Polyhedral Methods for Adaptive Choice-Based Conjoint Analysis

Abstract

We gratefully acknowledge the contribution of Robert M. Freund who proposed the use of the analytic center and approximating ellipsoids and gave us detailed advice on the application of these methods.This research was supported by the Sloan School of Management and the Center for Innovation in Product Development at M.I.T. This paper may be downloaded from http://mitsloan.mit.edu/vc. That website also contains (1) open source code to implement the methods described in this paper, (2) open source code for the simulations described in this paper, (3) demonstrations of web-based questionnaires based on the methods in this paper, and (4) related papers on web-based interviewing methods. All authors contributed fully and synergistically to this paper. We wish to thank Ray Faith, Aleksas Hauser, Janine Sisk, Limor Weisberg, Toby Woll for the visual design, programming, and project management on the Executive Education Study. This paper has benefited from presentations at the CIPD Spring Research Review, the Epoch Foundation Workshop, the Marketing Science Conferences in Wiesbaden Germany and Alberta Canada, the MIT ILP Symposium on "Managing Corporate Innovation," the MIT Marketing Workshop, the MIT Operations Research Seminar Series, the MSI Young Scholars Conference, the New England Marketing Conference, and Stanford Marketing Workshop, and the UCLA Marketing Seminar Series. Polyhedral Methods for Adaptive Choice-Based Conjoint Analysis AbstractChoice-based conjoint analysis (CBC) is used widely in marketing for product design, segmentation, and marketing strategy. We propose and test a new "polyhedral" question-design method that adapts each respondent's choice sets based on previous answers by that respondent. Individual adaptation appears promising because, as demonstrated in the aggregate customization literature, question design can be improved based on prior estimates of the respondent's partworths -information that is revealed by respondents' answers to prior questions. The otherwise impractical computational problems of individual CBC adaptation become feasible based on recent polyhedral "interior-point" algorithms, which provide the rapid solutions necessary for real-time computation.To identify domains where individual adaptation is promising (and domains where it is not), we evaluate the performance of polyhedral CBC methods with Monte Carlo experiments. We vary magnitude (response accuracy), respondent heterogeneity, estimation method, and question-design method in a We close by describing an empirical application to the design of executive education programs in which 354 web-based respondents answered stated-choice tasks with four service profiles each. The profiles varied on eight multi-level features. With the help of this study a major university is revising its executive education programs with new formats and a new focus.

Active Machine Learning for Consideration Heuristics

“…For choice-based conjoint analysis, efficient designs are a function of the parameters of compensatory decision rules, and researchers developed "aggregate customization" to preselect questions using data from prestudies (e.g., Arora and Huber 2001). More recently, faced with impatient online respondents, researchers developed algorithms for adaptive conjoint questions based on compensatory models (e.g., Toubia et al 2004). After data are collected adaptively, the likelihood principle enables the data to be reanalyzed with models using classical statistics, Bayesian statistics, or machine learning.…”

“…To the best of our knowledge, this is the first (nearoptimal) adaptive-question method focused on consumers' noncompensatory decision heuristics. Extant adaptive methods focus on compensatory decision rules and are unlikely to explore the space of noncompensatory decision rules efficiently (e.g., Evgeniou et al 2005;Toubia et al , 2004Sawtooth 1996). In prior noncompensatory applications, question selection was almost always based on either random profiles or profiles chosen from an orthogonal design.…”

“…Our focus is on adaptive question selection, but to select questions adaptively, we need intermediate estimates after each answer and before the next question is asked. To avoid excessive delays in online questionnaires, intermediate estimates must be obtained in a second or less (e.g., Toubia et al 2004). This is a difficult challenge when optimizing questions for noncompensatory heuristics because we must search over a discrete space of the order of 2 N decision rules, where N is the number of feature levels (called aspects, as in Tversky 1972).…”

“…Prior research using compensatory rules (e.g., Toubia et al 2004) suggests that adaptive questions are most efficient relative to random or orthogonal questions when consumers' heuristic decision rules are heterogeneous. We expect similar results for noncompensatory heuristics.…”

Selling vs. Profiling: Optimizing the Offer Set in Web-Based Personalization

“…When matching is aimed at profiling, the products in the offer set are chosen so as to improve the reliability of the profile. By carefully varying the composition of the offer set, a firm can effectively profile a customer using techniques such as choice-based conjoint analysis (Louviere and Woodworth 1983), Hierarchical Bayes estimation techniques (Lenk et al 1996), and the more recent adaptive conjoint techniques (Toubier et al 2004, Abernethy et al 2008). When matching is performed with a view to improve the reliability of the profile, it can be termed as active profiling.…”