Advertisement

Association

  • Tamás Rudas
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

The statistical analysis of associations is a central theme in this book. This chapter starts with a description of the properties of the odds ratio, including its maximum likelihood estimation. Because of its variation independence from the marginal distributions, it is argued the odds ratio is the most useful measure of association. The structure of I × J tables, as described by the systems of local or spanning cell odds ratios, which are generalizations of the simple odds ratio defined for 2 × 2 tables, is described and analyzed by association models. The odds ratio is generalized to higher-dimensional tables by introducing a hierarchical structure of conditional odds ratios. Independence may be seen as lack of association, but a related simple structure, conditional independence, is found more often in real data, and properties of the maximum likelihood estimates under conditional independence are studied.

References

  1. 6.
    Bartolucci, F., Forcina, A.: Extended RC Association Models Allowing for Order Restrictions and Marginal Modeling. Journal of the American Statistical Association, 97, 1192–1199 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 7.
    Becker, M.P., Clogg, C.C.: An alysis of Sets of Two-way Contingency Tables Using Association Models. Journal of the American Statistical Association, 84, 142–151 (1989)MathSciNetCrossRefGoogle Scholar
  3. 15.
    Clogg, C.C., Shihadeh, E.S.: Statistical Models for Ordinal Variables. Sage Publications, Thousand Oaks (1994)Google Scholar
  4. 34.
    Goodman, L. A.: Simple Models for the Analysis of Association in Cross- Classifications Having Ordered Categories. Journal of the American Statistical Association 74, 37–52 (1979)Google Scholar
  5. 72.
    Rudas, T.: Odds Ratios in the Analysis of Contingency Tables. Sage Publications, Thousand Oaks (1998)CrossRefGoogle Scholar
  6. 88.
    Tyree, A.: Mobility ratios and association in mobility tables. Population Studies, 27, 577–588 (1973)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Tamás Rudas
    • 1
    • 2
  1. 1.Center for Social SciencesHungarian Academy of SciencesBudapestHungary
  2. 2.Eötvös Loránd UniversityBudapestHungary

Personalised recommendations