This example uses data from a study of nesting horseshoe crabs. Each female crab had a male crab resident in her nest. This study investigated whether there were other males, called satellites, residing nearby. The data set CrabSatellites.jmp contains a response variable listing the number of satellites, as well as variables describing the female crab’s color, spine condition, weight, and carapace width. The data are shown in Crab Satellite Data.
Crab Satellite Data
Select Analyze > Fit Model
Assign satell as Y
Assign color, spine, width, and weight as Effects
Choose the Generalized Linear Model Personality
Choose the Poisson Distribution
The Log Link function should be selected for you automatically.
Click Run.
Crab Satellite Results
Second, goodness-of-fit statistics are presented. Analogous to lack-of-fit tests, they test for adequacy of the model. Low p-values for the ChiSquare goodness-of-fit statistics indicate that you may need to add higher-order terms to the model, add more covariates, change the distribution, or (in Poisson and binomial cases especially) consider adding an overdispersion parameter. AICc is also included and is the corrected Akaike’s Information Criterion, where
The Parameter Estimates table shows the estimates of the parameters in the model and a test for the hypothesis that each parameter is zero. Simple continuous regressors have only one parameter. Models with complex classification effects have a parameter for each anticipated degree of freedom. Confidence limits are also displayed.
The sample data table Ship Damage.JMP is adapted from one found in McCullagh and Nelder (1983). It contains information on 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 the ship was constructed (Yr Made) and the block of years the ship saw service (Yr Used).
In this analysis we use the variable Service, the log of the aggregate months of service, as an offset variable. An offset variable is one that is treated like a regression covariate whose parameter is fixed to be 1.0.
Generalized Linear Model as the Personality
Poisson as the Distribution, which automatically selects the Log link function
N to Y
Service to Offset
Type, Yr Made, Yr Used as effects in the model
Ship Damage Fit Model Dialog
When you click Run, you see the report shown in Ship Damage Report. Notice that all three effects (Type, Yr Made, Yr Used) are significant.
Ship Damage Report
Consider the following data set, where x is an explanatory variable and y is the response variable.
Nor.jmp data set
Using Fit Y By X, you can easily see that y varies nonlinearly with x and that the variance is approximately constant (see Y by X Results for Nor.jmp). A normal distribution with a log link function is chosen to model these data; that is, log(μi) = xi'β so that μi = exp(xi'β). The completed Fit Model dialog is shown in Nor Fit Model Dialog.
Y by X Results for Nor.jmp
Nor Fit Model Dialog
After clicking Run, you get the following report.
Nor Results