Beta regression misspecification tests

Abstract

The beta regression model is tailored for responses that assume values in the standard unit interval. It comprises two submodels, one for the mean response and another for the precision parameter. We develop tests of correct specification for such a model. The tests are based on the information matrix equality, which holds when the model is correctly specified. We establish the validity of the tests in the class of varying precision beta regressions, provide closed-form expressions for the quantities used in the test statistics, and present simulation evidence on the tests’ null and non-null behavior. We show that it is possible to achieve very good control of the type I error probability when data resampling is employed and that the tests are able to reliably detect incorrect model specification, especially when the sample size is not small. An empirical application is presented and discussed.