A linear model that describes the variation in the expected value of the logarithm of the response variable (see regression). Log-linear models arise naturally in the context of modelling the variation in the cell frequencies of a contingency table.

In the commonly used hierarchical log-linear models, the inclusion of a term corresponding to a multi-variable interaction necessitates the inclusion of terms corresponding to all simpler interactions.

For all log-linear models the expected frequencies are determined by the marginal totals of the table. In some cases there is a simple algebraic formula (as in the case of the independence model)—a model for which this is the case is called a direct model. See also logit model.