Improved estimators for a general class of beta regression models

By Alexandre B. Simas, W. Barreto‐Souza, Andréa V. Rocha. Computational Statistics & Data Analysis, 2008

316 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5bc42810cfdca89b3379bd43dd8eb8968176e10e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation (2012, background): “…Souza Forthcoming; Cribari-Neto and Zeileis 2010; Espinheira et al 2008a,b; Ferrari and Cribari-Neto 2004; Ferrari et al. 2011; Kieschnick and McCullough 2003; Ospina et al 2006; Paolino 2001; Rocha and Simas 2011; Simas et al 2010; Smithson and Verkuilen 2006; Vasconcellos and Cribari-Neto 2005).”
Reparameterized Birnbaum-Saunders regression models with varying precision (2016, methodology): “[38] assumed a non-linear regression structure for the precision parameter by using a beta distribution, whereas Rocha and Simas [31] derived local influence in this model.”
A New Robust Regression Model for Proportions (2012, methodology): “…model proposed by Ferrari and Cribari-Neto (2004) which is not an exponential family and so is not a GLM. Note also that, if solely α = 0 then we obtain the variable dispersion Beta regression model introduced by Paolino (2001), Smithson and Verkuilen (2006) and recently by Simas et al. (2010).”
Beta Regression in R (2010, methodology): “An extension of the beta regression model above which was employed by Smithson and Verkuilen (2006) and formally introduced (along with further extensions) by Simas et al. (2010) is the variable dispersion beta regression model.”
Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression (2019, methodology): “…estimators can lead to erroneous inference, and methods for bias–reduction and bias–correction are an active research area in statistics and in beta regression in particular (Grün et al., 2012; Kosmidis, 2014; Kosmidis & Firth, 2010; Ospina, Cribari‐Neto, & Vasconcellos, 2006; Simas et al., 2010).”
Kumaraswamy autoregressive moving average models for double bounded environmental data (2017, methodology): “The beta regression model (Ferrari and Cribari-Neto, 2004), for example, which resembles the generalized linear models (GLM) (McCullagh and Nelder, 1989), has been generalized, improved and applied in several works (Cribari-Neto and Zeileis, 2010; Simas et al., 2010; Ospina and Ferrari, 2012; Bayer ”