Advertisement

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

  • I. H. Dinwoodie
Article

Summary

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.

Keywords

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

References

  1. Agresti, A. (1999), Exact inference for categorical data: recent advances and continuing controversies. To appear inStatistics in Medicine.Google Scholar
  2. Breslow, N. E. (1981), Odds ratio estimators when the data are sparse.Biometrika, 68, 73–84.MATHCrossRefMathSciNetGoogle Scholar
  3. Brazzale, A. (1999), Approximate conditional inference in logistic and loglinear models,Jour. Computational and Graphical Statistics, 8, 653–661.CrossRefGoogle Scholar
  4. Capani, A. Niesi, G. andRobbiano, L., CoCoA: a system for doing computations in commutative algebra. http://cocoa.dima.unige.it.Google Scholar
  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.MATHGoogle 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.Google Scholar
  9. Diaconis, P. andSturmfels, B. (1998), Algebraic algorithms for sampling from conditional distributions.Annals of Statistics, 26, 363–397.MATHCrossRefMathSciNetGoogle Scholar
  10. Dinwoodie, I. H. (1998), The Diaconis-Sturmfels algorithm and rules of succession.Bernoulli, 4, 401–410.MATHCrossRefMathSciNetGoogle 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.Google Scholar
  12. Haberman, S. (1978),Analysis of qualitative data, Volume. I. New York: Academic Press.MATHGoogle 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.Google Scholar
  14. Liang, K. Y. (1985), Odds ratio inference with dependent data.Biometrika, 72, 678–682.CrossRefGoogle 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.CrossRefGoogle Scholar
  16. Pistone, G., Riccomagno, E. andWynn, H. P. (2000),Algebraic Statistics. Manuscript.Google Scholar
  17. Sturmfels, B. (1996),Gröbner Bases and Convex Polytopes. Rhode Island: AMS, Providence.MATHGoogle Scholar

Copyright information

© Società Italiana di Statistica 1998

Authors and Affiliations

  • I. H. Dinwoodie
    • 1
  1. 1.Department of StatisticsTulane UniversityNew OrleansUSA

Personalised recommendations