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| '''Generalized Linear Model''' ('''GLM''') is a linear regression method. | A '''generalized linear model''' ('''GLM''') is a generalized modeling method. |
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| The link function generally is a non-linear transformation, such as a logarithm. | 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. |
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| As an example, [[Econometrics/OrdinaryLeastSquares|OLS]] is a particular form of a GLM where: | As an example, [[Statistics/OrdinaryLeastSquares|OLS]] is a particular form of a GLM where: |
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