Using Survey Sampling Algorithms For Exact Inference in Logistic Regression. (31st May 2022)

• Record Type: Journal Article
• Authors: Rivest, Louis‐Paul; Gaye, Serigne Abib
• Is Part Of: International statistical review. Volume 91:Number 1(2023)
• Page Start: 18
• Page End: 34
• Publication Date: 2022-05-31
• Subjects: entropy -- null model analysis -- survey sampling -- weak law of large number; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12507
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: 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.