First Choice share of preference with conditional pricing

Question

Hello,

I am running a CBC with conditional pricing (price depends on 2 attributes). I extracted the zero-centered diffs from CBC HB and imported them to SMRT. I tried to run a "First Choice" share of preference simulation, and am obtaining results different from what I had computed myself manually.

To investigate the issue, I added some custom Customer Segments to allow me to filter by specific respondent, and am noticing some strange results for certain respondents. I created two offers, and am including "None" in the share of choice results.

When I add up the total utilities for each offer (using the individual-level utilities found from CBC HB), I get the following utilities:
Offer 2 = -32.5
None = +33

However, the share of choice results indicates that the respondent chose Offer 2, and not the None option  (I entered a None weight of 1, and other respondents do choose the None option). I am therefore wondering if maybe I am computing the total utility wrong ?

I am using conditional price, with -30%, 0% and +30%, and selected a Linear price from CBC HB, which gives me only one utility for the price. For these tests, I entered exactly the prices exactly at the medium level (+0%) from the conditional pricing table. Therefore, when adding up the total utilities for each offer, I simply add the value of the price utility as is to the existing offers (except None).

e.g. If the utilities for the respondent are as following, and the offer I select has att1_level1 and att2_level1:
att1_level1      -10
att1_level2      +5

att2_level1      +30
att2_level2       -46

price                  -45

none                  8

Then, utility for Offer2 is: -10 + 30 -45 = -25.
Since -25 is smaller than 8,  the respondent should choose None.

Am I doing anything wrong ?


EDIT: I've noticed that, in the example above, if I compare -25 to 8-45 = -37 (none utility - price utility), then I obtain exactly the same results as those from SMRT. This seems strange to me since the None option should not have a price. What would be the reason behind that ?

Answer 1

My guess is the trouble is in the linear coefficient.  When you ask CBC/HB to do a linear coefficient, it automatically zero-centers any values you specify for "Values" for the levels of the attribute to be treated as linear.  So, if you indeed specified as the three level values for price: 0.7, 0.0, and 1.3 (representing -30%, Average Price, and +30%) in the attribute level value interface, then the software will actually use the values -0.3, 0, and +0.3 in the design matrix for computing the betas for price (after zero-centering).

So, if you are trying to compute things manually, you'll need to recognize that the average price is level value = 0, so the utility for price for a product specified at "average price" will be 0 x beta for each respondent, of 0 utiles.