{{Short description|Mathematical model}} {{More citations needed|date=July 2012}}
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 :<math>\exp \left(c + \sum_{i} w_i f_i(X) \right)</math>, in which the {{math|''f<sub>i</sub>''(''X'')}} are quantities that are functions of the variable {{math|''X''}}, in general a vector of values, while {{math|''c''}} and the {{math|''w<sub>i</sub>''}} 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 {{math|''X''}}, or more immediately, the transformed quantities {{math|''f<sub>i</sub>''(''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.
==See also== *Log-linear analysis *General linear model *Generalized linear model *Boltzmann distribution *Elasticity
==Further reading== *{{cite book |last=Gujarati |first=Damodar N. |last2=Porter |first2=Dawn C.|author2-link=Dawn C. Porter |title=Basic Econometrics |location=New York |publisher=McGraw-Hill/Irwin |year=2009 |isbn=978-0-07-337577-9 |chapter=How to Measure Elasticity: The Log-Linear Model |pages=159–162 }}
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Category:Log-linear models
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