Log-linear model
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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 : \exp \left(c + \sum_{i} w_i f_i(X) \right) , in which the are quantities that are functions of the variable , in general a vector of values, while and the 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 , or more immediately, the transformed quantities 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.
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 \exp \left(c + \sum_{i} w_i f_i(X) \right) , in which the are quantities that are functions of the variable , in general a vector of values, while and the 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 , or more immediately, the transformed quantities 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
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