(July 2012). A log-linear model is a mathematical model that takes the form of a function whose logarithm is a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form. in which the fi(X) are quantities that are functions of the variables X, in general a vector of values, while c and the wi stand for the model parameters. The term may specifically be used for: 1  A log-linear plot or graph, which is a type of semi-log plot. 2  Poisson regression for contingency tables, a type of generalized linear model.