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Conjugate priors and bias reduction for logistic regression models

Author

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  • Rigon, Tommaso
  • Aliverti, Emanuele

Abstract

We address the issue of divergent maximum likelihood estimates for logistic regression models by considering a conjugate prior penalty which always produces finite estimates. We show that the proposed method is closely related to the reduced-bias approach of Firth (1993), and that the induced penalized likelihood can be expressed as a genuine binomial likelihood, replacing the original data with pseudo-counts.

Suggested Citation

  • Rigon, Tommaso & Aliverti, Emanuele, 2023. "Conjugate priors and bias reduction for logistic regression models," Statistics & Probability Letters, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:stapro:v:202:y:2023:i:c:s0167715223001256
    DOI: 10.1016/j.spl.2023.109901
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    References listed on IDEAS

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    1. Sander Greenland, 2003. "Generalized Conjugate Priors for Bayesian Analysis of Risk and Survival Regressions," Biometrics, The International Biometric Society, vol. 59(1), pages 92-99, March.
    2. Ioannis Kosmidis & David Firth, 2021. "Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models," Biometrika, Biometrika Trust, vol. 108(1), pages 71-82.
    3. E C Kenne Pagui & A Salvan & N Sartori, 2017. "Median bias reduction of maximum likelihood estimates," Biometrika, Biometrika Trust, vol. 104(4), pages 923-938.
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