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Poisson Models for Count Data

Chapter 4 Poisson Models for CountDataIn this chapter we study log-linear Models for Count data under the assump-tion of a Poisson error structure. These Models have many applications, notonly to the analysis of counts of events, but also in the context of Models forcontingency tables and the analysis of survival Introduction to Poisson RegressionAs usual, we start by introducing an example that will serve to illustrativeregression Models for Count data. We then introduce the Poisson distributionand discuss the rationale for modeling the logarithm of the mean as a linearfunction of observed covariates.

POISSON MODELS FOR COUNT DATA Then the probability distribution of the number of occurrences of the event in a xed time interval is Poisson with mean = t, where is the rate of occurrence of the event per unit of time and tis the length of the time interval. A process satisfying the three assumptions listed above is called a Poisson process. In the

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