Log-linear model

A log-linear model is a mathematical model that takes the form of a function whose logarithm is a first-degree polynomial function of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form

$\exp \left(c %2B \sum_{i} w_i f_i(X) \right)\,,$

in which the $f i (X)$ are quantities that are functions of the variables $X$ , in general a vector of values, while $c$ and the $w i$ 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
Log-linear modeling (economics), a technique among economists
Markov random field#Log-linear models, a Markov random field with a log-linear distribution
Poisson regression for contingency tables

Log-linear model

See also