Generalized Linear Model/Examples

Examples of Generalized Linear Models

One Variable

The generalized linear model for one cause variable $x$ is of the form:

$\map g \mu = \beta_0 + \beta_1 x$

where $\map g \mu$ is the link function.

Bernoulli Variable

Let $Y$ be a Bernoulli variable with expectation $\mu = p$.

Then the link function $\map g \mu$ of the generalized linear model for $Y$ is given by:

$\map g \mu = \map \ln {\dfrac p {1 - p} }$

Poission Distribution

Let $Y$ be a random variable with a Poisson distribution.

Let $Y$ have an expectation $\lambda$ which varies with $x$.

Then the link function $\map g \lambda$ of the generalized linear model for $Y$ is given by:

$\map g \lambda = \ln \lambda$

Probit Analysis

Probit analysis is a special case of a generalized linear model.

Note that, like least squares regression, it has been around since before the formulation of the generalized linear model.