Mixed Multinomial Logit Model

The Multinomial Logit Model estimates a single set of parameters. For example, if being used to predict preferences for different phones based on the prices and features of the phones it estimates a single parameter for price. Thus, it can be interpreted as assuming that everybody in the population is identical, with any differences in preferences reflecting random error (this is the Random Utility Theory interpretation of the model).

A 'mixed' logit model is a Generalization of the Multinomial Logit Model which accounts for Heterogeneity by estimating ranges of values of the parameters in the model. In this context the term 'mixed' means that the model that is estimated can be viewed as a combination (i.e., 'mixture') of multinomial logit models. Many different ways of accounting for heterogeneity have been developed for regression in general. In the case of the multinomial logit model, the most widely used mixture models are:

• Latent class logit, which assumes that the population contains a number of segments (e.g., a segment wanting low priced phones with few features and another segment willing to pay a premium for more features) and identifies the segments automatically.
• Random parameters logit, which assumes that the distribution of the parameters in the population is described by a multivariate normal distribution. This model is sometimes referred to in market research as Hierarchical Bayes, although this is a misnomer.