Transcription of BETA REGRESSION FOR MODELLING RATES AND …
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BETA REGRESSION FOR MODELLING RATES AND …
BETA REGRESSION FOR MODELLING RATES AND PROPORTIONSSILVIA FERRARID epartamento de Estat stica/IMEU niversidade de S ao PauloCaixa Postal 66281, S ao Paulo/SP, 05311 970, CRIBARI NETOD epartamento de Estat stica, CCENU niversidade Federal de PernambucoCidade Universit aria, Recife/PE, 50740 540, paper proposes a REGRESSION model where the response is beta distributedusing a parameterization of the beta law that is indexed by mean and dispersion pa-rameters. The proposed model is useful for situations where the variable of interest iscontinuous and restricted to the interval (0,1) and is related to other variables througha REGRESSION structure. The REGRESSION parameters of the beta REGRESSION model are inter-pretable in terms of the mean of the response and, when the logit link is used, of an oddsratio, unlike the parameters of a linear REGRESSION that employs a transformed is performed by maximum likelihood. We provide closed-form expressions forthe score function, for Fisher s information matrix and its inverse.
BETA REGRESSION FOR MODELLING RATES AND PROPORTIONS SILVIA L.P. FERRARI Departamento de Estat´ıstica/IME Universidade de S˜ao Paulo Caixa Postal 66281, S˜ao Paulo/SP, 05311–970, Brazil email: sferrari@ime.usp.br FRANCISCO CRIBARI–NETO Departamento de Estat´ıstica, CCEN Universidade Federal de Pernambuco
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