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Mixed beta regression: A Bayesian perspective

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  • Figueroa-Zúñiga, Jorge I.
  • Arellano-Valle, Reinaldo B.
  • Ferrari, Silvia L.P.

Abstract

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian approach. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter, and allow both parameters to be modeled through regression structures that may involve fixed and random effects. Specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and illustrative examples are presented.

Suggested Citation

  • Figueroa-Zúñiga, Jorge I. & Arellano-Valle, Reinaldo B. & Ferrari, Silvia L.P., 2013. "Mixed beta regression: A Bayesian perspective," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 137-147.
    • Handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:137-147
    DOI: 10.1016/j.csda.2012.12.002
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    1. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    2. 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.
    3. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. P. J. Everson & C. N. Morris, 2000. "Inference for multivariate normal hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 399-412.
    6. Carrigan, Gretchen & Barnett, Adrian G. & Dobson, Annette J. & Mishra, Gita, 2007. "Compensating for Missing Data from Longitudinal Studies Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i07).
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    Cited by:

    1. Ricardo Rasmussen Petterle & Wagner Hugo Bonat & Cassius Tadeu Scarpin, 2019. "Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 346-368, June.
    2. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    3. Ni, Linglin & Wang, Xiaokun, 2021. "Load factors of less-than-truckload delivery tours: An analysis with operation data," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    4. Acocella, Angela & Caplice, Chris & Sheffi, Yossi, 2020. "Elephants or goldfish?: An empirical analysis of carrier reciprocity in dynamic freight markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    5. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    6. Francesco Giovinazzi & Daniela Cocchi, 2022. "Social Integration of Second Generation Students in the Italian School System," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 160(1), pages 287-307, February.
    7. 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.
    8. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    9. Carolina Costa Mota Paraíba & Natalia Bochkina & Carlos Alberto Ribeiro Diniz, 2018. "Bayesian truncated beta nonlinear mixed-effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 320-346, January.
    10. Guillermo Ferreira & Jorge Figueroa-Zúñiga & Mário Castro, 2015. "Partially linear beta regression model with autoregressive errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 752-775, December.
    11. Maria Gheorghe & Werner Brouwer & Pieter Baal, 2015. "Did the health of the Dutch population improve between 2001 and 2008? Investigating age- and gender-specific trends in quality of life," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 16(8), pages 801-811, November.
    12. Francisco Cribari-Neto & Sadraque E.F. Lucena, 2015. "Nonnested hypothesis testing in the class of varying dispersion beta regressions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 967-985, May.
    13. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    14. Cepeda-Cuervo Edilberto & Garrido Liliana, 2015. "Bayesian beta regression models with joint mean and dispersion modeling," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 49-58, March.
    15. Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.

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