Variable dispersion beta regressions with parametric link functions

Diego Ramos Canterle () and Fábio Mariano Bayer ()
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Diego Ramos Canterle: Universidade Federal de Santa Maria
Fábio Mariano Bayer: Universidade Federal de Santa Maria

Statistical Papers, 2019, vol. 60, issue 5, No 6, 1567 pages

Abstract: Abstract This paper presents a new class of regression models for continuous data restricted to the interval (0, 1), such as rates and proportions. The proposed class of models assumes a beta distribution for the variable of interest with regression structures for the mean and dispersion parameters. These structures consider covariates, unknown regression parameters, and parametric link functions. Link functions depend on parameters that model the relationship between the random component and the linear predictors. The symmetric and asymmetric Aranda-Ordaz link functions are considered in details. Depending on the parameter values, these link functions refer to particular cases of fixed links such as logit and complementary log–log functions. Joint estimation of the regression and link function parameters is performed by maximum likelihood. Closed-form expressions for the score function and Fishers information matrix are presented. Aspects of large sample inferences are discussed, and some diagnostic measures are proposed. A Monte Carlo simulation study is used to evaluate the finite sample performance of point estimators. Finally, a practical application that employs real data is presented and discussed.

Keywords: Aranda-Ordaz link function; Maximum likelihood estimator; Parametric link functions; Variable dispersion beta regression; 62J99; 62-07 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00362-017-0885-9

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