Statistical Methods in Customer Relationship Management

Appendix K

Poisson Regression Model

(Source: Greene [1])

The Poisson regression model specifies that each is drawn from a Possion distribution with parameter , which is related to the regressors . The primary equation of the model is

(K.1)

The most common formulation for is the log-linear model,

(K.2)

It is easily shown that the expected number of events per period is given by

(K.3)

so

(K.4)

With the parameter estimates in hand, this vector can be computed using any data vector desired.

In practice, the Poisson model is simply a nonlinear regression. But it is far easier to estimate the parameters with maximum likelihood techniques. The log-likelihood function is

(K.5)

The likelihood equations ...