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WTP calculation using HB CBC Data estimation: Which price levels, which data?

Hi there,

I conducted a CBC Analysis and used Hierarchical Bayes to estimate the utility parameters.

Now, I would like to calculate the my sample's average marginal WTP for the change from one attribute level to the next higher attribute level.

In your technical paper you are explaining an approach, which might be misleading. Nonetheless, I'm considering to give it a try. Unfortunately, I'm not 100% sure how to do it, as you only have 2 price levels in your example. You further say, if there are more price levels, one should "analyze the utility of price using a single coefficient" as long as the price relationship is approx. linear. Now I'm wondering, which data I should use to calculate this "single coefficient"?

As I used HB, there are several options, which data I could use to calculate the "price coefficient" - the individual utilities or the average utilities?
Also, which price levels should I use? The lowest and the highest?

An example might illustrate the problem:

Assume I have two attributes, each with 4 different levels and 100 respondents in total:
Respondents: 100
Price (150$, 350$, 550$, 750$)
Range (150km, 300km, 450km, 600km)

Using HB estimation I have the individual utilites for each attribute level for each respondent.
But I also have the average utility score for each level based on all 100 respondents.

Now, I have severeal questions how to calculate the WTP:

1) Which price levels should I use?
The general formular to calculate the "price coefficient" explained in your paper is (change in price)/(change in utility of price). But which price levels should I use when I have 4 instead of 2 levels? The lowest and the highest? In this case 150$ and 750$, which means the change in price would be 600$?

2) Which data should I use to calculate the "price coefficient" and average WTP for an increase in range from 150km to 300km?

I can think of basically 3 different approaches:

2.1) Individual utilities only:
I could look at the individual price utilities and calculate a individual price coefficient for every respondent, and then calculate the individual WTP for an increase in range from 150km to 300km by using the individual range utilities.
Using these individual WTPs I could calculate an average WTP for range increase from 150km to 300km.

2.2) Mix of individual and average utilites:
But I could also calculate the mean "price coefficient" using the 100 individual "price coefficients" and use the average range utilities to calculate the average WTP for an increase in range from 150km to 300km.

2.3) Average utilities only
Also, I could simply use the average price utilities and calculate the mean "price coefficient" based on these values. I could then calculate the average WTP for an increase in range using the average range utilities.

Every approach results in a different average WTP for an increase in range from 150km to 300km. Is there a most accurate approach or is it totally up to me which approach I use as long as I stick to the once calculated "single price coefficient" when it comes to calculate the WTP for other changes in attribute levels?

I hope I was able to coney my problem and thoughts clearly.
I'm looking forward to your answers - thanks in advance! :)
asked Nov 10, 2018 by ma92 (125 points)

1 Answer

+1 vote
I usually take the endpoints of the price range, $150 and $750 in your case.  If the feature is one that might only be present at the high end of the product line, then I might use only the range in utilities between $550 and $750 and if it's a low end feature I might use the price in the $150 to $350 range.

Also, and this can really help get you to more credible WTP estimates, I usually compute WTP for the respondent level and then report the median (not mean) WTP estimate.  I usually find this to be much less exaggerated than the mean WTP for the sample.
answered Nov 10, 2018 by Keith Chrzan Platinum Sawtooth Software, Inc. (95,675 points)
Sorry for the late response, thanks a lot for your helpful answer!

Calculating the ind. WTPs and taking the median is a very nice approach.
As I'd like to stay to Sawtooth's calculations of average utilities and importances (using the average of the ind. values, not the mean) I just eliminated all statistical outliners regarding the ind. WTP.

The then calculated average WTPs for the different level changes are quite similar to the median, but actually also to the calculated WTPs using the average utility values.
Nonetheless, I think calculating the ind. WTP is slightly more accurate. As I only want to use the WTPs as a means to help understanding and interpreting the utilities rather then calculating the exact WTPs and give price recommendations, this approach should be sufficient.

Thanks again,
Great, Markus - I'm glad you found a solution that works for you.