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On connectivity of fibers with positive marginals in multiple logistic regression

Author

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  • Hara, Hisayuki
  • Takemura, Akimichi
  • Yoshida, Ruriko

Abstract

In this paper we consider exact tests of a multiple logistic regression with categorical covariates via Markov bases. In many applications 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.

Suggested Citation

  • Hara, Hisayuki & Takemura, Akimichi & Yoshida, Ruriko, 2010. "On connectivity of fibers with positive marginals in multiple logistic regression," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 909-925, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:909-925
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    Citations

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    Cited by:

    1. David Kahle & Ruriko Yoshida & Luis Garcia-Puente, 2018. "Hybrid schemes for exact conditional inference in discrete exponential families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 983-1011, October.
    2. Fabio Rapallo & Ruriko Yoshida, 2010. "Markov bases and subbases for bounded contingency tables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 785-805, August.
    3. Benchong Li & Liya Fu, 2018. "Exact test of goodness of fit for binomial distribution," Statistical Papers, Springer, vol. 59(3), pages 851-860, September.

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