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

$\exp \left(c+\sum _{i}w_{i}f_{i}(X)\right)\,,$

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
• Markov random field#Log-linear models, a Markov random field with a log-linear distribution
• Poisson regression for contingency tables

See also

• Multinomial logit, also known as a maximum entropy classifier
• General linear model
• Generalized linear model

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