Log-linear model

rdf:langString Log-linear model

rdf:langString 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 (possibly multivariate) linear regression. That is, it has the general form , in which the fi(X) are quantities that are functions of the variable X, in general a vector of values, while c and the wi 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 X, or more immediately, the transformed quantities fi(X) 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.