Robust beta regression through the logit transformation

• Ano de defesa: 2023
• Autor(a) principal: Maluf, Yuri Sampaio
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Beta regression; Dados de proporção; Estimadores robusto; Inferência robusta; Lq-likelihood; Lq-verossimilhança; Proportional data; Regressão Beta; Robust estimators; Robust inference
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-25052023-075046/

Beta regression models are employed for modeling continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications appear in several areas, such as medicine, environmental research, and finance. Under beta regression models, the usual inference procedure is essentially based on the classical maximum likelihood approach. Nevertheless, it is well known that the maximum likelihood-based inference is easily affected by the presence of outliers. The lack of robustness may bring a severe bias and misleading conclusions. Recently, robust estimators for beta regression models have been proposed. These estimators require non-trivial restrictions in the parameter space, which limit their application. This thesis proposes two new robust estimators, namely the logit minimum power divergence estimator (LMDPDE) and the logit surrogate maximum likelihood estimator (LSMLE), that overcome this drawback. The LMDPDE and the LSMLE belong to the general class of M-estimators, which allows us to derive some important properties, such as the asymptotic distribution and the influence function. We also develop robust versions of the Wald-type test. All robust estimators, statistical tests, and other tools treated in this work are implemented in the R package robustbetareg. The package is available on the official repository of R (CRAN). Through Monte Carlo simulation studies, we examine the performance of the proposed estimators and the robust Wald tests and compare them with the corresponding inference procedures presented in the literature. Real data applications in the context of sports of Australian athletes and access to health insurance coverage in a Brazilian state using the proposed methodologies are presented. The thesis closes with concluding remarks about its main contributions and points out some important aspects that deserve special attention for future research.