Improved point and interval estimation for a beta regression model

In this paper we consider the beta regression model recently proposed by Ferrari and Cribari-Neto [2004. Beta regression for modeling rates and proportions. J. Appl. Statist. 31, 799–815], which is tailored to situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. We derive the second order biases of the maximum likelihood estimators and use them to define bias-adjusted estimators. As an alternative to the two analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. The numerical evidence favors the bootstrap-based estimator and also one of the analytically corrected estimators. Several different strategies for interval estimation are also proposed. We present an empirical application.