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SAS for Linear Models, Fourth Edition by Ph. D. Ramon C. Littell, Ph. D. Rudolf J. Freund, Ph. D. Walter W. Stroup

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10.4 Count Data and Overdispersion

The examples in the previous sections of this chapter involved categorical data. Generalized linear models are useful for other types of non-normal data as well. Many studies, for example, use counts as the primary response variable. This section presents a typical example.

Historically, statistical theory has placed counting processes in a framework that implies a Poisson distribution. However, recent work, particularly in biological settings such as agriculture, ecology, and environmental science, suggests that the Poisson distribution is often inappropriate for counts. The Poisson assumes that the mean and variance are equal. In biological settings, the birds, insects, plants, and so forth being counted tend ...

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