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Distribution of Individual-Level Utilities from HB

Dear Bryan,

Thank you for your reply. I'll try to explain better.

In one of your papers (9 Things Clients Get Wrong about Conjoint Analysis) in mistake #4 the author says that "In examining Black vs. Tie-dye, we see that the individual-level estimates for Black have low variance while Tie-dye has high variance. Black is broadly acceptable, relative to other choices, while Tie-dye is polarizing."

I wondered if one can infer from the value of the average ZC diffs how the distribution of the individual-level utilities looks like. Does a large/small positive/negative value reveal any insights about the distribution on individual level?

In my study I have a problem with my two discount brands. Looking at the total utility per concept the utility for discount brand A is larger than the total utility of the second discount brand B. However, when running a Share of Preference Simulation, discount brand B is slightly more preferred than discount brand A. I don't know how to explain this twist and I thought it might be useful to look at the distribution of the individual ZC diffs.

In addition, what if I included the interaction term between brand and price. Can I look at the distribution of the individual-level brand utilities as in the paper or is it biased since I included interaction terms? Is there any smart solution to show an unbiased picture of the distribution of my seven individual-level brand utilities? I don't think any client would understand a figure with 7 brands shown at 3 different price levels each.

Thanks in advance
asked May 24, 2016 by anonymous

1 Answer

+1 vote
Best answer
One cannot infer from mean utilities what the distribution looks like.  The standard deviation will tell you something about the distribution, though.  Better, though, to look at histograms if you want to see something more about the distribution...especially if it is multi-modal.

Sometimes you will find that a brand that is preferred to another brand under average utilities actually becomes less preferred than the other brand within market simulations (even though you are holding all the other attribute levels constant for those two product alternatives within the market simulator).  This is more likely to occur if the following two issues are happening for your data:

1) Imagine that there are 5 brands in the study.  Imagine that Brand A is second best for all respondents, but never the best.  On average, Brand A will have a high utility, but its simulated share of preference versus the other brands will be lower than expected.  Simulated shares of preferences tend to give more weight to topmost brands because it tends to be a more extreme voting scheme than reflected by the underlying metric quality of the raw utilities.

2) The differences in utility between the two brands in question is actually fairly small.

If you are using our CBC software and its default "effects-coding" (part-worth) coding method and if you have no prohibitions between the two attributes you are interacting, then the main effects are estimated orthogonally to the interaction effects.  That means that you can directly interpret just the main effects of brands with respect to one another, ignoring the interaction effects.
answered May 24, 2016 by Bryan Orme Platinum Sawtooth Software, Inc. (163,415 points)
edited May 24, 2016 by Bryan Orme
Thank you very much. This was really helpful.

Can I refer to any Research oder technical paper for the last part regarding the interaction effects? I thought w┬┤that with main effects one cannot Interpret the main effects of the attributes involved. However, the interaction effects can still be seen as a correction of the main effects, right?
Distribution of Individual-Level Utilities from HB