ApolloChoiceModelling forum

Hello

I am running a simple MNL model in WTP space.
The model is as follows:

V = list()
V[["alternative1"]] = b_COST *( asc_SQ + b_SB * SB1 + b_JOB * JOB1 + b_SAL * SAL1 + COST1)
V[["alternative2"]] = b_COST *( b_SB * SB2 + b_JOB * JOB2 + b_SAL * SAL2 + COST2)
V[["alternative3"]] = b_COST *( b_SB * SB3 + b_JOB * JOB3 + b_SAL * SAL3 + COST3)

The model can't be fully estimated due to singular Hessian matrix, implying that standard errors can't be produced.

I change the model to this version:

V = list()
V[["alternative1"]] = asc_SQ + b_COST *( b_SB * SB1 + b_JOB * JOB1 + b_SAL * SAL1 + COST1)
V[["alternative2"]] = b_COST *( b_SB * SB2 + b_JOB * JOB2 + b_SAL * SAL2 + COST2)
V[["alternative3"]] = b_COST *( b_SB * SB3 + b_JOB * JOB3 + b_SAL * SAL3 + COST3)

And then everything is fine. Mean WTPs estimated, standard errors produced.

Now I wonder what might the reason be that prevents me from estimating the ASC in WTP-space?

Model diagnostics for the model that fails are as follows:
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 364
Number of rows in database : 2912
Number of modelled outcomes : 2912

Number of cores used : 3
Model without mixing
LL(start) : -3199.16
LL at equal shares, LL(0) : -3199.16
LL at observed shares, LL(C) : -3122.48
LL(final) : -3074.01
Rho-squared vs equal shares : 0.0391
Adj.Rho-squared vs equal shares : 0.0376
Rho-squared vs observed shares : 0.0155
Adj.Rho-squared vs observed shares : 0.0139
AIC : 6158.01
BIC : 6187.9


Thank you for any reply.

Best regards,
Margrethe

Margrethe

first, if you are not using random parameters, there is no reason at all to work in WTP space. It is much easier to work in preference space and calculate your WTP and use the delta method for the associated standard errors. WTP space is a non-linear utility function and this affects estimation and convergence. WTP space is useful for mixed logit, but there's no real benefit for MNL

In relation to your problem, this could be related to the above, could be due to starting values, or other reasons. Also, a WTP for an ASC doesn't make a lot of sense in most cases

Stephane

Thank you for the very clarifying response.
I see the point in keeping to a simpler model compared to more complex when estimating parameters, and the reason I prefer the model in WTP-space is the direct interpretation of the parameters, and not having to think of potential differences in the scale parameter when comparing estimates e.g. from different regions or different treatments within one and the same dataset.

Regarding the ASC in WTP-space, I used to keep it in preference space. But a referee in a journal commented on this and asked us to have the ASC as well in WTP-space. In the literature both are used, i.e. the ASC is sometimes presented in preference space and sometimes in WTP-space.

I interpret your answer as if it does not make sense to monetize peoples preference for (or avoidance of) e.g. the SQ-alternative (if the ASC is only present in the SQ-alternative)?

Best regards,
Margrethe

Hi Margrethe,

If you estimate a model in preference space and do not use additional scale parameters (as the ones used in the MNL_RP_SP example), then all your parameters will have the same scale, allowing you to compare among them. However, you have to keep in mind the scale of their associated explanatory variables as well, e.g. if you have two times in your utility function, one in minutes and another in hours, then you should divide the first by 60 before comparing it to the second. The benefit of WTP-space is not so much about the scale parameter, but about the interpretation of the parameters, that in WTP-space have a meaningful unit (i.e. monetary units).

Regarding the ASC in WTP-space, what I believe Stephane meant when saying "WTP for an ASC doesn't make a lot of sense in most cases" is that ASCs are mostly there to reproduce the market share. They are meaningful only if your sample is representative. In all other cases, you would need to adjust your ASCs, so there isn't much value in calculating a WTP for the asc, be in WTP-space or preference space.

Best wishes
David

Thanks a lot for these insights. It is very useful to have your comments.
The reason why we were considering the scale was that the dataset included a split sample, where half of the respondents got one version of the choice cards whereas the other half got another version. Thus we reasoned that the scale may differ across the two versions. We did test this in a preference space model, and didn't find that the scale parameter for one version was significantly different from one, which we normalised the scale for the other version to be. But as you said, WTP-space makes the parameters easily interpretable, and that was another reason to use this model.

The ASC represented a "Business-as-usual" (BAU) alternative. I am not quite sure I understand the "market share" explanation, I thought the reason that an ASC in WTP-terms doesn't make sense was that the ASC, in addition to express preferences for BAU (i.e. no change), also include preferences for other variables systematically affecting utility. As we don't know what these variables may be, e.g. what units they are measured in, and can't disentangle them from the BAU-preferences it doesn't make sense to put a monetary value on them.

best regards,
Margrethe

Margrethe

a few points.

If you combine data from different sources, as in your example different versions of the survey, then testing for differences in the scale (i.e. inverse of the error variance) makes sense, whether working in preference space or willingness to pay space. Again, the two models are equivalent, and it's not that one of them avoids the need to test for such differences.

In relation to ASCs, what they do is to capture the mean of all unobserved effects and thus allow you to work with the assumption that the extreme value error terms have the same mean. The reason I don't tend to look at monetising ASCs, whether calculating a WTP for them in preference space or including them in the WTP part of a WTP space model, is exactly because they capture a whole range of different effects. Of course, there may be cases where it makes sense, for example if you're looking at different brands in a consumer goods context

Stephane