Medidas de diagnóstico em modelos de regressão beta prime

Abstract

In the context of models for positive continuous response variables, the beta prime regression model, proposed by Bourguignon et al. (2021), is attractive to model asymmetrical positive data. In the validation stage of a regression model, one of the most commonly used diagnostic techniques is the analysis of residuals. For that, it is important to use residuals with known properties and that present good performance. In the present work, we performed a detailed study of the residuals in the BP regression model. To that end, in addition to the quantile residual and Pearson residual used by Bourguignon et al. (2021), we defined the weighted, standardized weighted (ESPINHEIRA et al., 2008) and standardized Pearson (MCCULLAGH; NELDER, 1989) residuals for this model. Afterward, we evaluate the empirical distribution of those five residuals in different scenarios of the BP regression model and compared their performances to detect misspecification. Studies of Monte Carlo simulations and applications to real data are used for that purpose. Furthermore, we investigated the performance of some prediction and goodness-of-fit measures as model selection criteria in BP regression. In this perspective, we propose the prediction coefficient 𝑃2, based on the PRESS statistic, and we evaluate the behavior of this measure and the pseudo-𝑅2 type criteria through Monte Carlo simulation studies, considering correct and incorrect specifications of the BP regression model in different scenarios. Applications to real data are presented to illustrate the performance of the proposed measures.