7.5. Other Applications

The two discrete choice examples that we examined in the previous sections had two features in common:

• Each person had the same set of options.

• Each person chose one and only one option.

Neither of these features is essential to the discrete choice methodology. In the chocolate bar example, instead of receiving all eight chocolate bars, each person could have been given two chocolate bars and asked to decide which was better. Or some people could get two while others get three or four. In studies of travel mode choice, some cities might not have train service, which removes that option from the choice set of persons traveling to those cities. This creates no special difficulty for data processing and analysis. Each person has a distinct record for every available option—some people may have more records, others may have fewer. The only limitation is that, if you want to include dummy variables for each option, there has to be a substantial amount of overlap in people’s option sets.

If the principal aim is to estimate the effects of the characteristics of the options on each person’s choice, there’s no need for the option sets to have any items in common. For example, one well-known study examined the factors affecting students’ choices of where to attend graduate school (Punj and Staelin 1978). Each person’s option set consisted of the schools to which he or she had been accepted. Obviously, this set varied enormously in size and composition. Explanatory variables included such things as student body size, tuition, financial aid, academic reputation, and distance from the applicant. While there was undoubtedly some overlap in students’ option sets, the analysis could have proceeded even if every student had been accepted by a completely distinct set of colleges.

The methodology can also be extended to studies in which people choose two or more options from among their option sets. Imagine a multi-city study of people’s preference for radio stations. Each person’s option set consists of the stations broadcasting in his or her city, and the question asked is “Which radio stations do you listen to regularly?” Obviously, the number of choices will vary greatly from one person to another. Most discrete-choice software can’t handle multiple choices. But PROC PHREG does it easily with the syntax we’ve already been using. The only difference is that the choice variable will have a value of 1 for more than one item in the choice set.

This is as good a point as any to note that there is a modification to the PHREG syntax that can reduce computation time. With large data sets, this can make a substantial difference. However, the modified syntax only works when the respondent makes a single choice per option set. For the travel data, the alternative syntax is:

PROC PHREG DATA=travel NOSUMMARY;
  MODEL choice*choice(2) = ttme time cost;
  STRATA id;
RUN;

which produces exactly the same results we saw in Output 7.3. In this program, I have removed the TIES=DISCRETE option and changed the specification of the dependent variable. The number in parenthesis should be the value of the variable that denotes a nonchoice. Why does this syntax work? Don’t ask. The answer is both complicated and unenlightening.