10 Methods for Count Data
Chapter 1 was devoted to descriptive methods for categorical data, but most
topics were centered on binary data and the binomial distribution. Chapter 9
continues on that direction with logistic regression methods for binomial-
distributed responses. This chapter is devoted to a di¤erent type of categorical
data, count data; the eventual focus is the Poisson regression model; the Pois-
son distribution was introduced very briefly in Chapter 3. As usual, the purpose
of the research is to assess relationships among a set of variables, one of which
is taken to be the response or dependent variable, that is, a variable to be
predicted from or explained by other variables; other variables are called
predictors, explanatory variables, or independent variables. Choosing an
appropriate model and analytical technique depends on the type of response
variable or dependent variable under investigation. The Poisson regression
model applies when the dependent variable follows a Poisson distribution.
10.1 POISSON DISTRIBUTION
The binomial distribution is used to characterize an experiment when each trial
of the experiment has two possible outcomes (often referred to asfailureand
success. Let the probabilities of failure and success be, respectively, 1pand
p; the target for the binomial distribution is the total numberXof successes in
ntrials. The Poisson model, on the other hand, is used when the random vari-
ableXis supposed to represent the number of occurrences of some random
event in an interval of time or space, or some volume of matter, so that it is not
bounded bynas in the binomial distribution; numerous applications in health
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