Advertisement

Log-Linear Models: Interpretation

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

Abstract

This chapter starts with the specification and handling of regression type problems for categorical data. The log-linear parameters can be transformed into multiplicative parameters, and these are useful in dealing with the regression problem for categorical variables, where this approach provides a clear and testable concept of separate effects versus joint effect of the explanatory variables. Further topics related to the use of log-linear models in data analysis are also considered. First, the selection and interpretation of log-linear models are illustrated in regression type and non-regression type problems, using real data sets. Two special classes of log-linear models, decomposable and graphical log-linear models, are presented next. Decomposable log-linear models may be seen as direct generalizations of conditional independence. Graphical log-linear models, which are the basis of many current applications of log-linear models, may also be interpreted using generalized conditional independence statements, called Markov properties. Further, these models admit a representation using graphs, where the nodes are the variables in the model. Next, a representation of every log-linear model as the intersection of several log-linear models is discussed, where all of the latter models belong to one of two classes of simple log-linear models. One is the model of conditional joint independence of a group of variables, given all other variables (and graphical log-linear models) may be represented as intersections of such models only and (in the case of non-graphical models) no highest-order conditional interaction among a group of variables.

References

  1. 25.
    Edwards, D., Havranek, T.: A fast procedure for model search in contingency tables. Biometrika, 72, 339–351 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 28.
    Fox, J., Andersen, R.: Effect displays for multinomial and proportional-odds logit models. Sociological Methodology 36, 225–255 (2006)Google Scholar
  3. 29.
    Fox, J., Weisberg, S.: An R Companion to Applied Regression, Second Edition. Thousand Oaks CA: Sage. URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion (2011)Google Scholar
  4. 39.
    Hosmer, D.W., Lemeshow, S.: Applied Logistic Regression, 2nd ed. Wiley, New York (2000)CrossRefzbMATHGoogle Scholar
  5. 48.
    Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)zbMATHGoogle Scholar
  6. 53.
    Leimer, H.-G., Rudas, T.: Conversion between GLIM- and BMDP-type log-linear parameters. GLIM Newsletter, 19, 47 (1989)Google Scholar
  7. 58.
    Miller, R: Simultaneous Statistical Significance, 2nd ed.. Springer, New York (1981)Google Scholar
  8. 70.
    Rudas, T.: A Monte Carlo comparison of the small sample behaviour of the Pearson, the likelihood ratio and the Cressie-Read statistics. Journal of Statistical Computation and Simulation, 24, 107–120 (1986)CrossRefGoogle Scholar
  9. 74.
    Rudas, T.: Canonical representation of log-linear models. Communications in Statistics – Theory and Methods, 31, 2311–2323 (2002)MathSciNetCrossRefzbMATHGoogle 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