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Correlated binomial regression models


  • Pires, Rubiane M.
  • Diniz, Carlos A.R.


In this paper, a class of correlated binomial regression models is proposed. The model is based on the generalized binomial distribution proposed by Luceño (1995) and Luceño and Ceballos (1995). The regression structure is modeled by using four different link functions and the dependence between the Bernoulli trials is modeled by using three different correlation functions. A data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. A Bayesian method for inference is developed for the proposed model which relies on both the data augmentation scheme and the MCMC algorithms to obtain the posterior estimate for the parameters. Two types of Bayesian residuals and a local influence measure from a Bayesian perspective are proposed to check the underlying model assumptions, as well as to identify the presence of outliers and/or influential observations. Simulation studies are presented in order to illustrate the performance of the developed methodology. A real data set is analyzed by using the proposed models.

Suggested Citation

  • Pires, Rubiane M. & Diniz, Carlos A.R., 2012. "Correlated binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2513-2525.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2513-2525
    DOI: 10.1016/j.csda.2012.02.004

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    References listed on IDEAS

    1. Hyunsoon Cho & Joseph G. Ibrahim & Debajyoti Sinha & Hongtu Zhu, 2009. "Bayesian Case Influence Diagnostics for Survival Models," Biometrics, The International Biometric Society, vol. 65(1), pages 116-124, March.
    2. Kolev, Nikolai & Paiva, Delhi, 2008. "Random sums of exchangeable variables and actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 147-153, February.
    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.
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