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How to "correct" individual level utilities

I'm having here the results of an HB analysis of CBC data which shows inconsistencies between levels. As I don't have access to the raw data I cannot rerun the HB with constraints and I'm thinking about how to "correct" the individual level utilities for the market share model.

Assume a product with just 2 attributes: price and volume
And assume that for all respondents lower price and larger volume should be better.

The data I have has partial "reversals" on individual level. For illustrative purposes let's assume they are
Price     Utility                 Volume   Utility
2.00       -1.00                     0.4             -0.2
1.50       0.66                      0.5              -0.3
1.00       0.33                      0.6               0.5
It also includes a "none" with utility 0.5

Before using the data for further simulation I'd like to adjust the individual level utilities so that at most they are level where utility should be increasing (lower prices, higher volume). I'm confused whether I can
a) just change the utility for a single attribute (say change the utility for $1.00 to 0.66) or whether
b) I should make sure that the overall utilities within one attribute are zero-centered again.

I know that both approaches are "wrong", I just wonder which one of them messes less with the outcomes especially taking into account the fixed "none" utility against which buying decisions are measured. Thankful for any thoughts.

Also, if there are better approaches to deal with this problem by all means let me know.
asked Feb 26, 2020 by Patrik

1 Answer

0 votes
The first critical question to ask yourself is whether you should do anything to impose utility constraints at the individual level.  Utilities come from respondents who answer conjoint questions with some degree of error.  And, importantly, we don't tax any one respondent too much by asking them too many conjoint questions (so our data are sparse at the individual level).  Indeed, because of these two issues, utilities at the individual level can be noisy.  And, utilities can look "out of order" compared to rational assumptions about preference for ordered attributes--especially for attributes that were of little or no importance to the respondent.

But, across respondents, these errors tend to wash out.  Most conjoint analysts avoid imposing constraints on the utilities in most situations.  However, there are certain situations where it may be useful to impose constraints.

I'm concerned that you don't have access to the raw CBC data, as it would be better (if you need to impose utility constraints) to re-estimate the model using our automatic functionality for "simultaneous tying".  Or, if you had access to the individual-level draws of HB (the multiple draws per respondent), it works well to remedy the out of order utilities at the individual draw level, then aggregate across the draws to compute new point estimates (summary utilities) for each respondent.
answered Feb 26, 2020 by Bryan Orme Platinum Sawtooth Software, Inc. (186,865 points)
Thanks Bryan, very helpful. I'm hearing you and I'm now thinking of other ways to deal with the reversions in the aggregate data.