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Why are utility ranges different for the same importances in different survey?

Hi everyone,

I have a few questions about calculating the part worth utilities.

I have analyzed the utility values with the logit approach. What is the mathematical background of the calculation? How exactly are the utilities calculated?

What indicates the size of the ranges of utilities? I have done the same conjoint survey in several cities and partly the results of the importances are identical and so are the relations between the utitilies. However, the size of the ranges of utilities are different (e.g. importances are identical, but in survey 1 e.g. maximum and minimum utility of an attratribute are 0.3 and -0.12, while in survey 2 the maximum and minimum utilities are 0.44 and -0.09). The same pattern or the same factor runs through all utilities of a survey (utility range is by the factor larger in survey 1 than in survey 2). How do these differences occur?

Thank you very much!
asked Jul 29 by Pia (440 points)

1 Answer

0 votes
Pia, you have several questions which I'll address in turn.

Utilities are calculated using a hierarchical Bayesian (HB) version of the conditional multinomial logit model.  You can google conditional multinomial logit to find more about it (not a bad place to start if you read the conditional logit section:  https://en.wikipedia.org/wiki/Discrete_choice).

The reason you can see the same importance for different utility ranges is because you're looking at the utility range of the average utilities but importances are calculated at the respondent level and then averaged. let me give you an example.  Say we have a study with several attributes, among them color (orange or blue) and price.  It turns out that both color and price have an importance of 30%.  As you might imagine, everyone wants lower prices, and the range of the average importances for the highest and lowest prices is 17 utility points.  But when you look at the average utilities for color, the range is 0 because orange and blue have the same average utility, 0.00.  But respondents are heterogeneous with respect to color.  Exactly half of them LOVE orange (utility +17) and hate blue (utility -17).  The other half LOVE blue ( +17 utility) and hate orange (-17 utility).  So the average utility cancels out all this heterogeneity and shows two average utilities of 0.00.  The importances, on the other hand, were calculated at the respondent level, and they're as large at the respondent level as the importances for price, namely 30%.  Something like this mismatch in heterogeneity is what's causing what you're seeing.  this is common, because I find myself explaining this at least a couple of times a month, and I'm one of several folks here at Sawtooth Software who ends up explaining this to folks.
answered Jul 29 by Keith Chrzan Platinum Sawtooth Software, Inc. (114,400 points)
Hi Keith, Thank you so much for your quick and very helpfil answer. Do I understand you correctly that importances are also calculated at the individual respondent level when using the aggregate logit method? Then I cannot calculate the importances based on the aggregate logit utilities? Thank you so much!
No, if you use aggregate MNL you'd calculate the importances using the aggregate MNL utilities - you only calculate importances at the respondent level when you have respondent level utilities.
Thank you for your reply. When I analyze everything with the aggregate logit method, utilities of attributes with the same importances are still different (as decribed in my first message). What are the reasons for theese differences? I really appreciate your help!
Please give me an example.  Only the range of the attributes' utilities matters, so same importance should mean same range.
The difference becomes clear when I try to calculate the importances based on the utilities. As already noted, I calculate utilities and importances not on the individual but on the average level. When I calculate the utility ranges and sum them up per CBC, I notice that the sum of the utility ranges of different surveys is different (e.g. 2.48 for CBC1 and  1.69 for CBC2). Both is for raw utilities. When I then calculate the importances, I get the same importance for attributes with different utility ranges of the two CBCs. The reason for this is of course the different sum of utility ranges per survey. Innerhalb einer Umfrage führt die gleiche utility range natürlich immer zur gleichen importance. How does this happen? What is the reason for the sum of the utility ranges?