log-linear models

Linear models that describe the variations in the expectation of the logarithm of the response variable. They arise naturally in the context of modelling the variations 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) — models for which this is the case are called direct models. See also logit models.