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| To estimate the parameters of the model (i.e., the coefficients), [[Statistics/MaximumLikelihoodEstimation|maximum likelihood]] methods are usually used and solved with [[Statistics/IterativelyReweightedLeastSquares|IRLS]]. |
Generalized Linear Model
A generalized linear model (GLM) is a generalized modeling method.
Contents
Design
A GLM has three components.
A distribution to characterize outcomes.
A linear model to relate an outcome with one or more independent variable(s).
A link function to relate the linear model with expected outcomes.
The distribution can be any PDF.
The link function generally is a non-linear transformation, such as a logarithm. It is also typically stated and notated as a function g, as in g(E[y|X]) = Xb. It could equivalently be stated like E[y|X] = g-1(Xb), which can be a more straightforward approach, but the other orientation is simpler for interpretation.
As an example, OLS is a particular form of a GLM where:
outcomes are assumed to be normally distributed
outcomes are linearly modeled like y = Xb
a link function of 1 is implicitly used
To estimate the parameters of the model (i.e., the coefficients), maximum likelihood methods are usually used and solved with IRLS.