Model-Averaged Confidence Intervals

Abstract

Model averaging is commonly used to allow for model uncertainty in parameter estimation. In the frequentist setting, a model-averaged estimate of a parameter is a weighted mean of the estimates from the individual models, with the weights being based on an information criterion, such as AIC. A Wald confidence interval based on this estimate often performs poorly, as its sampling distribution is generally non-normal and estimation of the standard error is problematic. A natural alternative is to use a bootstrap approach. The current method is based on the percentile method, which bootstraps the estimate from the best model. Little previous research has been carried out to assess its coverage properties. These issues demonstrate the need for further development into the interval estimation when making multi-model inference. In this thesis, we propose a new method for constructing a model-averaged confidence interval using studentized bootstrap. We carry out simulations when the data are either normal or lognormal. Our results suggest that the studentized bootstrap interval provides the best coverage for approximately the same interval width as competing intervals in the lognormal setting. It is also shown to be the best approach for both normal and lognormal data when the sample size is small.

Furthermore, we consider the use of model-averaging in the analysis of overdispersed count data. In a single-model setting, the default method for dealing with overdispersion is to either use a quasi-Poisson approach, or to fit the data using a negative binomial model. We examine the performance of the two methods in a model-averaging setting. Our results suggest that the quasi-Poisson approach leads to a better coverage rate, even when a negative binomial model is used to generate the data.