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What is the formula for share of preference scores in the online simulator?

Below is the explanation of what I'm seeing, and here is a link to a blinded file for reference/example:
https://www.dropbox.com/s/n5u8f4mt4q839td/Checking%20differences%20between%20calculations%20and%20online%20simulator%20-%20blinded.xlsx

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I am getting slightly different results when comparing a very basic Excel simulator and the online simulator with share of preference results.  My online simulator formulas are:

Total utility: The sum of all individual attribute level utilities, =SUM(C3,T3,AE3,AF3,BC3)

I did this for each of the 6 products in my simulation (I completely ignored the NONE product)

Share of preference: The antilog of product 1 divided by the sum of the antilogs of products 1 through 6, =EXP(BG3)/(EXP($BG3)+EXP($BH3)+EXP($BI3)+EXP($BJ3)+EXP($BK3)+EXP($BL3))

I've double and triple checked my formulas and even recreated it from scratch but I'm still getting different results.  I think there is an aspect of a formula I am missing.  It's probably simple, but I have never built an Excel simulator before.
asked Mar 18, 2013 by Joel Anderson Bronze (1,310 points)

3 Answers

+2 votes
Your formula sounds right.  But, make sure you're doing the share of preference computations for each respondent individually and then averaging the shares of preference across people.  Don't do it from average utilities.
answered Mar 18, 2013 by Bryan Orme Platinum Sawtooth Software, Inc. (148,340 points)
Thanks for the quick reply!

Yes, I am calculating these formulas at the respondent level and then averaging them.  But I am still getting different results.

I have posted a blinded version of my Excel file here in case it helps:

https://www.dropbox.com/s/n5u8f4mt4q839td/Checking%20differences%20between%20calculations%20and%20online%20simulator%20-%20blinded.xlsx
The online simulator defaults to the randomized first choice algorithm, which is different than the "share of preference" calculation.  You can edit a project and change the settings, I'm betting that's the issue.
Hi Brian,

That's not the issue either.  I had it set it to Share of Preference.  To confirm, I just changed it to Randomized First Choice and the numbers are different than the Share of Preference numbers.  See the comparison table below, where OS=Online simulator and XL=Excel.

SOP    SOP    RFC
XL    OS    OS
5%    5%    5%
20%    26%    27%
27%    25%    24%
20%    18%    20%
15%    14%    12%
14%    13%    11%

There must be some other issue.
+2 votes
Your Excel file has correct calculations for a share of preference simulation using no interaction effects.  I took the Excel file and uploaded the utilities to the Online Simulator and ran a share of preference simulation and the results I saw matched the results your Excel file is calculating.  So there must be something different in your online simulator.  Does it have the exact same utilities?  Do those utilities have interactions?
answered Mar 18, 2013 by David Squire Silver Sawtooth Software, Inc. (5,730 points)
0 votes
The formula for antilogs in Excel is incorrect. It should be:

 =10^x    where x is your individual utility score.

(assuming base 10)

Anyone reading this will need to check me -- I am not a mathematician but this formula appears to return the correct answer.
answered Jan 17, 2017 by Brandon
Although in theory base 10 could possibly work, the utilities estimated by most all choice/conjoint applications follow the multinomial logit framework which assumes natural base.  So, you need to take =exp(x) in Excel, where x is the total utility of each product concept.
Ah, that makes sense. Thanks for the clarification, Bryan!
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