modelling decision weights with NGENE

[cdelamaz]

Hi all,

I am building a conjoint experiment asking respondent to trade off between two risky options. I am aiming to model some of the proposed models in prospect theory for binary choice that are nonlinear in parameters? Is it possible to do this in NGENE?

In the manual it's shown how to specify nonlinear models with effect codes but the functions in prospect theory are a bit more complex.

I reviewed the following paper by Hensher et al that used NGENE with the same objective, but I wonder if the experimental design pre defined this type of formulation for the utilities of each alternative.

Hensher, David A., William H. Greene, and Zheng Li. "Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings." Transportation research part B: methodological 45.7 (2011): 954-972.

Any recommendations?

Best

Cristobal

[johnr]

Hi Cristobal

Hensher et al. (2011) used data from an experiment I generated for consulting project. I generated the design for that project outside of Ngene as Ngene at the time could not handle the fact that the combination of the probability attributes had to sum to one. We have since implemented the ability to do this. Here is an example (from another project I worked on), where I have three attributes for Probability (CPr1, CPr2 and CPr3, each associated with different travel times (CTT1, CTT2, CTT3), similar to how the data was set up in the paper you cite. Here, the probabilities are interacted with the travel times. Note that the last probability CPr3, is a function of the probabilities for the first two attributes (1 - pr1 - pr2), hence, if Pr1 = 0.2 and Pr2 = 0.3, then Pr3 = 0.5...

... + Pr1TT1[-0.04] * CPr1[0.1,0.2,0.3,0.4] * CTT1[49,56,63]
+ Pr2TT2[-0.05] * CPr2[0.2,0.3,0.4,0.5] * CTT2[66.5,70,73.5]
+ Pr3TT3[-0.06] * CPr3[fcn(1 - Car.CPr1 - Car.CPr2)] * CTT3[77,84,91] ....

Other than that, the experiment you mention was actually a pivot design, hence the attributes were pivoted off of a respondent reported reference alternative. it was not generated specifically for the testing prospect theory (though given that it is based on a respondents reported reference alternative, it can test aspects of this theory (see Hess et al. 2008). This type of design is discussed in

Rose, J.M., Bliemer, M.C.J., Hensher, D.A. and Collins, A.T. (2008) Designing Efficient Stated Choice Experiments Involving Respondent Based Reference Alternatives, Transportation Research Part B, 42(4), 395-406.

Hess, S., Rose, J.M. and Hensher, D.A. (2008) Asymmetric Preference Formation in Willingness to Pay Estimates in Discrete Choice Models, Transportation Research Part E, 44(5), 847-863.

This type of design is also implemented in Ngene. So, in theory, if you combine the pivot design approach with the attribute function command shown above, Ngene should be able to generate a similar type of design to the original one.

John

[cdelamaz]

Thanks John for your answer. I finally managed to post my reply.

I could not follow what Pr1TT1[] stands for in your formulation.

I can see that you have three different intervals for CTT with 3 levels
each in each CTT i [,,]. Why did you set the design for those intervals?
Are you restricting the number of combinations probability*travel time in
some way?

Is it possible to specify non linear in parameters functions directly for
the utility function in NGENE by specifying the AVC? My decision weight
for probability could be w(p)=exp(-(-log(p))^teta).

Best

Cristobal

[johnr]

Hi Cristobal

Unfortunately not yet. We have done the math for working dealing with non-linear utility functions, however we have not implemented it yet in Ngene. What you can do however is do it manually.

Assume p takes levels {1,2,}, and teta (theta?) is 0.8, then the levels for w(p) would transform to {1, 2.108264804,2.939210478}.

You then use w(p) directly in your utility functions in Ngene.

john

[cdelamaz]

Thanks John, I will try that.

Best

Cristobal