12.2. Methodology for Poisson Regression
Suppose that a response variable Y is distributed as Poisson and has expected value μ. Recall that the variance of a Poisson variable is also μ. If you have a single explanatory variable x, you can write a regression model for μ as
g(μ) = α + xβ
where g is a link function, in terms of a GLM (generalized linear model). Usually, g is taken to be the log function. If so, you have a loglinear model
log(μ) = α + xβ
You can rewrite this model as
μ = eαexβ
If you increase the explanatory variable x by one unit, it has a multiplicative effect of eβ on μ. Since this model is specified as a GLM, with a log link and a Poisson distribution, you can fit it with the GENMOD procedure and use the usual deviance and likelihood ...
Get Categorical Data Analysis Using The SAS® System, 2nd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
