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Using Survey Sampling Algorithms For Exact Inference in Logistic Regression

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  • Louis‐Paul Rivest
  • Serigne Abib Gaye

Abstract

Several exact inference procedures for logistic regression require the simulation of a 0‐1 dependent vector according to its conditional distribution, given the sufficient statistics for some nuisance parameters. This is viewed, in this work, as a sampling problem involving a population of n units, unequal selection probabilities and balancing constraints. The basis for this reformulation of exact inference is a proposition deriving the limit, as n goes to infinity, of the conditional distribution of the dependent vector given the logistic regression sufficient statistics. It is proposed to sample from this distribution using the cube sampling algorithm. The interest of this approach to exact inference is illustrated by tackling new problems. First it allows to carry out exact inference with continuous covariates. It is also useful for the investigation of a partial correlation between several 0‐1 vectors. This is illustrated in an example dealing with presence‐absence data in ecology.

Suggested Citation

  • Louis‐Paul Rivest & Serigne Abib Gaye, 2023. "Using Survey Sampling Algorithms For Exact Inference in Logistic Regression," International Statistical Review, International Statistical Institute, vol. 91(1), pages 18-34, April.
    • Handle: RePEc:bla:istatr:v:91:y:2023:i:1:p:18-34
    DOI: 10.1111/insr.12507
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    References listed on IDEAS

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    1. Rivest, Louis-Paul, 2021. "Limiting properties of an equiprobable sampling scheme for 0–1 matrices," Statistics & Probability Letters, Elsevier, vol. 172(C).
    2. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
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