Resampling-based prediction intervals in beta regressions under correct and incorrect model specification

Abstract

We introduce a new bootstrap-based prediction interval for missing responses in beta regressions and, using numerical experiments, compare it to two other resampling-based intervals that are available in the literature. Additionally, we evaluate the impact of model misspecification on the empirical coverages of different beta regression prediction intervals. The numerical evidence we provide shows that the prediction interval we propose typically displays coverage rates that are slightly closer to the desired coverage levels than the competing prediction intervals. We also investigate the impact of model misspecification on three bootstrap prediction intervals. The numerical evidence shows that in some cases interval prediction remains accurate. In particular, misspecification of the model link functions has little impact on interval prediction accuracy. In contrast, the prediction intervals display substantial overcoverages when one fails to account for varying precision or for existing nonlinearity. An empirical application is also presented and discussed.