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Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters

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  • Edilberto Cepeda-Cuervo
  • Jorge Alberto Achcar
  • Liliana Garrido Lopera

Abstract

In this paper a bivariate beta regression model with joint modeling of the mean and dispersion parameters is proposed, defining the bivariate beta distribution from Farlie--Gumbel--Morgenstern (FGM) copulas. This model, that can be generalized using other copulas, is a good alternative to analyze non-independent pairs of proportions and can be fitted applying standard Markov chain Monte Carlo methods. Results of two applications of the proposed model in the analysis of structural and real data set are included.

Suggested Citation

  • Edilberto Cepeda-Cuervo & Jorge Alberto Achcar & Liliana Garrido Lopera, 2014. "Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 677-687, March.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:3:p:677-687
    DOI: 10.1080/02664763.2013.847071
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    References listed on IDEAS

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    4. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    5. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
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    Cited by:

    1. Guillermo Martínez-Flórez & Sandra Vergara-Cardozo & Roger Tovar-Falón & Luisa Rodriguez-Quevedo, 2023. "The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    2. Souza Debora F. & Moura Fernando A. S., 2016. "Multivariate Beta Regression with Application in Small Area Estimation," Journal of Official Statistics, Sciendo, vol. 32(3), pages 747-768, September.
    3. Ceren Eda Can & Gul Ergun & Refik Soyer, 2022. "Bayesian Analysis of Proportions via a Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3121-3139, December.
    4. Tourani-Farani, Fahimeh & Kazemi, Iraj, 2022. "Transformed mixed-effects modeling of correlated bounded and positive data with a novel multivariate generalized Johnson distribution," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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