ABSTRACT
Multinomial models The multinomial logit model The ordered probit model discussed in the previous section applies to ordered categorical variables. Multinomial models apply to discrete dependent variables that can take unordered multinomial outcomes, for example, y = 0, 1, 2, 3..., that represent a set of mutually exclusive choices. Again, the numerical values of y are arbitrary and in this case they do not imply any natural ordering of the outcomes. A classic example in economics is ‘modal choice’ in transport. Here, the outcomes could represent different modes of transport, for example plane, train, car, and the individual faces a choice of one of these mutually exclusive modes of transport. This choice will depend on characteristics of the alternatives, such as price, convenience, quality of service and so on, and the characteristics of individuals, such as their level of income. Some of the characteristics of the alternatives, such as distance to the nearest hospital, may vary across individuals as well. There is unlikely to be a natural ordering of the choices that applies to all individuals in all situations. In health economics, multinomial models are often applied to the choice of health insurance plan or of healthcare provider. They could also be used to model a choice of a particular treatment regimen for an individual patient.
