Multiplicative utility function

[cerrosimo]

Dear all,

I have a simple question, it is possible to generate designs considerino non-linear utility functions? I’m not talking about dummy or effect coding, but I have another problem.

In my choice experiment I have three attributes:

A. Outcome with 3 levels
B. Probability that the outcome will happen with 4 levels
C. Cost 4 levels

The standard additive utility of alternative n is:

U(altn) = b1 + b2 * A + b3 * B + b4 * C

The related utility in Ngene for alternative n is:

U(altn) = b1 + b2 * A[0,1,2] + b3 * B[0,1,2,3] + b4 * C[0,1,2,3] /

How can I generate a design considering the following expected utility theory?

U(altn) = b1 + B * (b2 * A) + b3 * C

Do you guys have a solution?

Thank you

Simone

[johnr]

Dear Simone

It is not possible for non-linear utility functions in the current version of Ngene. We have worked out the theory for this and are working on a paper currently, however it requires substantial re-programming and testing. We have plans to introduce this feature in a future release version of Ngene.

John

[cerrosimo]

Hi John,

ok, I'm looking forward to see the new version of Ngene. Thank you for the quick reply.

Simone

[premc]

Hi Everyone,
We also have a similar situation for our survey. We are trying to use prospect theory type questions in our survey and wanted to include weights (function of probability) for the attribute levels which would result in a non-linear utility function like what Simone had.

U(altn) = b1 +W * (b2 * A) + b3 * C

where W is the weighting function of the probability.
A is the travel time
C is toll

A sample choice situation:

Alt A:- toll : $3:00, 70% chance that the travel time would be 10 minutes, and a 30% chance that the travel time would be 15 minutes.
Alt B:- toll : $0.00, 30% chance that the travel time would be 15 minutes, and a 70% chance that the travel time would be 20 minutes.

Since the current version does not have the capability to generate this type of design, can we do the following:

Generate a utility function for each value of W (say 30%) and then get an efficient design with a few choice situations. Then repeat this for several possible values of W (20%, 30%, etc.). Then treat each W-value (20%, 30%,etc.) design as a block that one group of respondents will get.

Would such a design, as a whole, still be an efficient design ?

or do any of you have any suggestions as how to do a prospect theory survey design with travel time savings and tolls. Any help in this regard is highly appreciated.


Thank you,

Prem

[johnr]

The good news is that we working on setting up Ngene to support this type of problem. We hope to have the next version of Ngene (V1.1.1) released sometime soon. For the present, the syntax proposed for this type of problem will look something like this:

Design
;alts = alt1, alt2
;rows = 12
;eff = (mnl,d)
;model:
U(alt1) = b1[0.2] * pbEa[0.2,0.4] * Early[10,12,14] + b2[0.5]* pbOn[0.5,0.3] * Ontime[20,22,24]
+ b3[-0.4] * pbLa[fcn(1 - alt1.pbEa - alt1.pbOn)] * Late[25,27,29] /

U(alt2) = b1 * pbEa * Early + b2 * pbOn * Ontime + b3 * pbLa[f(1-alt2.pbEa -alt2.pbOn)] * Late $

Note that this is somewhat more complex than at first glance. This is because your W (or in the above my pbLa) must sum to 1 (or 100) – which is a new feature in Ngene. This will be handled via the fcn command above which makes the level of an attribute a function of the levels of another attribute. Secondly, it also requires the estimation of an interaction term without a main effect being estimated (b2 * A*W where A and W do not have priors - in the above my pbLa and Late for example are interactions but not main effects). This also is a new feature.

As you can hopefully appreciate, this requires substantive testing in that we need to test thoroughly any new feature to ensure that it is compatible with all other functionality – e.g., what will happen if the design is orthogonal and you want to do this – this attribute cannot be orthogonal hence we need to ensure that the program doesn’t crash when users do things that are not possible. We also have to test that it is compatible with other model types, with other features such as pivoting, etc. This is a non-trivial task

Thus stay tuned. It is coming and hopefully, subject to there being no substantive compatibility issues, sometime very soon.

John

[premc]

Thank You John,
I look forward for the new version.

-Prem

[chao]

Hi John,

I was wondering if the newer version will be ready anytime soon?

Thank you,

Chao

[Andrew Collins]

Hi Chao

We should have the new version up within two days. I will post back here when it is up.

Andrew

[chao]

Hi Andrew,

Thanks for your kind reply. We look forward to seeing the new version of NGene.

Regards,

Chao

[Andrew Collins]

Version 1.1.1 is now available for download on the website. This can handle the syntax John demonstrated above. There is also some documentation in the updated manual, at the end of the Advanced Features chapter.

Andrew