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Efficient estimation of the link function parameter in a robust Bayesian binary regression model

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  • Roy, Vivekananda

Abstract

It is known that the robit regression model for binary data is a robust alternative to the more popular probit and logistic models. The robit model is obtained by replacing the normal distribution in the probit regression model with the Student’s t distribution. Unlike the probit and logistic models, the robit link has an extra degrees of freedom (df) parameter. It is shown that in practice it is important to estimate (rather than use a prespecified fixed value) the df parameter. A method for effectively selecting the df parameter of the robit model is described. The proposed method becomes computationally more effective if efficient MCMC algorithms are available for exploring the posterior distribution associated with a Bayesian robit model. Fast mixing parameter expanded DA (PX–DA) type algorithms based on an appropriate Haar measure are developed for significantly improving the convergence of DA algorithms for the robit model. The algorithms built for sampling from the Bayesian robit model shed new light on the construction of efficient PX–DA type algorithms in general. In spite of the fact that Haar PX–DA algorithms are known to be asymptotically “optimal”, through an empirical study it is shown that it may take millions of iterations before they provide improvement over the DA algorithms. Contrary to the popular belief, it is demonstrated that a partially reparameterized DA algorithm can outperform a fully reparameterized DA algorithm. The proposed methodology of selecting the df parameter is illustrated through two detailed examples.

Suggested Citation

  • Roy, Vivekananda, 2014. "Efficient estimation of the link function parameter in a robust Bayesian binary regression model," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 87-102.
    • Handle: RePEc:eee:csdana:v:73:y:2014:i:c:p:87-102
    DOI: 10.1016/j.csda.2013.11.013
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    References listed on IDEAS

    as
    1. Sungduk Kim & Ming-Hui Chen & Dipak K. Dey, 2008. "Flexible generalized t-link models for binary response data," Biometrika, Biometrika Trust, vol. 95(1), pages 93-106.
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    4. Roy, Vivekananda, 2012. "Spectral analytic comparisons for data augmentation," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 103-108.
    5. 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.
    6. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    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.
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    9. Claudia Czado & Adrian Raftery, 2006. "Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors," Statistical Papers, Springer, vol. 47(3), pages 419-442, June.
    10. A. Kong & P. McCullagh & X.‐L. Meng & D. Nicolae & Z. Tan, 2003. "A theory of statistical models for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 585-604, August.
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    Cited by:

    1. Vivekananda Roy, 2016. "Improving efficiency of data augmentation algorithms using Peskun’s theorem," Computational Statistics, Springer, vol. 31(2), pages 709-728, June.

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