Fast Polyhedral Adaptive Conjoint Estimation

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 Limor Weisberg for creating the graphics in this paper. This paper has benefited from presentations at the CIPD Spring Research Review, the Epoch Foundation Workshop, the MIT ILP Symposium on "Managing Corporate Innovation," the MIT Marketing Workshop, the MSI Young Scholars Conference, and the Stanford Marketing Workshop. Fast Polyhedral Adaptive Conjoint Estimation AbstractWeb-based customer panels and web-based multimedia capabilities offer the potential to get information from customers rapidly and iteratively based on virtual product profiles. However, web-based respondents are impatient and wear out more quickly. At the same time, in commercial applications, conjoint analysis is being used to screen large numbers of product features. Both of these trends are leading to a demand for conjoint analysis methods that provide reasonable estimates with fewer questions in problems involving many parameters.In this paper we propose and test new adaptive conjoint analysis methods that attempt to reduce respondent burden while simultaneously improving accuracy. We draw on recent "interior-point" developments in mathematical programming which enable us to quickly select those questions that narrow the range of feasible partworths as fast as possible. We then use recent centrality concepts (the analytic center) to estimate partworths. These methods are efficient, run with no noticeable delay in web-based questionnaires, and have the potential to provide estimates of the partworths with fewer questions than extant methods.After introducing these "polyhedral" algorithms we implement one such algorithm and test it with Monte Carlo simulation against benchmarks such as efficient (fixed) designs and Adaptive Conjoint Analysis (ACA). While no method dominates in all situations, the polyhedral algorithm appears to hold significant potential when (a) profile comparisons are more accurate than the self-explicated importance measures used in ACA, (b) when respondent wear out is a concern, and (c) when the product development and marketing teams wish to screen many features quickly. We also test a hybrid method that combines polyhedral question selection with ACA estimation and show that it, too, has the potential to improve predictions in many contexts. The algorithm w...

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