An Exact Hierarchical Algorithm for Determining Aggregate Statistics from Individual Choice Data

A review of the literature from many disciplines reveals conceptual agreement that individuals choose among alternatives by comparing the attributes of the alternatives in a sequential process. Yet in almost all the published empirical work the model used is a simultaneous compensatory model such as regression, logit, or probit. The sequential choice modeling approach has been severely retarded by the lack of an algorithm to generate the sample statistics projectable to hold-out samples and populations. This paper attempts to fill this void by presenting a prototype aggregate hierarchical model, called HIARC, for analyzing individual choice decisions. HIARC can be viewed as a semi-order lexicographic model that empirically estimates a set of tolerances directly from the data. HIARC and logit are applied to the same empirical data set. While the predictive accuracy is about equal, the two approaches yield different types of diagnostic information and the set of individuals whose choice is correctly predicted by one method is substantially different from the set correctly predicted by the other method.