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Summing raw utilities by individual respondent


I have a similar question. Using the Discover product for a simple CBC with a none option included, I am trying to determine, for each individual respondent, the aggregate utilities for specific product configurations. For example:
Utility(Attr1, Level1) + Utility(Attr2, Level 3) + Utility(Attr3, Level 1) = Total utility for this product, compared to total utilities for other product combinations

My questions are:
1) Should I be using raw or the zero centered utilities?
2) I understand that even the raw utilities that are output by Sawtooth are zero centered as a result of effects coding, but what I am struggling to understand is how this centering affects the ability to sum utilities from different attributes. Do I need to transform the raw utilities such that the lowest value one corresponds to a small or zero utility, for example? If so, how should I do this?
3) How do I treat the interpretation of a "negative" utility? I understand that a negative utility is not necessarily bad - it is just the lowest within that attribute if zero centered.
asked Feb 8, 2017 by anonymous

1 Answer

0 votes
For your purposes of just comparing for each respondent whether a total utility for a product concept exceeds the None utility, then either using raw utilities or zero-centered diffs (normalized) utilities will give you exactly the same answer.  (Assuming you are just logically comparing whether the sum of utilities exceeds the None utility).

The zero-centering doesn't affect the ability to make these comparisons.  Both the raw utilities and the zero-centered diffs utilities are already zero-centered (assuming you have used our software to compute these under Discover).

Since the utilities within each attribute are zero-centered, some levels just have to be negative and some have to be positive.  Negative utilities just mean less preferred than other levels within the SAME attribute.  

Within an attribute, all the levels could have been great for a respondent, but some levels are relatively better than others.  By the same token, all the levels could have been terrible for the respondent, but some levels are relatively more terrible than others.  Conjoint analysis doesn't let you tell whether for a given respondent the levels for a given attribute were either all great or all terrible.  Other techniques (such as MaxDiff scaling) allow you to do that, if you use "anchored MaxDiff".
answered Feb 8, 2017 by Bryan Orme Platinum Sawtooth Software, Inc. (136,265 points)
Thanks Bryan.

What I am struggling with is comparison with a basic CVA that uses a linear regression and dummy variables. In that case, the signs of the coefficient do matter (or so I thought), since the equation will sum up to a certain value/rating.

Perhaps I am oversimplifying in comparing the raw utilities in a effects-coded CBC, but it seems like the zero-centering of each attribute will affect the sum of the different levels of each attribute. I would think you would need to add or subtract the same constant to ALL of the levels/attributes, not just the levels within one attribute.  Or do I not need to worry about this, since the "none" option also takes the centering into account?
If you are using our CVA system, then there is no None option.

With CBC, the zero-centering happened due to our process of coding the design matrix (via Effects Coding).  Thus, when the utilities for levels and the None parameter were estimated, the None parameter was scaled properly with respect to the zero-centered other attributes.

So, if we want to convert the raw (zero-centered) utilities in CBC to zero-centered diffs, we just take the scaling multiplier and also multiply the None parameter by that multiplier.  The scaling of the None relative to the scaling of the other attributes and levels stays proper.
Makes sense. I am using CBC with Discover. But what about comparing utilities of different product configurations with each other (for an individual respondent), rather than comparing against the None option? Is this still valid given the scaling that has been done? Thank you!
Absolutely.  You can compare summed utilities (one level per attribute always) between multiple product alternatives, no matter which (Sawtooth Software-generated) utility rescaling method.