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Bayesian binary regression with exponential power link

Author

Listed:
  • Naranjo, L.
  • Martín, J.
  • Pérez, C.J.

Abstract

A flexible Bayesian approach to a generalized linear model is proposed to describe the dependence of binary data on explanatory variables. The inverse of the exponential power cumulative distribution function is used as the link to the binary regression model. The exponential power family provides distributions with both lighter and heavier tails compared to the normal distribution, and includes the normal and an approximation to the logistic distribution as particular cases. The idea of using a data augmentation framework and a mixture representation of the exponential power distribution is exploited to derive efficient Gibbs sampling algorithms for both informative and noninformative settings. Some examples are given to illustrate the performance of the proposed approach when compared with other competing models.

Suggested Citation

  • Naranjo, L. & Martín, J. & Pérez, C.J., 2014. "Bayesian binary regression with exponential power link," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 464-476.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:464-476
    DOI: 10.1016/j.csda.2012.07.022
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    References listed on IDEAS

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    1. Zellner, Arnold & Rossi, Peter E., 1984. "Bayesian analysis of dichotomous quantal response models," Journal of Econometrics, Elsevier, vol. 25(3), pages 365-393, July.
    2. Meza, Cristian & Jaffrézic, Florence & Foulley, Jean-Louis, 2009. "Estimation in the probit normal model for binary outcomes using the SAEM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1350-1360, February.
    3. Huang, Yangxin, 2008. "Long-term HIV dynamic models incorporating drug adherence and resistance to treatment for prediction of virological responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3765-3778, March.
    4. Carlos Daniel Paulino & Paulo Soares & John Neuhaus, 2003. "Binomial Regression with Misclassification," Biometrics, The International Biometric Society, vol. 59(3), pages 670-675, September.
    5. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    6. Nott, David J. & Leng, Chenlei, 2010. "Bayesian projection approaches to variable selection in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3227-3241, December.
    7. 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.
    8. Carter, C.K. & Kohn, R., "undated". "Robust Bayesian nonparametric regression," Statistics Working Paper _004, Australian Graduate School of Management.
    9. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

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