider choice of model weights, and find that AIC weights are preferable to either AICc or BIC weights in terms of coverage.