Statistics Toolbox

Generalized Linear Models

So far, the functions in this section have dealt with models that have a linear relationship between the response and one or more predictors. Sometimes you may have a nonlinear relationship instead. To fit nonlinear models you can use the functions described in Nonlinear Regression Models.

There are some nonlinear models, known as generalized linear models, that you can fit using simpler linear methods. To understand generalized linear models, first let's review the linear models we have seen so far. Each of these models has the following three characteristics:

• The response has a normal distribution with mean µ.
• A coefficient vector b defines a linear combination X*b of the predictors X.
• The model equates the two as µ = X*b.

In generalized linear models, these characteristics are generalized as follows:

• The response has a distribution that may be normal, binomial, Poisson, gamma, or inverse Gaussian, with parameters including a mean µ.
• A coefficient vector b defines a linear combination X*b of the predictors X.
• A link function f(·) defines the link between the two as f(µ) = X*b.

The following example explores this in greater detail.

Stepwise Regression Diagnostics Table

Example: Generalized Linear Models