On connectivity of fibers with positive marginals in multiple logistic regression

TL;DR

This paper investigates the connectivity of fibers with positive marginals in multiple logistic regression using Markov bases, providing explicit bases and simplified subsets for specific cases to facilitate exact tests.

Contribution

It introduces an explicit Markov basis for multiple Poisson regression and a simplified subset for bivariate logistic regression, enhancing the understanding of fiber connectivity.

Findings

Explicit Markov basis for multiple Poisson regression

A simple subset of the basis for bivariate logistic regression

Connectivity guaranteed for fibers with positive marginals

Abstract

In this paper we consider exact tests of a multiple logistic regression, where the levels of covariates are equally spaced, via Markov beses. In usual application of multiple logistic regression, the sample size is positive for each combination of levels of the covariates. In this case we do not need a whole Markov basis, which guarantees connectivity of all fibers. We first give an explicit Markov basis for multiple Poisson regression. By the Lawrence lifting of this basis, in the case of bivariate logistic regression, we show a simple subset of the Markov basis which connects all fibers with a positive sample size for each combination of levels of covariates.