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

Abstract

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.marketing, marketing: buyer behavior, decision analysis: sequential

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“…15 For instance, the purchase decision for 'Ford', 'Dodge' or 'Chevrolet' is a function of a consumer's series of assessments of car attributes, such as price, size and fuel economy. 16 Gensch 5 proposes a two-stage choice model where Stage 1 is for attribute processing to screen alternatives down to a few choices; and Stage 2 is for brand processing, where a smaller set of choices are reassessed by comparing their attributes simultaneously. A body of literature is then built upon this notion and a general consensus is reached, where a two-stage choice model captures the consumer decision process well.…”

An Empirical Two-Stage Choice Model with Varying Decision Rules Applied to Internet Clickstream Data

“…Researchers have long hypothesized a two-stage choice process in which consumers first select a subset of available products to form a consideration or choice set and then, from that reduced set of products, choose a single product to purchase (Bettman 1979;Gensch 1987;Shocker et al 1991;Wright and Barbour 1977). These studies have also proposed that consumers use different decision rules in each of the two stages.…”

“…Since the idea of a two-stage choice process was presented, there have been several efforts to capture the process empirically in models of consumer choice (e.g., Andrews and Srinivasan 1995;Gensch 1987;Siddarth, Bucklin, and Morrison 1995). However, the available data have not allowed Stage 1 choice to be observed directly, and therefore many of the two-stage models that have been devel-oped have focused on crafting ways to capture the unobservable first stage rather than evaluating the differences between the stages.…”

A hybrid compensatory-noncompensatory model of residential preference structures

“…His model has been extended by Lioukas (1984) to the case of more than two choice alternatives. In the same way, Young and his associates have incorporated thresholds in elimination-by-aspect models, which they applied to location problems and residential choice behaviour (Young, 1983(Young, , 1984Young and Ogden, 1983;Young and Richardson, 1980, 1983}, while Recker and Golob (1979 and Gensch and Svestka (1979) included thresholds in lexicographic decision rules. Finally, Meyer and Johnson's stochastic elimination model is also based on the idea that choice alternatives should meet certain threshold values to remain in an individual's choice set (Johnson and Meyer, 1984).…”