Generalized linear model: Difference between revisions

Revision as of 03:42, 15 September 2023

Revision as of 18:22, 9 November 2023

Line 18:

==Overview==

In a generalized linear model (GLM), each outcome '''Y''' of the [[dependent variable]]s is assumed to be generated from a particular [[probability distribution|distribution]] in an [[exponential family]], a large class of [[probability distributions]] that includes the [[normal distribution|normal]], [[binomial distribution|binomial]], [[poisson distribution|Poisson]] and [[gamma distribution|gamma]] distributions, among others. The conditional mean, '''''μ''''', of the distribution depends on the independent variables, '''X''', through:

: <math>\operatorname{E}(\mathbf{Y}\mid\mathbf{X}) = \boldsymbol{\mu} = g^{-1}(\mathbf{X}\boldsymbol{\beta}) </math>