MaxDiff

The MaxDiff model is a special case of the more general Best-Worst Scaling (BWS) technique, a discrete choice model invented by Jordan Louviere in 1987 while on the faculty at the University of Alberta. It's application, and how it differs from other well-known cognitive processes (sequential etc) that might produce best and worst data, is described in the definitive textbook by Jordan Louviere (University of South Australia), Terry N Flynn (TF Choices Ltd) and Anthony A. J Marley (University of Victoria and University of South Australia).

The maxdiff is a long-established academic mathematical theory with very specific assumptions about how people make choices: it assumes that respondents evaluate all possible pairs of items within the displayed set and choose the pair that reflects the maximum difference in preference or importance. It may be thought of as a variation of the method of Paired Comparisons. Consider a set in which a respondent evaluates four items: A, B, C and D. If the respondent says that A is best and D is worst, these two responses inform us on five of six possible implied paired comparisons:

A > B, A > C, A > D, B > D, C > D

The only paired comparison that cannot be inferred is B vs. C. In a choice among five items, MaxDiff questioning informs on seven of ten implied paired comparisons.

It should be recognised that respondents can produce best-worst data in any of a number of ways. Instead of evaluating all possible pairs (the maxdiff model), they might choose the best from n items, the worst from the remaining n-1, or vice versa. Or indeed they may use another method entirely. Thus it should be clear that maxdiff is a subset of BWS. Indeed as the number of items increases, the number of possible pairs increases in a multiplicative fashion: n items produces n(n-1) pairs (where best-worst order matters). Assuming respondents do evaluate all possible pairs is a strong assumption and in 14 years of presentations, the three co-authors have virtually never found a course or conference participant who admitted to using this method to elicit their best and worst choices. Virtually all use sequential models (best then worst or worst then best). Early work did use the term maxdiff to refer to BWS, but with the recruitment of Marley to the team developing the method, correct academic terminology has been disseminated throughout Europe and Asia-Pacific (if not North America, which continues to use the maxdiff term). Indeed it is far from clear that the major software manufacturers of discrete choice models actually implement maxdiff models in estimating parameters of their models, despite this continuing advertising of maxdiff capabilities.

The re-naming of the method, to make clear that maxdiff scaling is BWS but BWS is not necessarily maxdiff, was decided by Louviere in consultation with his two key contributors (Flynn and Marley) in preparation for the book, and was presented in an article by Flynn.

External sources

• Almquist, Eric; Lee, Jason (April 2009), What Do Customers Really Want?, Harvard Business Review, retrieved 15 February 2010
• Cohen, Steve and Paul Markowitz (2002), “Renewing Market Segmentation: Some New Tools to Correct Old Problems,” ESOMAR 2002 Congress Proceedings, 595-612, ESOMAR: Amsterdam, The Netherlands.
• Cohen, Steven H. (April 2003). "Maximum Difference Scaling: Improved Measures of Importance and Preference for Segmentation". Proceedings of the Sawtooth Software Conference. San Antonio, TX. pp. 61–74. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help)
• Louviere, J. J. (1991), “Best-Worst Scaling: A Model for the Largest Difference Judgments,” Working Paper, University of Alberta.
• Louviere, J.J.; Flynn, T.N.; Marley, A.A.J., “Best-Worst Scaling: Theory, Methods and Applications”, Cambridge University Press, Cambridge (September 2015)
• Thurstone, L. L. (1927), “A Law of Comparative Judgment,” Psychological Review, 4, 273-286.

• Max Diff Survey Example