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In this paper we consider exact tests of a multiple logistic regression,where the levels of covariates are equally spaced, via Markov beses. In usualapplication of multiple logistic regression, the sample size is positive foreach combination of levels of the covariates. In this case we do not need awhole Markov basis, which guarantees connectivity of all fibers. We first givean explicit Markov basis for multiple Poisson regression. By the Lawrencelifting of this basis, in the case of bivariate logistic regression, we show asimple subset of the Markov basis which connects all fibers with a positivesample size for each combination of levels of covariates.

On connectivity of fibers with positive marginals in multiple logistic regression