Improved estimators for a general class of beta regression models

TL;DR

This paper extends beta regression models to include nonlinear structures for both the mean and precision parameters, deriving bias correction formulas and comparing estimators through simulations and empirical data.

Contribution

It introduces a flexible extension of beta regression with nonlinear components and develops second-order bias correction formulas for maximum likelihood estimators.

Findings

Bias-corrected estimators outperform uncorrected ones in simulations.

The proposed methods are easily implemented via weighted linear regressions.

Empirical application demonstrates practical usefulness.

Abstract

In this paper we consider an extension of the beta regression model proposed by Ferrari and Cribari-Neto (2004). We extend their model in two different ways, first, we let the regression structure be nonlinear, second, we allow a regression structure for the precision parameter, moreover, this regression structure may also be nonlinear. Generally, the beta regression is useful to situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. We derive general formulae for second-order biases of the maximum likelihood estimators and use them to define bias-corrected estimators. Our formulae generalizes the results obtained by Ospina et al. (2006), and are easily implemented by means of supplementary weighted linear regressions. We also compare these bias-corrected estimators with three different estimators which are also bias-free to the second-order, one analytical and the other two based on bootstrap methods. These estimators are compared by simulation. We present an empirical application.