Fast Polyhedral Adaptive Conjoint Estimation

Abstract

Web-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 we test helps to illustrate how polyhedral methods can be combined effectively and synergistically with the wide variety of existing conjoint analysis methods. We close with suggestions on how polyhedral algorithms can be used in other preference measurement contexts (e.g., choice-based conjoint analysis) and other marketing problems.