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How to calculate utilities from choice probabilities, and reverse (Logit)?

Dear Sawtooth community,

A (multinomial) logit estimation of cbc data computes choice probabilities in the firstplace. If I understood your descriptions correctly, Sawtooth then calculates the part-worth utilities from these probabilities. Can you please provide a (mathematical) formula how to derive part-worth utilities from choice probabilities, and the other way round?

Thank you in advance for your support!
asked Feb 24, 2017 by summand (385 points)
retagged Feb 24, 2017 by Walter Williams

1 Answer

0 votes
We don't compute choice probabilities first and then try to calculate part-worth utilities from these probabilities.

Multinomial logit estimation finds a vector of part-worth utilities (betas) such that when multiplied by the design vector (for each product alternative) and submitted to the logit equation produces a maximum likelihood fit to the choices respondents actually made.

The logit equation is Pa = e^Ua / (e^Ua + e^Ub + e^Uc + ...)

, where Pa is the probability is selecting alternative A.  e is Euler's constant.  Ua is the utility for alternative a, etc.

If you want more info, you can write me at bryan "at" sawtoothsoftware.com I'll send you a non-technical article that explains more how it works.
answered Feb 24, 2017 by Bryan Orme Platinum Sawtooth Software, Inc. (153,180 points)
Hi Bryan, thanks for the quick answer. I got it :-)