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Estimation of the utility of each option relative to the non-buying option


My survey is about WTP for organic food using CBC. It contains 2 attributes, Price (4 levels) and Label (2 levels), made 12 choice sets. I am going to estimate the relevance between choice A, B and C(non-buying) for my study. Below is the data that I want to include in my result. ( numbers are created only for example)

Coefficients    Estimates(Utilities)   Std. error   T-values      P-values
Choice A            3.1                                    0.09              34.16           0.0000
Choice B            3.5                                    0.06              59.56           0.0000
Price                  -0.4                                    0.008          -52.96           0.0000
Label 1               1.4                                    0.06               25.6             0.0000
Label 2               0.5                                    0.04               10.47           0.0000
Number                 respondents * 12 choice sets
Log likelihood     xxxxxx
Chi Square            xxxxxxx

In this case,
Q 1: I am not sure if I can estimate with Logit (MNL) and HB (Bayesian version of mixed logit).
Q 2:  How can I get the data for Choice A & B?
Can anyone please kindly advise? Thanks.
asked Jul 2, 2018 by linjing (185 points)

1 Answer

+1 vote
Supposing your design is viable, you can estimate with either MNL or HB-MNL.  

If your Choice A and Choice B are "generic" (they aren't identified by any attribute) then you don't get a separate utility for them - their utilities will vary from one choice set to the next depending on the values of the price and label levels they contain.  You should get a utility for the none option (Choice C) however - let's say for example it is -0.75.

So if Choice A was Label 1 for $3, then its utility will be 1.4 + 3(-0.4) = 0.2.  And if Choice B was Label 2 for $1, then its utility will be 0.5 - 0.4 = 0.1.
And the none alternative has a utility of -0.75, as assumed above.  

In some cases people build "alternative specific" or  "labeled" designs.  In that case Choice A always has a single level of one of the attributes associated with it (e.g. Non-GMO for a food product or Train for a transportation study) while Choice B would always have a different level of that attribute associated with it (e.g. GMO or Bus in the examples above).  In this case Choices A and B would have what are called alternative-specific constants associated with them.  From your description it does NOT sound like this is the kind of design you have.
answered Jul 2, 2018 by Keith Chrzan Platinum Sawtooth Software, Inc. (74,725 points)
thank you for your remind. Alternative-specific constants (Choice A and Choice B), that is what I want to estimate them to indicate the utility of each option relative to the NONE (Choice C).  I have run the Analysis with Logit, and I get the data shown below. In that case, is still possible to calculate Choice A & B?

Coefficients    Effect (Estimates?)             Std. error           T-Ratio      P-values
Choice A            ?                                                    ?                          ?                                    
Choice B            ?                                                    ?                          ?
Price 1               0.30220                                   0.09754               3.09835
Price 2               0.09345                                   0.09782               0.95527
Price 3              -0.10742                                   0.09890              -1.08612
Price 4              -0.28823                                   0.10167              -2.83481
Label 1               0.02067                                   0.04767              0.43358
Label 2              -0.02067                                   0.04767             -0.43358         
None                  -1.09368  
Number                528 ( 44 NumResp * 12 choice sets)
Log likelihood     -521.70079
Chi Square            116.73300
You will only have alternative specific constants if you specifically made a design that was alternative-specific.  If you did, what is the name of the attribute that distinguishes Choice A from Choice B?

If you ran the model and received the output above, then you did not code in an alternative-specific effect, which makes me suspect you do not have one.
The design is alternative-specific. The attribute distinguishing Choice A fro Choice B is "Label".
Choice A always is "Label 1"
Choice B always is "Label 2".
The none option has no label.
If Choice A is always Label 1 and Choice B is always Label 2, then there can be no separate alternative-specific utilities for Choices A and B - they are identical to the utilities for Labels 1 and 2.
I hope I did not misunderstand. I think the design is alternative-specific. Below is the 12 choice sets:

Choice A                  Choice B             Choice C
Label 1 * ¥40         Label 2 * ¥22      None
Label 1 * ¥40         Label 2 * ¥28      None
Label 1 * ¥40         Label 2 * ¥34      None
Label 1 * ¥34         Label 2 * ¥22      None
Label 1 * ¥34         Label 2 * ¥28      None
Label 1 * ¥34         Label 2 * ¥40      None
Label 1 * ¥28         Label 2 * ¥22      None
Label 1 * ¥28         Label 2 * ¥34      None
Label 1 * ¥28         Label 2 * ¥40      None
Label 1 * ¥22         Label 2 * ¥28      None
Label 1 * ¥22         Label 2 * ¥34      None
Label 1 * ¥22         Label 2 * ¥40      None
Yes, in your case the labels will take the place of your alternative-specific constants, so the utilities you showed are all you will need.
In this case (alternative-specific constants), how to get the Effect/utility for Choice A and Choice B? Will it be the same way that you mentioned above?

The total utility for Choice A is Label 1 utility plus (the price utility times the price variable).  That's it, that's all there is.  There is no other utility for Choice A because Choice A and Label 1 are perfectly correlated.
Thank you!