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:
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 . And since the responses involve choices of items rather than expressing strength of preference, there is no opportunity for scale use bias.
In 1938 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.
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The basic steps are:
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. 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.
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.