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Conversions of RLH into Percent-Certainty and Log-Likelihood

Dear Bryan,

now it happend - I´ll have to convert my data to report Percent-Certainties and Log-Likelihood.. I don´t know if i do have enough data / information to make it happen. What I do have in ecxel is: Individual Utilities (ZC Diffs),  Individual Utilities (Raw), Individual Importances and Summary. I look forward to your reply and I am very grateful for your support and help!

Thank you so much!

BR Anna
asked Aug 2, 2013 by anonymous
retagged Dec 7, 2014 by Walter Williams

1 Answer

0 votes
You’ll need the RLH (Root Likelihood) fit value also per respondent.  When you export or create utility files using our software, this is either automatically provided in the report or may be requested as an option during export.  So, let’s assume you get that RLH value per respondent.  To convert RLH to Pct. Certainty and Log-Likelihood, you’ll need to do the following:

To Convert RLH to LL:

A)  For each respondent, take the natural log of the RLH and multiply it by the number of tasks completed by that respondent: LN(RLH)*#Tasks.  This gives you the LL per respondent.

B)  Multiply that amount by the number of respondents, giving you the total LL across respondents.

To Convert LL to Pct. Certainty:

A)  First, determine the Null LL to be expected using a Naïve set of utilities (utilities of zero).  For each respondent, this is simply LN(1/#Concepts)*#Tasks, where #Concepts is the number of concepts shown to the respondent (including any None concept).

B)  Next, determine the LL to be expected if the fit were perfect.  This is simply LN(1)*#Tasks, or zero.

C)  Lastly, compute the percentage between the Null LL and perfect fit LL that the LL per respondent lies.  For example, if the Null LL for a respondent is -10 and the perfect fit has a LL of 0, then an observed LL of -5 for a respondent is 50% of the way between the Null LL and the perfect fit.  Thus, the Pct. Certainty for this respondent is 0.5.  

All the above assumes a standard CBC study with a standard None alternative (or no None alternative).  Dual-Response None certainly makes things more nasty than the above, since the number of tasks differs per respondent and the number of concepts per task differs per respondent.
answered Aug 2, 2013 by Bryan Orme Platinum Sawtooth Software, Inc. (152,955 points)
So how does this apply to best worst?
On the computation and meaning of LL
Converting to pct. Certainty
Total LL across respondents?
Computing the Adjusted McFadden's Rho-squared