Inflated beta regression models / Modelos de regressão beta inflacionados
AUTOR(ES)
Raydonal Ospina Martinez
DATA DE PUBLICAÇÃO
2008
RESUMO
The last years have seen new developments in the theory of beta regression models, which are useful for modelling random variables that assume values in the standard unit interval such as proportions, rates and fractions. In many situations, the dependent variable contains zeros and/or ones. In such cases, continuous distributions are not suitable for modeling this kind of data. In this thesis we propose mixed continuous-discrete distributions to model data observed on the intervals [0, 1],[0, 1) and (0, 1]. The proposed distributions are inflated beta distributions in the sense that the probability mass at 0 and/or 1 exceeds what is expected for the beta distribution. Properties of the inflated beta distributions are given. Estimation based on maximum likelihood and conditional moments is discussed and compared. Empirical applications using real data set are provided. Further, we develop inflated beta regression models in which the underlying assumption is that the response follows an inflated beta law. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, Fishers information matrix and its inverse. Interval estimation for different population quantities (such as regression parameters, precision parameter, mean response) is discussed and tests of hypotheses on the regression parameters can be performed using asymptotic tests. We also derive the second order biases of the maximum likelihood estimators and use them to define bias-adjusted estimators. The numerical results show that bias reduction can be effective in finite samples. We also develop a set of diagnostic techniques that can be employed to identify departures from the postulated model and influential observations. To that end, we adopt the local influence approach based in the conformal normal curvature. Finally, we consider empirical examples to illustrate the theory developed.
ASSUNTO(S)
estimação por máxima verossimilhança modelo de regressão beta inflacionado conformal normal curvature fractional data residuals dados de frações inflated beta regression model inflated beta distribution resíduos curvatura normal conforme distribuição beta inflacionada maximum likelihood estimation
