This example uses Poisson regression to model count data from a study of nesting horseshoe crabs. Each female crab had a male crab resident in her nest. The study investigated whether there were other males, called satellites, residing nearby. The data table CrabSatellites.jmp contains a response variable listing the number of male satellites, as well as variables that describe the color, spine condition, weight, and carapace width of the female crab. You are interested in the relationship between the number of satellites and the variables that describe the female crabs.

The Whole Model Test shows that the difference between log-likelihoods for the full and reduced models is 41.6. The Prob>ChiSq value is equivalent to the p-value for a whole model F test. A p-value less than 0.0001 indicates that the model as a whole is significant. The report also contains the corrected Akaike Information Criterion (AICc), 921.7613. This value can be compared with other models to determine the best-fitting model for the data. Smaller AICc values indicate better fitting models.

The Effects Tests report shows that weight is a significant factor in the model. Note that the p-value for weight, 0.0026, is the same in the Parameter Estimates table as well, since weight is a continuous variable.

The Effect Tests report also shows that the categorical variable color is significant. Color has four levels, Light Med, Medium, Dark Med, and Dark, where Dark is the reference variable. In the Parameter Estimates table, you see that the only significant difference within color is between Dark and Light Med, although Dark Med is close to being significant at the 0.05 level.