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Greedoid-Based Noncompensatory Inference

Lincoln Laboratory, Massachusetts Institute of Technology, 244 Wood Street, Lexington, Massachusetts 02420-9108
UCLA Anderson School, 110 Westwood Plaza, B-514, Los Angeles, California 90095
Massachusetts Institute of Technology, E40-179, 50 Memorial Drive, Cambridge, Massachusetts 02142
Massachusetts Institute of Technology, E53-363, 50 Memorial Drive, Cambridge, Massachusetts 02142
myee{at}ll.mit.edu
edahan{at}ucla.edu
jhauser{at}mit.edu
jorlin{at}mit.edu

Greedoid languages provide a basis to infer best-fitting noncompensatory decision rules from full-rank conjoint data or partial-rank data such as consider-then-rank, consider-only, or choice data. Potential decision rules include elimination by aspects, acceptance by aspects, lexicographic by features, and a mixed-rule lexicographic by aspects (LBA) that nests the other rules. We provide a dynamic program that makes estimation practical for a moderately large numbers of aspects.

We test greedoid methods with applications to SmartPhones (339 respondents, both full-rank and consider-then-rank data) and computers (201 respondents from Lenk et al. 1996). We compare LBA to two compensatory benchmarks: hierarchical Bayes ranked logit (HBRL) and LINMAP. For each benchmark, we consider an unconstrained model and a model constrained so that aspects are truly compensatory. For both data sets, LBA predicts (new task) holdouts at least as well as compensatory methods for the majority of the respondents. LBA’s relative predictive ability increases (ranks and choices) if the task is full rank rather than consider then rank. LBA’s relative predictive ability does not change if (1) we allow respondents to presort profiles, or (2) we increase the number of profiles in a consider-then-rank task from 16 to 32. We examine trade-offs between effort and accuracy for the type of task and the number of profiles.

Key Words: lexicography; noncompensatory decision rules; choice heuristics; optimization methods in marketing; conjoint analysis; product development; consideration sets
History: Received: January 25, 2005;