Transcription of Poisson Models for Count Data
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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. The result is a generalized linear model withPoisson response and link The Children Ever Born DataTable , adapted from Little (1978), comes from the Fiji Fertility Surveyand is typical of the sort of table published in the reports of the WorldFertility Survey.
multiplicative e ect of the j-th predictor on the mean. Increasing x j by one unit multiplies the mean by a factor expf jg. A further advantage of using the log link stems from the empirical obser-vation that with count data the e ects of predictors are often multiplicative rather than additive. That is, one typically observes small e ects for ...
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