# Linear pricing, interaction effects and WTP

Hi there,

i have several questions concerning my CBC:

1) I have price levels of 37.99, 30.99 and 24.99. I set them to be linear using a coding of 3.8, 3.1 and 2.5 is that correct?

2) If I run HB my price value is -142.8. What exactly does that stand for?

3) Now if I take a look at my interaction effects I get two different results in opposite directions: If I use linear price the effect of Attribute 1 level 1 and Attribute2 level 1 is positive. If I use price constraints or neither constraints nor linear pricing the effects of Attribute 1 level 1 and Attribute2 level 1 turns out to be negative. Is there an explanation for this? Am I doing something wrong?

4) I would like to analyse the WTP of my interaction effects. I know there are concerns about calculating WTP with CBC results still I would like to take a closer look into what effect the combination of two attribute levels has on the WTP. Is there a formula to do that?

Thanks in advance!
asked May 27, 2018

## 1 Answer

0 votes
Paul, to answer your questions,

1.  Yes
2.  It is the slope of your (linear) price function.  Of course it makes a bit more sense as a raw utility than transformed as ZCD, but either way you get the idea that it's large and negative.
3.  Are the interactions even significant?  If not this question is moot.
If they are, then models with different attribute coding and with or with out constraints are different models and they can make for differences in other attributes.  In that case (i.e. the case where the interactions are significant) I don't think you're doing anything wrong, but you're going to want to choose and interpret your model carefully.
4.  There's not a simple formula but there is a simple procedure.  Make a simulation with two versions of your product, one with the attribute levels set to produce the relevant interaction and one without.   Now vary the prices of the two products until shares are equal.  This is the share equalization estimate of the value of the attributes+interaction.  If you want to see what ONLY the interaction is doing for you then you'll want to simulate WITH and WITHOUT the interaction (but somehow with the attributes set in a way that should produce the interaction).  There are a few ways to do this, but all of them involve using a model (the one without the significant interaction) that you know is wrong.
answered May 27, 2018 by Platinum (103,225 points)
Hi Keith,

Thank you for your help!
Concerning your response to question 3: Is there a rule on how to choose to set the price to be linear? My ZC diff utilities for the price are linear could that be an indication?

I would like to run a regression analysis explaining the WTP for different attribute levels and interaction effects on the individual level. If I were to calculate the WTP with the not recommended formula would it be possible to calculate the interaction effects in the same way all other attribute levels are calculated?
Do I use the ZC diff value for the linear price as price coefficient? Or do I have to do something with it?

Thank you!