# MaxDiff

Maximum difference scaling (MaxDiff) is a discrete choice model first described by Jordan Louviere in 1987 while on the faculty at the University of Alberta. The first working papers and publications occurred in the early 1990s. With MaxDiff, survey respondents are shown a set of the possible items and are asked to indicate the best and worst items (or most and least important, or most and least appealing, etc.). According to Louviere, MaxDiff 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. MaxDiff 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. MaxDiff questionnaires are relatively easy for most respondents to understand. Furthermore, humans are much better at judging items at extremes than in discriminating among items of middling importance or preference[citation needed]. And since the responses involve choices of items rather than expressing strength of preference, there is no opportunity for scale use bias.

In 1983 Richardson introduced a choice method in which subjects reported the most alike pair of a triad and the most different pair. The component of this method involving the most different pair may be properly called “MaxDiff” in contrast to a “most-least” or “best-worst” method where both the most different pair and the direction of difference are obtained. Ennis, Mullen and Frijters (1988) derived a Thurstonian scaling model for Richardson’s method of triads so that the results could be scaled under normality assumptions about the item percepts. Richardson’s method of triad and most-least methods belong to a class of methods that do not require the estimation of a cognitive parameter as occurs in the analysis of ratings data. Other methods in this class include the 2- and 3-alternative forced choice methods, the triangular method, the duo-trio method and the specified and unspecified methods of tetrads. All of these methods have well-developed Thurstonian scaling models. There are a number of possible processes through which subjects may make a most-least decision, including paired comparisons and ranking, but it is not known how the decision is reached.

## Process

The basic steps are:

• select products to be tested
• show products to potential consumers (textually or visually)
• respondents choose the best and worst from each task
• input the data from a representative sample of potential customers into a statistical software program and choose the MaxDiff analysis procedure. The software will produce utility functions for each of the features. In addition to utility scores, you can also request raw counts which will simply sum the total number of times a product was selected as best and worst. These utility functions indicate the perceived value of the product on an individual level and how sensitive consumer perceptions and preferences are to changes in product features.

## Why use maximum difference scaling?

Max Diff is an antidote to standard rating scales or importance scales. Respondents find these ratings scales very easy but they do tend to deliver results which indicate that everything is "quite important", making the data not especially actionable.[citation needed] Max Diff on the other hand forces respondents to make choices between options, while still delivering rankings showing the relative importance of the items being rated.

## Analysis

Estimation of the utility function is performed using multinomial discrete choice analysis, in particular multinomial logit. Several algorithms could be used in this estimation process, including maximum likelihood, neural networks, and the Hierarchical Bayes model. The Hierarchical Bayes model is beneficial because it allows for borrowing across the data.

## 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.
• Ennis, Daniel M, Kenneth Mullen, and Jan E.R. Frijters. (1988). "Variants of the method of triads: Unidimensional Thurstonian models," British Journal of Mathematical and Statistical Psychology, 41, 25-36.
• Richardson, M.W. (1938). "Multidimensional psychophysics," Psychological Bulletin, 35, 659-660.
• Louviere, J. J. (1991), “Best-Worst Scaling: A Model for the Largest Difference Judgments,” Working Paper, University of Alberta.
• Thurstone, L. L. (1927), “A Law of Comparative Judgment,” Psychological Review, 4, 273-286.