Generating functions for exactp-values of odds ratios in logistic regression


Specialized algebraic methods are presented for computing exactly thep-value of the odds ratio in a conditional hypothesis test. The method uses normal forms of generating functions with respect to a Gröbner basis.

This is a preview of subscription content, access via your institution.


  1. Agresti, A. (1999), Exact inference for categorical data: recent advances and continuing controversies. To appear inStatistics in Medicine.

  2. Breslow, N. E. (1981), Odds ratio estimators when the data are sparse.Biometrika, 68, 73–84.

    MATH  Article  MathSciNet  Google Scholar 

  3. Brazzale, A. (1999), Approximate conditional inference in logistic and loglinear models,Jour. Computational and Graphical Statistics, 8, 653–661.

    Article  Google Scholar 

  4. Capani, A. Niesi, G. andRobbiano, L., CoCoA: a system for doing computations in commutative algebra.

  5. Collett, D. (1991),Modelling Binary Data. New York: Chapman and Hall.

    Google Scholar 

  6. Cox, D., Little, J. andO’Shea, D. (1992),Ideals, Varieties, and Algorithms. New York: Springer.

    MATH  Google Scholar 

  7. Diaconis, P. andGangolli, A. (1995), Rectangular arrays with fixed margins. InDiscrete Probability and Algorithms (ed. D. Aldous et al.). New York: Springer.

    Google Scholar 

  8. Diaconis, P., Graham, R. andHolmes, S. P. (1999),Statistical problems involving permutations with restricted positions. Stanford University Technical Report No. 1991-1.

  9. Diaconis, P. andSturmfels, B. (1998), Algebraic algorithms for sampling from conditional distributions.Annals of Statistics, 26, 363–397.

    MATH  Article  MathSciNet  Google Scholar 

  10. Dinwoodie, I. H. (1998), The Diaconis-Sturmfels algorithm and rules of succession.Bernoulli, 4, 401–410.

    MATH  Article  MathSciNet  Google Scholar 

  11. Forster, J. J., McDonald, J. W. andSmith, P. W. F. (1999),Markov chain Monte Carlo exact inference for binomial and multinomial logistic regression models. Manuscript.

  12. Haberman, S. (1978),Analysis of qualitative data, Volume. I. New York: Academic Press.

    MATH  Google Scholar 

  13. Holliday, T., Riccomagno, E., Wynn, H. P. andPistone, G. (1997),The application of algebraic geometry to the design and analysis of experiments: a case study. Technical Report, Department of Statistics, University of Warwick.

  14. Liang, K. Y. (1985), Odds ratio inference with dependent data.Biometrika, 72, 678–682.

    Article  Google Scholar 

  15. Liang, K. Y. andPatel, N. (1983), A network algorithm for performing Fisher’s exact test inr ×c contingency tables.Jour. Amer. Statist. Assoc., 78, 427–434.

    Article  Google Scholar 

  16. Pistone, G., Riccomagno, E. andWynn, H. P. (2000),Algebraic Statistics. Manuscript.

  17. Sturmfels, B. (1996),Gröbner Bases and Convex Polytopes. Rhode Island: AMS, Providence.

    MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to I. H. Dinwoodie.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dinwoodie, I.H. Generating functions for exactp-values of odds ratios in logistic regression. J. Ital. Statist. Soc. 7, 221 (1998).

Download citation


  • Conditional test
  • exponential family
  • Gröbner basis
  • logistic regression
  • normal form
  • odds ratio