Improved estimators for a general class of beta regression models

In this article, we extend the beta regression model proposed by Ferrari and Cribari-Neto (2004), which is generally useful in situations where the response is restricted to the standard unit interval in two different ways: we let the regression structure to be nonlinear, and we allow a regression structure for the precision parameter (which may also be nonlinear). We derive general formulae for second order biases of the maximum likelihood estimators and use them to define bias-corrected estimators. Our formulae generalize the results obtained by Ospina et al. (2006), and are easily implemented by means of supplementary weighted linear regressions. We compare, by simulation, these bias-corrected estimators with three different estimators which are also bias-free to second order: one analytical, and two based on bootstrap methods. The simulation also suggests that one should prefer to estimate a nonlinear model, which is linearizable, directly in its nonlinear form. Our results additionally indicate that, whenever possible, dispersion covariates should be considered during the selection of the model, as we exemplify with two empirical applications. Finally, we also present simulation results on confidence intervals.