IDEAS home Printed from https://ideas.repec.org/a/ben/tostpj/v8y2017i1p27-38.html
   My bibliography  Save this article

Bayesian Inference for Three Bivariate Beta Binomial Models

Author

Listed:
  • David Peter Michael Scollnik

    (Department of Mathematics and Statistics, University of Calgary, Calgary, Canada)

Abstract

Background : This paper considers three two-dimensional beta binomial models previously introduced in the literature. These were proposed as candidate models for modelling forms of correlated and overdispersed bivariate count data. However, the first model has a complicated form of bivariate probability mass function involving a generalized hypergeometric function and the remaining two do not have closed forms of probability mass functions and are not amenable to analysis using maximum likelihood. This limited their applicability. Objective : In this paper, we will discuss how the Bayesian analyses of these models may go forward using Markov chain Monte Carlo and data augmentation. Results : An illustrative example having to do with student achievement in two related university courses is included. Posterior and posterior predictive inferences and predictive information criteria are discussed.

Suggested Citation

  • David Peter Michael Scollnik, 2017. "Bayesian Inference for Three Bivariate Beta Binomial Models," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 27-38, October.
  • Handle: RePEc:ben:tostpj:v:8:y:2017:i:1:p:27-38
    DOI: 10.2174/1876527001708010027
    as

    Download full text from publisher

    File URL: https://benthamopen.com/DOWNLOAD-PDF/TOSPJ-8-27/
    Download Restriction: no

    File URL: https://benthamopen.com/ABSTRACT/TOSPJ-8-27/
    Download Restriction: no

    File URL: https://libkey.io/10.2174/1876527001708010027?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
    ---><---

    References listed on IDEAS

    as
    1. Danaher, Peter J. & Hardie, Bruce G.S., 2005. "Bacon With Your Eggs? Applications of a New Bivariate Beta-Binomial Distribution," The American Statistician, American Statistical Association, vol. 59, pages 282-286, November.
    2. Goro Ishii & Reiko Hayakawa, 1960. "On the compound binomial distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(1), pages 69-80, February.
    3. Bibby, Bo Martin & Væth, Michael, 2011. "The two-dimensional beta binomial distribution," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 884-891, July.
    Full references (including those not matched with items on IDEAS)

    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. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    2. Bibby, Bo Martin & Væth, Michael, 2011. "The two-dimensional beta binomial distribution," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 884-891, July.
    3. Kim, Chul & Jun, Duk Bin & Park, Sungho, 2018. "Capturing flexible correlations in multiple-discrete choice outcomes using copulas," International Journal of Research in Marketing, Elsevier, vol. 35(1), pages 34-59.
    4. repec:jss:jstsof:46:i12 is not listed on IDEAS
    5. Cho, Wendy K. Tam & Judge, George G., 2007. "Information theoretic solutions for correlated bivariate processes," Economics Letters, Elsevier, vol. 97(3), pages 201-207, December.
    6. André Bonfrer & Xavier Drèze, 2009. "Real-Time Evaluation of E-mail Campaign Performance," Marketing Science, INFORMS, vol. 28(2), pages 251-263, 03-04.
    7. D. J. Best & J. C. W. Rayner & O. Thas, 2010. "Four tests of fit for the beta-binomial distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1547-1554.
    8. Peter S. Fader & Bruce G. S. Hardie & Jen Shang, 2010. "Customer-Base Analysis in a Discrete-Time Noncontractual Setting," Marketing Science, INFORMS, vol. 29(6), pages 1086-1108, 11-12.
    9. Glady, Nicolas & Lemmens, Aurélie & Croux, Christophe, 2015. "Unveiling the relationship between the transaction timing, spending and dropout behavior of customers," International Journal of Research in Marketing, Elsevier, vol. 32(1), pages 78-93.
    10. Emilio Gómez-Déniz & Jorge Pérez-Rodríguez, 2015. "Closed-form solution for a bivariate distribution in stochastic frontier models with dependent errors," Journal of Productivity Analysis, Springer, vol. 43(2), pages 215-223, April.
    11. Olivier Toubia & Laurent Florès, 2007. "Adaptive Idea Screening Using Consumers," Marketing Science, INFORMS, vol. 26(3), pages 342-360, 05-06.
    12. Luo, Sheng & Chen, Yong & Su, Xiao & Chu, Haitao, 2014. "mmeta: An R Package for Multivariate Meta-Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(i11).
    13. Peter J. Danaher & Janghyuk Lee & Laoucine Kerbache, 2010. "Optimal Internet Media Selection," Marketing Science, INFORMS, vol. 29(2), pages 336-347, 03-04.
    14. Peter J. Danaher & Michael S. Smith, 2011. "Modeling Multivariate Distributions Using Copulas: Applications in Marketing," Marketing Science, INFORMS, vol. 30(1), pages 4-21, 01-02.
    15. repec:tiu:tiutis:52e91e47-4a2d-4e7b-bb23-3926b842ae30 is not listed on IDEAS
    16. David A. Schweidel & Peter S. Fader & Eric T. Bradlow, 2008. "A Bivariate Timing Model of Customer Acquisition and Retention," Marketing Science, INFORMS, vol. 27(5), pages 829-843, 09-10.
    17. Ong, Seng-Huat & Lee, Wen-Jau & Low, Yeh-Ching, 2020. "A general method of computing mixed Poisson probabilities by Monte Carlo sampling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 98-106.

    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:ben:tostpj:v:8:y:2017:i:1:p:27-38. 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: Rehana Raza (email available below). General contact details of provider: .

    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.