Log-Linear Models: Estimation

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

Abstract

Maximum likelihood estimation of log-linear models is considered as a special case of maximum likelihood estimation in exponential families, with the mixed parameterization used in the definition of log-linear models playing a central role: the canonical parameters on the ascending class are specified by the model, while the marginal distributions on the descending class are taken from the observed data in the maximum likelihood estimates. Then, the main tool of computing maximum likelihood estimates, the Iterative Proportional Fitting Procedure, is described, and its convergence is proved.

References

  1. 3.
    Anderson, B.: Estimating small-area income deprivation: An iterative proportional fitting approach. In Tanton, R., Edwards, K. (ed.) Spatial Microsimulation: A Reference Guide for Users, pp. 49–67. Springer, New York (2012)CrossRefGoogle Scholar
  2. 17.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd ed. Wiley, New York (2006)MATHGoogle Scholar
  3. 18.
    Csiszár, I.: I-divergence geometry of probability distributions and minimization problems. Annals of Probability, 3, 146–158. (1975)MathSciNetCrossRefMATHGoogle Scholar
  4. 19.
    Csiszár, I., Körner, J.: Information Theory: Coding Theorems for Discrete Memoryless Channels. Cambridge University Press, (2011)Google Scholar
  5. 26.
    Fienberg, S.E, Rinaldo, A. Maximum likelihood estimation in log-linear models. Annals of Statistics, 40, 996–1023 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 36.
    Haberman, S.J.: The Analysis of Frequency Data. Univ. Chicago Press, Chicago, IL. (1974)MATHGoogle Scholar
  7. 42.
    Klimova, A., Rudas, T.: Iterative scaling in curved exponential families. Scandinavian Journal of Statistics, 42, 832–847. (2015)MathSciNetCrossRefMATHGoogle Scholar
  8. 55.
    Lumley, T.: Complex Surveys: A Guide to Analysis Using R, Wiley, New York (2010)CrossRefGoogle Scholar
  9. 71.
    Rudas, T.: Prescribed conditional interaction structure models with application to the analysis of mobility tables. Quality & Quantity 25, 345–358 (1991)Google Scholar
  10. 84.
    Rudas, T., Leimer, H.-G.: Analysis of contingency tables with known conditional odds ratios or known log-linear parameters. In: Francis, B., Seeberg, G. U. H., van der Heijden, P. G. M., Jansen, W. (eds.) Statistical Modeling, pp. 313–322, Elsevier, xxxxx (1992)Google 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