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How to calculate chip allocation market share in the simulator

Ran a chip allocation CBC and now have our utilities from the pilot.  Just want to make sure we set up our simulator correctly.

Have never done a chip allocation before.  Normally, we would simulate our 5 products in the market and for EACH RESPONDENT we take the highest utility and that's the product they would purchase.  But for chip allocation, the eggs should be distributed across the 5 product/egg baskets.  

I'm sure its some simple treatment of the summed utility score that allows me to then simulate the chip allocation: Respondent 1 would buy 2 of Product A, 3 of Product B, etc.  

What is that conversion or formula?

Many thanks.
asked Apr 10, 2015 by anonymous

1 Answer

+1 vote
You're currently using the "First Choice" rule for your conjoint simulations, which is an old rule from decades ago.  Sometimes works fine, but often produces shares of choice that are a bit too extreme (too big of ratio difference between best products and worst products).  Also, first choice only simulations are a  weaker way to use your conjoint data.  Only the product with the largest utility gets any share for a respondent, whereas a product that is nearly as good as it gets no share.

For even your standard CBC questionnaires, please think about moving to some method that "splits the votes" within each respondent.  This will give you greater precision for your market simulations and allow you to tune the degree of steepness or flatness of simulated shares of preference.  

Now, regarding your question about simulating for chip allocation, you could use either the Share of Preference (Logit Rule) or Randomized First Choice.  Either of these will give you continuous probabilities of choice across the concepts for a given respondent that sum to 100%.  Share of Preference (Logit) rule is much easier to compute in Excel or similar tool, but it doesn't correct for product similarity.  The Logit Rule is as follows:

Logit Rule (Share of Preference) simulation:

Assuming your utilities have been estimated using some logit-based routine (aggregate logit, latent class MNL, or HB), the probability of choosing Product a from the set {a, b, c, ...etc.} is:

Pa = e^Ua / [e^Ua + e^Ub + e^Uc + ...]

And, it follows that probability of choosing Product b from that same set is:

Pb = e^Ub / [e^Ua + e^Ub + e^Uc + ...]

Then, if your respondents allocated 10 chips per task, then you multiply those probabilities by 10 to obtain the prediction of # of chips allocated to each concept for each respondent.
answered Apr 10, 2015 by Bryan Orme Platinum Sawtooth Software, Inc. (169,915 points)
Clarification on formula