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Encyclopedia Entry

Log-Linear Model

Mark P. Becker

Cross-classifications of categorical variables ( CONTINGENCY TABLE ) are ubiquitous in the social sciences, and log-linear models provide a powerful and flexible framework for their analysis. The log-linear model has direct analogies to the linear model routinely used to perform an ANALYSIS OF VARIANCE . There are, of course, important issues that are particular to contingency tables analysis, and those are the primary focus of this entry. This entry begins with an exposition of the log-linear model in the context of the 2 × 2 contingency table, and from the basic concepts and models of this simple setting, extensions or generalizations are made to a illustrate how log-linear models can be applied to applications with more than two categories per variable, more than two variables, or a one-to-one matching between the categories of two variables. The concept and representation of the odds ratio are fundamental to understanding the log-linear model ...

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