DISCRETE CHOICE MODELS
The preceding chapters were focused on discussion of modeling techniques where the responses were continuous. In practice, we often encounter responses that are discrete. For example, direct marketing companies often model the response behavior of consumers receiving an offer to buy their products. Here, y, the response variable, equals 1 if the consumer responds to the mail offer, and it equals 0 otherwise. Direct marketing companies also build conversion models where again the response variable equals 1 if the consumer’s inquiry about a mail offer results in a sale; the response variable equals 0 otherwise. Another example involves attrition models built by insurance companies that predict the likelihood that an existing consumer will cancel his or her policy to take up a new policy with a competitor. Here, the response variable equals 1 if the consumer cancels a policy, and it equals 0 otherwise. Attrition models can also be built by using duration models but the common approach in industry is to treat the attrition response as 0 or 1. A common theme in each example is the binary nature of the response variable. Of course, the response variable can assume more than two discrete values. This chapter deals with estimating parameters of models where the distribution of the response variable is not continuous but discrete. We will focus our attention on logistic regression with dichotomous responses, and Poisson regression.
By definition, ...