Log-Linear Model
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Description
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 ( c + ∑ i w i f i ( X ) ) {\displaystyle \exp \left(c+\sum _{i}w_{i}f_{i}(X)\right)} ,
in which the f i( X ) are quantities that are functions of the variable 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.
- 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 f i( 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.
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- Slug: log-linear-model
- Added: Jul 20, 2024