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Parametric Quantile Beta Regression Model

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  • Marcelo Bourguignon
  • Diego I. Gallardo
  • Helton Saulo

Abstract

In this paper, we develop a fully parametric quantile regression model based on the generalised three‐parameter beta (GB3) distribution. Beta regression models are primarily used to model rates and proportions. However, these models are usually specified in terms of a conditional mean. Therefore, they may be inadequate if the observed response variable follows an asymmetrical distribution. In addition, beta regression models do not consider the effect of the covariates across the spectrum of the dependent variable, which is possible through the conditional quantile approach. In order to introduce the proposed GB3 regression model, we first reparameterise the GB3 distribution by inserting a quantile parameter, and then we develop the new proposed quantile model. We also propose a simple interpretation of the predictor–response relationship in terms of percentage increases/decreases of the quantile. A Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates and the choice of the link functions. Finally, a real COVID‐19 dataset from Chile is analysed and discussed to illustrate the proposed approach.

Suggested Citation

  • Marcelo Bourguignon & Diego I. Gallardo & Helton Saulo, 2024. "Parametric Quantile Beta Regression Model," International Statistical Review, International Statistical Institute, vol. 92(1), pages 106-129, April.
    • Handle: RePEc:bla:istatr:v:92:y:2024:i:1:p:106-129
    DOI: 10.1111/insr.12564
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    References listed on IDEAS

    as
    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    3. Angela Noufaily & M. C. Jones, 2013. "Parametric quantile regression based on the generalized gamma distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(5), pages 723-740, November.
    4. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2021. "Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 53-73, January.
    5. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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