Figure 2.—

Relationships among models. Arrows are drawn pointing from simpler models to more complex models of which they are nested subsets. Numbers adjacent to arrows indicate the degrees of freedom separating the models. The models with higher numbers of rate classes become equal to the next lower number of rate-class models when two rate classes within them become equal. Variable-frequency rate-class models become equal to constant-frequency rate-class models when all frequencies equal 1/k, where k is the number of classes. The gamma model is equivalent to the Poisson model when α = ∞. Although the gamma model is not technically “nested” within the multiple-rate-class models, discrete approximations of the gamma model with the same number of rate categories would be nested.