5 An unordered multinomial dependent variable. In the previous chapter we considered the Logit and Probit models for a binomial dependent variable. These models are suitable for modeling binomial choice decisions, where the two categories often correspond to no/yes situations. | 5 An unordered multinomial dependent variable In the previous chapter we considered the Logit and Probit models for a binomial dependent variable. These models are suitable for modeling binomial choice decisions where the two categories often correspond to no yes situations. For example an individual can decide whether or not to donate to charity to respond to a direct mailing or to buy brand A and not B. In many choice cases one can choose between more than two categories. For example households usually can choose between many brands within a product category. Or firms can decide not to renew to renew or to renew and upgrade a maintenance contract. In this chapter we deal with quantitative models for such discrete choices where the number of choice options is more than two. The models assume that there is no ordering in these options based on say perceived quality. In the next chapter we relax this assumption. The outline of this chapter is as follows. In section we discuss the representation and interpretation of several choice models the Multinomial and Conditional Logit models the Multinomial Probit model and the Nested Logit model. Admittedly the technical level of this section is reasonably high. We do believe however that considerable detail is relevant in particular because these models are very often used in empirical marketing research. Section deals with estimation of the parameters of these models using the Maximum Likelihood method. In section we discuss model evaluation although it is worth mentioning here that not many such diagnostic measures are currently available. We consider variable selection procedures and a method to determine some optimal number of choice categories. Indeed it may sometimes be useful to join two or more choice categories into a new single category. To analyec the fit of the models we consider within- and out-of-sample forecasting and the evaluation of forecast performance. The illustration in section concerns
