Designs for MMNL models in willingness-to-pay space

[Matteo Corsi]

Dear all,

I'm building the code for my first design with ngene (making it gradually more complex as suggested in the manual) and, after practicing a little with the ;wtp property, I realized that it only works for MNL models. I initially thought that models which, according to the manual, "are to be optimized based on the variance of the ratio of two or more parameters" were essentially models in wtp-space as in Train and Weeks (2005) and that the issue was having mmnl models where wtp estimates distributions are derived from the ratio of the distributions of a monetary and a non-monetary attribute. I was clearly wrong but I am not sure why. Could someone suggest:

1) which MNL models should better be optimized based on the variance of the ratio of two or more parameters and, most importantly,

2) is there a specific design approach with ngene if I am planning models in willingness-to-pay space?

Thank you very much for your help.
Matteo Corsi

[Michiel Bliemer]

All models in Ngene are assumed to be specified in preference space, not WTP space. When using ;wtp Ngene optimises the covariances of the ratios of parameters according to the Delta method. The Delta method can also be applied for mixed MNL models but this is very complicated, see Bliemer and Rose (2013) for the mathematical formulations. Note that optimising designs for panel mixed MNL models (e.g., using rppanel in Ngene) is extremely computationally expensive and only possible for models with only a few parameters (unless one accepts computation times of weeks or months). Therefore, in almost all cases a researcher is better off optimising for the MNL model and then testing the design (instead of optimising the design) for the mixed MNL model.

Note that while models in WTP space have the advantage of directly estimating WTP distributions, these models have their own issues (e.g. multiplications with a scale parameter). While they were promoted for a couple of years, in recent years people seem to have moved away again from models in WTP space. Given that the vast majority of models are estimated in preference space, we did not believe it was important to also implement WTP space models in Ngene, which are quite different from preference space models. If in the future more researchers would like to optimise design for WTP space models, we may reconsider and include in Ngene.

Reference:

Bliemer, M.C.J., and J.M. Rose (2013) Confidence intervals of willingness-to-pay for random coefficient logit models. Transportation Research Part B, Vol. 58, pp. 199-214.

Best wishes,
Michiel

[Matteo Corsi]

Dear Michiel,

thank you very much for the answer, as well as for the insight into the current trends in choice experiments.
Some of those dynamics are definitely not clear when you approach the field as a beginner.

Best regards,
Matteo Corsi