Statistical Modelling 19 (6) (2019), 617–633

Flexible quasi-beta regression models for continuous bounded data

Wagner H Bonat,
Laboratory of Statistics and Geoinformation,
Department of Statistics,
Paraná Federal University,
Curitiba,
Brazil.
e-mail: wbonat@ufpr.br


Ricardo R Petterle,
Sector of Health Sciences, Medical School,
Paraná Federal University,
Curitiba, PR,
Brazil.


John Hinde,
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland Galway,
Galway,
Ireland.


Clarice GB Demétrio,
Departamento de Ciências Exatas,
Escola Superior de Agricultura Luiz de Queiroz,
São Paulo University,
Piracicaba,
Brazil.


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 form ϕμp(1−μ)p, where μ, ϕ and p 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 an R implementation and the datasets as supplementary materials.

Keywords:

bounded data; estimating functions; beta distribution; simplex distribution; regression models.

Downloads:

Datasets and related code are available through this link.
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