IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v61y2013icp137-147.html
   My bibliography  Save this article

Mixed beta regression: A Bayesian perspective

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312004239
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    5. 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).
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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).
    4. 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.
    5. 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.
    6. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    12. Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.
    13. Natália Caroline Costa Oliveira & Vinícius Diniz Mayrink, 2024. "Generalized mixed spatiotemporal modeling with a continuous response and random effect via factor analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 723-752, July.
    14. 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.
    15. 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.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.
    2. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. Dries P.J. Kuijper & Jakub W. Bubnicki & Marcin Churski & Bjorn Mols & Pim van Hooft, 2015. "Context dependence of risk effects: wolves and tree logs create patches of fear in an old-growth forest," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(6), pages 1558-1568.
    4. Bassetti, Federico & De Giuli, Maria Elena & Nicolino, Enrica & Tarantola, Claudia, 2018. "Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1107-1121.
    5. Maria Gheorghe & Susan Picavet & Monique Verschuren & Werner B. F. Brouwer & Pieter H. M. Baal, 2017. "Health losses at the end of life: a Bayesian mixed beta regression approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 723-749, June.
    6. Jobst, Rainer & Kellner, Ralf & Rösch, Daniel, 2020. "Bayesian loss given default estimation for European sovereign bonds," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1073-1091.
    7. Hong, Yi & Jin, Xing, 2022. "Pricing of variance swap rates and investment decisions of variance swaps: Evidence from a three-factor model," European Journal of Operational Research, Elsevier, vol. 303(2), pages 975-985.
    8. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    9. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    10. Assaf, A. George & Tsionas, Mike & Oh, Haemoon, 2018. "The time has come: Toward Bayesian SEM estimation in tourism research," Tourism Management, Elsevier, vol. 64(C), pages 98-109.
    11. Kathryn M. Irvine & T. J. Rodhouse & Ilai N. Keren, 2016. "Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 619-640, December.
    12. Antolín-Díaz, Juan & Drechsel, Thomas & Petrella, Ivan, 2024. "Advances in nowcasting economic activity: The role of heterogeneous dynamics and fat tails," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Saleem Bahaj, 2014. "Systemic Sovereign Risk: Macroeconomic Implications in the Euro Area," Discussion Papers 1406, Centre for Macroeconomics (CFM).
    14. Olivier Parent & James P. LeSage, 2008. "Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 235-256.
    15. Edilberto Cepeda-Cuervo & Vicente Núñez-Antón, 2013. "Spatial Double Generalized Beta Regression Models," Journal of Educational and Behavioral Statistics, , vol. 38(6), pages 604-628, December.
    16. João B. M. Pereira & Widemberg S. Nobre & Igor F. L. Silva & Alexandra M. Schmidt, 2020. "Spatial confounding in hurdle multilevel beta models: the case of the Brazilian Mathematical Olympics for Public Schools," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1051-1073, June.
    17. Afrânio M.C. Vieira & Roseli A. Leandro & Clarice G.B. Dem�trio & Geert Molenberghs, 2011. "Double generalized linear model for tissue culture proportion data: a Bayesian perspective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1717-1731, September.
    18. Hiroaki Chigira & Tsunemasa Shiba, 2012. "Dirichlet Prior for Estimating Unknown Regression Error Heteroscedasticity," Global COE Hi-Stat Discussion Paper Series gd12-248, Institute of Economic Research, Hitotsubashi University.
    19. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:137-147. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.