Models for Unordered Multiple Choices

The unordered multiple choice model assumes the relationship:

where the response of the variable Y is measured in one of k+1 different categories, and is the parameter vector for each j. This model is made operational by a particular choice of the distributional form of g. Although two models, logit and probit could be considered as before, the probit model is practically hard to employ. Two different logit models are commonly used; one is multinomial logit or generalized logit model and the other is conditional logit (McFadden, 1974, "Conditional Logit Analysis of Qualitative Choice Behavior," Frontiers in Econometrics, Zarembka ed., New York, Academic Press, pp. 105-142) or discrete choice model (this is also often referred as multinomial logit model, resulting in a conflict in terminology). The major difference between the two models is found in the characteristics of the vector x. The multinomial logit model is typically (but not necessarily) used for the data in which x variables are the characteristics of individuals, not the characteristics of the choices. The conditional logit model is typically (but not necessarily) employed in the case where x variables are the characteristics of the choices, often called attributes of the choices.