Influence measures in beta regression models through distance between distributions

Abstract

In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frechet distance (Frechet in Comptes Rendus hebdomadaires des seances de l’Academie des Sciences de Paris 244:689–692, 1957), and the Rao distance (Rao in Indian J Stat Ser A 9:246–291, 1949). Moreover, a jackknife-after-bootstrap transformation of the diagnostics is also proposed to make clear the decision about cases to be considered as influential. Artificial and real examples are included to illustrate the usefulness of the diagnostics and to compare them to others in the literature.