Flexible quasi-beta regression models for continuous bounded data. (December 2019)

• Record Type: Journal Article
• Authors: Bonat, Wagner H; Petterle, Ricardo R; Hinde, John; Demétrio, Clarice GB
• Is Part Of: Statistical modelling. Volume 19:Number 6(2019)
• Page Start: 617
• Page End: 633
• Publication Date: 2019-12
• Subjects: bounded data -- estimating functions -- beta distribution -- simplex distribution -- regression models; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18790847
• Languages: English
• ISSNs: 1471-082X

Abstract

We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the formϕ μ p ( 1 − μ ) p, whereμ, ϕ andp are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide anR implementation and the datasets as supplementary materials.