The GENMOD Procedure

Examples of Generalized Linear Models

Traditional Linear Model
Logistic Regression
Poisson Regression in Log-Linear Model
Gamma Model with Log Link

You construct a generalized linear model by deciding on response and explanatory variables for your data and choosing an appropriate link function and response probability distribution. Some examples of generalized linear models follow. Explanatory variables can be any combination of continuous variables, classification variables, and interactions.

Traditional Linear Model

response variable: a continuous variable
distribution: normal
link function: identity, $g(\mu ) = \mu$

Logistic Regression

response variable: a proportion
distribution: binomial
link function: logit, $\displaystyle {g(\mu ) = \log \left(\frac{\mu }{1-\mu }\right)}$

Poisson Regression in Log-Linear Model

response variable: a count
distribution: Poisson
link function: log, $g(\mu ) = \log (\mu )$

Gamma Model with Log Link

response variable: a positive, continuous variable
distribution: gamma
link function: log, $g(\mu ) = \log (\mu )$