Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data

Abstract

The models used in small-area inference often involve unobservable random effects. While this can significantly improve the adaptivity and flexibility of a model, it also increases the variability of both point and interval estimators. If we could test for the existence of the random effects, and if the test were to show that they were unlikely to be present, then we would arguably not need to incorporate them into the model, and thus could significantly improve the precision of the methodology. In this article we suggest an approach of this type. We develop simple bootstrap methods for testing for the presence of random effects, applicable well beyond the conventional context of the natural exponential family. If the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small-area means. Such estimators can be substantially more effective, for example, because they enjoy much faster convergence rates than their counterparts when the model includes random effects. If the null hypothesis is rejected then the next step is either to make the model more elaborate (our methodology is available quite generally) or to turn to existing random effects models. This article has supplementary material online.