ApolloChoiceModelling forum

Hi All,

I estimated a mixed logit in WTP space with uncorrelated random parameters. Survey respondents could choose a program alternative or a status quo alternative. The program option has four attributes including a cost attribute. I specify normal distributions for the non-cost attributes and a negative lognormal for the cost attribute. The cost attribute and one of the non-cost attributes are continuous. The other two non-cost attributes are dummy coded. I also include an ASC, which I assume is normally distributed. There are no interactions in the model.

I would like to accomplish two post-estimation tasks:

1) Calculate the mean and sd of WTP for various bundles of the attributes and test for significance.
2) Test for differences in mean WTP for these bundles between different subsamples. (I have estimated separate models for each of the subsamples for comparison.)

Is it appropriate to use the delta method to calculate the measures in (1) or is it better to use the unconditionals for this purpose? Is it appropriate to use a t-test of the unconditionals for (2)?

Thank you!
-Kaylee

Hi

the delta method per se can only be used to calculate standard errors for functions of parameters. In your case, that is not possible, as you cannot analytically define the moments of the ratio of a normal and lognormal. You can of course simulate the means and sd using apollo_unconditionals, but you cannot get a measure of statistical significance for them or conduct any tests.

A key thing you need to understand here is the difference between the properties of estimates (estimate and standard error) and the properties of distributions of tastes (mean and standard deviation). The former relate to statistical tests for differences. You can of course use the latter to see how the distributions overlap, but this will not relate to statistical significance tests

Stephane

This is helpful! Thanks, Stephane!

Would it be appropriate instead to bootstrap the mixed logit estimates and calculate the WTP for each bundle and boostrap iteration to calculate SEs for the means and sds?

-Kaylee

Hi

yes, that would work, though it is of course quite time consuming

The other option is to simulate let's say 100 sets of values for the model parameters using the estimates and asymptotic covariance matrix, and then for each set, create draws for the random coefficients using those parameters, and then calculate the moments of wtp in each of these runs

Stephane