Modeling and Multivariate Methods - SAS

Chapter 16 Performing Choice Modeling 423
Segmentation
• Select Profiler from the drop-down menu to obtain the results shown in Figure 16.28. Notice that the
parameter estimates and the likelihood ratio test results are identical to the results obtained for the
Choice Model with only two tables, shown in Figure 16.6 and Figure 16.7.
Figure 16.28 Prediction Profiler for Pizza Data One-Table Analysis
Segmentation
Market researchers sometimes want to analyze the preference structure for each subject separately in order to
see whether there are groups of subjects that behave differently. However, there are usually not enough data
to do this with ordinary estimates. If there are sufficient data, you can specify “By groups” in the Response
Data or you could introduce a Subject identifier as a subject-side model term. This approach, however, is
costly if the number of subjects is large. Other segmentation techniques discussed in the literature include
Bayesian and mixture methods.
You can also use JMP to segment by clustering subjects using response data. For example, after running the
model using the Pizza Profiles.jmp, Pizza Responses.jmp, and the optional Pizza Subjects.jmp data sets,
click on the drop-down menu for the Choice Model platform and select Save Gradients by Subject. A
new data table is created containing the average Hessian-scaled gradient on each parameter, and there is one
row for each subject.
Note: This feature is regarded as an experimental method, since, in practice, little research has been
conducted on its effectiveness.
These gradient values are the subject-aggregated Newton-Raphson steps from the optimization used to
produce the estimates. At the estimates, the total gradient is zero, and
Δ = H – 1 g = 0
where g is the total gradient of the log-likelihood evaluated at the MLE, and
H – 1 is the inverse Hessian function or the inverse of the negative of the second partial derivative of the
log-likelihood.