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Respondents prefer higher prices to lower prices (utility reversal)

I am conducting an analysis of a CBC data set that included pricing (or some other ordered, attribute). There seems to be a problem because the price utilities showed that the utility of a higher price was higher than a lower price. What that means to me is that at a certain price level the respondents preferred the higher price even though there is no "luxury" product. This seems strange to me. How can this be corrected?

There are several potential issues when utilities seem to indicate that respondents prefer worse levels to better levels in ordered attributes.

One potential option is just noise.  If a respondent didn't pay attention to the difference between $12 and $14, it might have been that the best fit to their data shows $14 is preferred to $12 because they were making choices based on other attributes.

Another potential cause is prohibitions.  If you always showed poor options at low prices and good options (or a respondent's preferred brand) at higher prices, the best fit to their data might be that they only purchase more expensive options (which, based on how the concepts were displayed, would be a correct model).

A third cause could be from conditional pricing tables.  In a vacuum, I might prefer a Ferrari to a Toyota, but if you set up a conditional pricing table that always showed Ferraris at $200,000 to $500,000, then I (unfortunately) would never be able to select a Ferrari in my choice tasks.  

Keep in mind that a respondent's utilities are all relative to my study and reflect any correlation or confounding effects that is inherent in the design.

As far as corrections, using constraints in utility estimation is probably a good route for the noise issue.  For the other issues you probably want to respect any prohibitions that you had in the design, and forcing the utility estimation to follow a preset order might end up hurting your overall fit considerably.

Also, whenever anything looks fishy, make sure to go back and check the programming of the exercise to make sure there wasn't any confusing text or other programming issues.

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