Example of Poisson Regression with an Offset
In the Generalized Linear Model personality, you can specify an offset variable to scale the modeling of the mean in a Poisson regression model with a log link function. Offset variables are most often used to scale the modeling of the mean in Poisson regression situations with a log link.
The data table used in this example contains information about a certain type of damage caused by waves to the forward section of the hull. Hull construction engineers are interested in the risk of damage associated with three variables: ship type, the year in which the ship was constructed, and the block of years the ship was in service.
You use log(months of service) as the offset variable since you expect that the number of repairs are proportional to the number of months in service.
To see how an offset variable is used, assume the linear component of the GLM is called η. Then, with a log link function, the model for the mean with the offset included is specified as follows:
exp[Log(months of service) + η] = [(months of service) * exp(η)].
To run this example, follow these steps:
1. Select Help > Sample Data Folder and open Ship Damage.jmp.
2. Select Analyze > Fit Model.
3. From the Personality list, select Generalized Linear Model.
4. From the Distribution list, select Poisson.
In the Link Function list, Log should be selected for you automatically.
5. Select N and click Y.
6. Select Service and click Offset.
7. Select Type, Yr Made, Yr Used and click Add.
8. Click the check mark box for Overdispersion Tests and Intervals.
9. Click Run.
From the report, notice that all three effects (Type, Yr Made, Yr Used) are significant.
Figure 13.7 Partial Report for a Poisson with Offset Model
