Choice Models

Many modeling problems do not have a continuous outcome, or dependent variable. It is common to have modeling problems in which the outcome is the selection of one of a set of possible discrete outcomes, like which mode to take to work, or whether to buy or rent a property. This class of problem we will refer to as discrete choice situations, and we develop choice models to address them.

Recall from Section 2.6.1 that the standard multinomial logit model [#!mcfadden-1974!#,#!mcfadden-1981!#] can be specified as:

$$P_i = \frac{\mathrm{e}^{V_i}}{\sum_j \mathrm{e}^{V_j}},$$ (7)

where $j$ is an index over all possible alternatives, $V_i = \beta\cdot {x}_i$ is a linear-in-parameters function, $x_i$ is a vector of observed, exogenous, independent alternative-specific variables that may be interacted with the characteristics of the agent making the choice, and $\beta$ is a vector of $k$ coefficients estimated with the method of maximum likelihood [#!Greene-2002!#].

The multinomial logit model is a very robust and widely used model in practical applications in transportation planning, marketing, and many other fields. It is easy to compute and is therefore fast enough to use on large-scale computational problems such as residential location choice. For explanatory purposes, we will focus initially on choice problems with small numbers of alternatives, such as the choice to rent or own a house, or the number of vehicles a household will choose to own.

Note that there are limitations to the MNL model, and assumptions a user should be aware of. The most important of these is the Independence of Irrelevant Alternatives (IIA) property, which implies that adding or eliminating an alternative from a choice set will affect all of the remaining alternatives proportionately. Stated another way, the relative probabilities of any two alternatives will be unaffected by adding or removing another alternative. See [#!train-book-2003!#] for a thorough introduction to discrete choice modeling using MNL and other choice model specifications.

We now turn to a tutorial for creating models of some of these types using the OPUS GUI. In the following sections, we provide a worked example of creating a new model of each type. The other model types follow the same pattern in the OPUS GUI.