Log-Linear Models: Interpretation

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


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.


  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: (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

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© 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

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