Calibrate Purchase Likelihood with 2 factors

Question

is it possible to set lower & upper limit for purchase likelihood in conjoint based on the Worst Case (all level 1) and Best case (all level 3 ) for attributes respectively. For e.g. Purchase Likelihood for Worst case is 1.2% which we want to set 40% and Best case is 99% which we want to set 48%. Please advice

Answer 1

I'm trying to understand your question, and my best guess is that you are trying to figure out the raw utility of a product concept that when evaluated by Sawtooth Software's "Purchase Likelihood" simulation rule in our Market Simulator results in purchase likelihood scores of 1.2%, 40%, 48%, or 99%.

The Purchase Likelihood rule is:

e^U/(1+e^U)*100

where,

e is Euler's constant, or approximately 2.718282
U is the utility of the product concept

So, the approximate utilities (to the 100th decimal place of precision)associated with different purchase likelihoods as you described are:

Utility --> Purchase Likelihood
-4.41 --> 1.2%
-0.41 --> 40%
-0.08 --> 48%
+4.60 --> 99%

So, if you have obtained a respondent's part-worth utilities using some individual-level conjoint analysis method, you will want to perform a linear transformation of each respondent's utilities (by subtracting a constant from  all utilities and multiplying all utilities by a constant) such that when all the level 1s summed result in the utility score that leads to the target worst purchase likelihood and that all level 3s summed result in the utility score that leads to the target best purchase likelihood.