On connectivity of fibers with positive marginals in multiple logistic regression

Details On connectivity of fibers with positive marginals in multiple logistic regression On connectivity of fibers with positive marginals in multiple logistic regression

2008-10-10

arxiv.org/abs/0810.1793v1

J. Multivariate Anal., Vol.101 (2010), 909-925

Mathematics

Statistics Theory

26 pages

Scientific paper

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.

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