Bias correction of second order of the maximum likelihood estimators of the parameters of the beta regression model.
Fit beta regression models for rates and proportions via maximum likelihood using a parametrization with mean (depending through a link function on the covariates) and precision parameter (called phi).
The parameters of the beta regression model are estimated by the maximum likelihood method (see Ferrari and Cribari-Neto, 2004). These estimators are generally biased in models that use link function. This bias is not a serious problem when the sample size is large, however, when the sample is small, this bias can be large compared with the standard-error estimator.
Simas et al (2010) defines formulas general for second-order biases of the beta regression model with constant or variable-precision accuracy.
bias() returns a matrix with corrected coefficients.
Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799-815.
Simas, A.B., Barreto-Souza, W., and Rocha, A.V. (2010). Improved Estimators for a General Class of Beta Regression Models. Computational Statistics and Data Analysis, 54(2), 348-366.
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require(betareg) ## Section 4 from Ferrari and Cribari-Neto (2004) data("GasolineYield", package = "betareg") bbt <- betareg(yield ~ batch + temp, data = GasolineYield) bias(bbt) ## Section 3 from online supplements to Simas et al. (2010) ## mean model as in gy above ## precision model with regressor temp bbt2 <- betareg(yield ~ batch + temp | temp, data = GasolineYield) bias(bbt2)