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Part-worth interpretation

Hi everyone,

Using HB estimation I got the following partworths for my three levels of the attribute Discount:
low: -100
medium: 25
high: 75

A high discount is preferred three times as much as a medium discount. However, how much more preferred is a high discount in comparison with a low discount? The negative scaling makes it a bit difficult to correctly assess the difference.

Kind regards
asked Aug 6 by maxive94 Bronze (1,410 points)

1 Answer

0 votes
Max, were the discounts percents, or measured in currency or did they really say "high", "medium" and "low"?
answered Aug 6 by Keith Chrzan Platinum Sawtooth Software, Inc. (114,400 points)
No that was just a simplification, they were given in percent (0%, 30% and 60% discount).
If you're positive that higher levels of discount should be more preferred, you may want to add a constraint to the utility estimation to let the model know that higher levels of discount should have higher utility.  This is something that happens fairly often with smallish sample sizes.
My question is regarding the interpretation.  If a 60% discount has a utility of 75 and 0% discount has a utility of -100, how much more preferred is a 60% discount compared to a 0% discount?

I am a bit confused about adding a constraint. Why would I do that and how would that benefit the utility estimation?
I'm sorry, I was reading your utilities incorrectly - the utilities make perfect sense as they are and you don't need to add a constraint.  Utilities tell you which levels are more preferred, and your current ones tell you that respondents like a 30% discount more than 0% and 60% more than 30% - that makes sense, right?

If you want to know how much more they like it, you can create a simulation.  The easiest way would be to imagine that you have products that are identical but for level of discount.  And let's say that for a given respondent the raw (logit-scaled, not ZCD utilities, which latter you are showing at -100, 25 and 75) for a given respondent Karl are -3, 1 and 2.  Using the logit choice rule, you exponentiate those 3 raw utilities (i.e. take the anti-log) to get 0.05, 2.72 and 7.39, respectively.  You can take ratios of these to get shares:    so if Karl faced the choice between a product with a 30% discount and one with a 0% discount, which were comparable in all other ways, we predict he would pick the 30% discount product 0.05/(0.05+2.72) = 98% of the time.  The logit choice rule is a standard way of helping you interpret utilities from a logit model.  Of course you would do this calculation in Excel for each individual respondent an then take the respondent's average shares.  

And rather than program this yourself in Excel, you might want just to build a simulator which will do all the math work for you.
You might also look into the odds ratio, which is an entity a lot of my academic clients report when they're reporting on their logit models.  An introductory txt on logit models will tell you more about the odds ratio and how to calculate it from your (raw, logit-scaled) utilities.