Inferência via bootstrap no modelo de regressão gama unitária: desenvolvimento e aplicação do pacote UnitGammaReg em R

Abstract

The unit gamma regression model is an alternative to the beta regression model, which is used for modeling data restricted to the unit interval (0,1). There are several practical situations in which these models can be applied, such as: modeling interest rates; discount rates; the proportion of individuals who survive a given period of time with a certain disease; the incidence rate of respiratory diseases in a given population; proportions of responses in a survey; student pass or fail rates in exams; teams’ win rates in sports, among others. In this study, we use a real dataset referring to the Índice de Desenvolvimento Humano Municipal (IDHM) of Brazilian states in the year 2021, obtained from the Pesquisa Nacional por Amostra de Domicílios Continua (PNAD Continua), to illustrate the applicability of the unit gamma regression model with bootstrap-based inference. We also propose an R package that allows users to implement this methodology and perform hypothesis testing for the model coefficients.