# Is there a formula for calculating the zero-centered diffs?

Yesterday a client ask me about the meaning of zero-centered diffs. I was able to explain what they mean, but the client wanted to know exactly how these utilities are calculated. I told him, I will give him the formula in the upcoming days. I tried to calculate the ZC-Diffs from the part-worths of a HB/CBC estimation of a recent study, but was not able to get the right values for the ZC-Diffs. I already read the article from Sawtooth Solutions, 1999, Issue 10 and the explanation in die SSI Web Manual.

Can anybody help me with this issue, please? I would really appreciate it!

Frank

+1 vote
For each respondent...

1. Within each attribute, compute the mean utility.  Within each attribute, subtract the mean utility from each utility (this zero-centers the utilities within each attribute...which often doesn't have to be done since they are often already zero-centered in their raw form).

2. Then, for each attribute compute the difference between best and worst utilities.  Sum those across attributes.

3.  Take 100 x #attributes and divide it by the sum achieved in step 2.  This is a single multiplier that you use in step 4.

4.  Multiply all utilities from step 1 by the multiplier.  Now, the average difference between best and worst utilities per attribute is 100 utility points.
answered Jun 4, 2014 by Platinum (201,265 points)
I just read this here somewhere in a paper: "Part-worth utilities (...) were re-scaled in zero-centered diffs (summing up to zero) to make the part-worth utility values within an attribute comparable."

This is confusing, as the "raw" utilities provided by Lighthouse are already zero-centered. Zero-centered diffs just puts them on another scale, but the "raw" output is still zero-centered, correct?
I'm not really sure what is the actual benefit of zero-centered diffs if I just want to report utilities (without market simulation). Does it help compare levels within an attribute? Not really right?
No, it doesn't allow you to directly compare levels between attributes.  Zero-centering is a long tradition dating back to the 70s and 80s.  One benefit of zero-centering is that it makes it less likely that people will try to interpret the utility scores on a ratio scale, which isn't appropriate in most situations.  But, you probably don't want to be reporting utilities anyway.  Reporting results of market simulations is more intuitive and market simulations produce shares of preference that indeed are ratio scaled, with bounds of 0% and 100%.
Thanks. this is really useful. As a follow up, does this method still apply if I have included interaction effects in the model?  That is, should I be summing my utility-differences across ALL effects, including interaction, or only main effects?
We ignore the interaction effects for coming up with the multiplier (to scale up to zero-centered diffs) for each respondent, but we apply the multiplier also the interaction effects.