Flexible quasi-beta prime regression models for dependent continuous positive data

Abstract

In many situations of interest, it is common to observe positive responses measured along several assessment conditions, within the same subjects. Usually, such a scenario implies a positive skewness on the response distributions, along with the existence of within-subject dependency. It is known that neglecting these features can lead to a misleading inference. In this paper we extend the beta prime regression model for modeling asymmetric positive data, while taking into account the dependence structure. We consider a useful predictor for modeling a suitable transformation of the mean, along with homogeneous covariance structure. The proposed model is an interesting competitor of the flexible Tweedie regression models, which include distributions such as Gamma and Inverse Gaussian. Furthermore, residual analysis and influence diagnostic tools are proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed methodology, under small and moderate sample sizes, along with suitable discussions. The methodology is illustrated with the analysis of a real longitudinal dataset. An R package was developed to allow the practitioners to use the methodology described in this paper.