The Log-Linear Model

The term log-linear derives from the fact that we can, through logarithmic transformations, restate the problem of analyzing multi-way frequency tables in terms that are very similar to ANOVA.

Specifically, we may think of the multi-way frequency table to reflect various main effects and interaction effects that add together in a linear fashion to bring about the observed table of frequencies. Bishop, Fienberg, and Holland (1974) provide details on how to derive log-linear equations to express the relationship between factors in a multi-way frequency table.