|
Size: 1263
Comment: Killing Econometrics page
|
← Revision 4 as of 2025-01-10 14:29:41 ⇥
Size: 1199
Comment: Killing Econometrics page
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| ## page was renamed from Econometrics/GeneralizedLinearModel | |
| Line 24: | Line 23: |
| 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