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Scaling Conjoint Part Worths: Points vs. Zero-Centered Diffs

For over a decade, a re-scaling method called "Points" has been the default for reporting conjoint part worths (utilities) in Sawtooth Software's conjoint simulators. This approach gives equal weight to each respondent by making the total sum of part worths equal to the number of attributes times 100. Since conjoint part worths are scaled to an arbitrary constant within each attribute, it seemed to us early on that setting the worst level of each attribute for each respondent to zero was as reasonable a decision as any. This held promise of making it easier to present part worths to clients, since the values would generally fall in a comfortable range of about 0 to 100 (the values can actually exceed 100). However, we now suspect that fostering familiarity has sometimes led to misinterpretation. With the benefit of years of hindsight, we think that Points was a mistake.

We are abandoning the Points re-scaling method in all future versions of our software for the following reasons:

  1. When the worst level of each attribute is set to zero and the range falls within the interval of roughly 0 to 100, some people misinterpret the part worths using the assumptions appropriate to ratio-quality data (which conjoint part worths are not). For example, some interpret a part worth of 30 as twice as preferred as a part worth of 15, which is not correct.
  2. The 0 to 100 range for part worths entices people to directly compare the part worth of a single level of one attribute to a single level of another, which is not appropriate. Across attributes, the part worths have arbitrary scaling with respect to one another. Scaling the part worths to a common point (zero) for the worst level of each attribute de-emphasizes the true ambiguity, and can lead some to altogether forget about it.
  3. It seems to us that the appropriate scaling of conjoint data should reflect the relative weight (importance) of attributes, where the weight of attributes is determined by the difference between the best and worst levels within each attribute. In contrast, Points allows the interior levels of attributes to influence the scaling of utilities.

In early versions of our software, we recognized that scaling part worths to reflect the sum of the range of the part worths within attributes was desirable and we offered an alternate re-scaling method to that end called Diffs. Diffs also weights respondents so as to be equal, but on a different criterion: total difference between best and worst levels rather than total points. As with Points, we also set the worst level of each attribute to zero for each individual. Whereas Diffs deals with point number three above, the pitfalls associated with the first two concerns remain.

We do not plan to offer the Points re-scaling method in future versions of our conjoint software systems. Rather, zero-centered Diffs will be the default method. (That method has been the default for our CBC Latent Class Module.)

We have noticed only one small benefit of Points or Diffs relative to zero-centered Diffs. If the worst level of an attribute has an average utility of zero or near-zero, it means that nearly all of the respondents agree that this level is the least preferred. If respondents disagree about the order of preference (say, for brand), the worst level of an attribute is significantly greater than zero. When viewing average zero-centered Diffs, one cannot gain a feel for the degree of disagreement regarding attribute levels. However, a new option available in the next generation market simulator captures that information in a different way by displaying average attribute importances. If you are using individual-level or latent-class part worths, the attribute importances can help you gain a feel for the level of agreement or disagreement regarding level order. Assume you are studying two brands and the average part worths are nearly tied at zero (zero-centered Diffs). If brand also has a significant attribute importance, you would know that respondents really aren't indifferent about brand. Rather, there are distinct groups that feel strongly, but oppositely, about which brand is preferred.

We don't expect that making the change from Points (or Diffs) to zero-centered Diffs will come easily to those used to seeing part worths scaled as Points. Some may argue that the zero-centered Diffs are not as easily interpreted or useful as Points utilities. We contend that zero-centered Diffs communicate the real information available from the part worths and their use minimizes the opportunity for misinterpretation. Since our software always makes part worths available in ASCII files, users bent on using one of the previous methods can always re-scale the data to their preference using other analysis software.