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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.

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.

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