Greedoid-Based Noncompensatory Inference

quot;Greedoid languagesquot; 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 moderately large numbers of aspects.We test greedoid methods with application to SmartPhones (339 respondents, both fullrank 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 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 pre-sort profiles or (2) we increase the number of profiles in a consider-then-rank task from 16 to 32. We examine tradeoffs between effort and accuracy for the type of task and the number of profiles