# 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)
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)
5. 48.
Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)
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)
9. 74.
Rudas, T.: Canonical representation of log-linear models. Communications in Statistics – Theory and Methods, 31, 2311–2323 (2002)