Commonly in applied statistics, there is some uncertainty as to which explanatory variables should be included in the model. Frequentist model averaging has been proposed as a method for properly incorporating this “model uncertainty” into confidence interval construction. Such proposals have been of particular interest in environmental and ecological statistics.
The earliest approach to the construction of frequentist model averaged confidence intervals was to first construct a model averaged estimator of the parameter of interest consisting of a data-based weighted average of the estimators of this parameter under the various models considered. The model averaged confidence interval is centered on this estimator and has width proportional to an estimate of the standard deviation of this estimator. However, the distributional assumption on which this confidence interval is based has been shown to be completely incorrect in large samples.
An important conceptual advance was made by Fletcher & Turek (2011) and Turek & Fletcher (2012) who put forward the idea of using data-based weighted averages across the models considered of procedures for constructing confidence intervals. In this way the model averaged confidence interval is constructed in a single step, rather than first constructing a model averaged estimator.
We review the work of Kabaila et al (2016, 2017) which evaluates the performance of the model averaged tail area confidence interval of Turek & Fletcher (2012) in the “test scenario” of two nested normal linear regression models. Our assessment of this confidence interval is that it performs quite well in this scenario, provided that the data-based weight function is carefully chosen.
Kabaila, P., Welsh, A.H., & Abeysekera, W. (2016) Model-averaged confidence intervals. Scandinavian Journal of Statistics.
Kabaila, P., Welsh, A.H. and Mainzer, R. (2017) The performance of model averaged tail area confidence intervals. Communications in Statistics – Theory and Methods.