Log-linear model

A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply linear regression. That is, it has the general form
in which the are quantities that are functions of the variable, in general a vector of values, while and the stand for the model parameters.
The term may specifically be used for:

A log-linear plot or graph, which is a type of semi-log plot.
Poisson regression for contingency tables, a type of generalized linear model.

The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables, or more immediately, the transformed quantities in the range −∞ to +∞. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. Thus the contexts where these models are useful or realistic often depends on the range of the values being modelled.