Beta regression

Author(s)

Patricia Leone Espinheira Ospina

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2007-03-29

Examining board members

Silvia Lopes de Paula Ferrari; Reiko Aoki; Clarice Garcia Borges Demetrio; Gilberto Alvarenga Paula; Klaus Leite Pinto Vasconcellos

• Advisor: Silvia Lopes de Paula Ferrari; Francisco Cribari Neto

Abstract

Practitioners oftentimes wish to investigate how certain variables influence continuous variable that assumes values on the standard unit interval $(0,1)$, such as percentages, proportions, rates and fractions. Linear regression models are not suitable for modelling such data. A class of beta regression models which is in many aspects similar to that of generalised linear models was proposed by Ferrari and Cribari--Neto~(2004). The mean response is related to a linear predictor, which involves covariates and unknown regression parameters, through a link function. The model is also indexed by a precision parameter. Smithson e Verkuilen~(2005), among others, consider the beta regression model with variable dispersion, i.e., beta regression in which the precision parameter is not constant across observations. In this dissertation we develop diagnostic methods for beta regression models with both constant and variable dispersion. The method of local influence (Cook,~1986) proved to be particularly useful, since it is able to identify variable dispersion in the data. We have also used Monte Carlo simulation to evaluate the finite sample performance of maximum likelihood estimators in beta regression models with variable dispersion; we have also evaluated the consequences os misspecifying the model by incorrectly assuming constant dispersion when dispersion is variable and the finite sample behavior of heteroskedasticity tests based on first order asymptotics. of estimating the model supposing constant dispersion when Prediction bootstrap intervals (Davison e Hinkley,~1997) for the beta regression model with constant dispersion are also considered.Practical applications that employ real data are presented and discussed. (AU)