Re: How to define the start value of mu and sigma when adding random parameters to the mixed logit model?
Posted: 11 Jun 2024, 06:08
You could start the offset and range both at zero, or you could start the offset at MNL estimates
Dear Stephane,
I run a hybrid choice model with subsdies attribute so I assume it should be always positive. Therefore I used the following positive log-normal transformation when creating random coeffcient:
randcoeff[["b_subsidies"]] = exp(mu_b_subsidies + sig_b_subsidies * draws_subsidies + b_subsidies_shift_lambda * randcoeff[["LV"]]).
The mu_subsidies that I have obtained was negative (-7.92) but significant. I run the deltaMethod to obtain the mean of parameter and the mean was positive and significant. Is that ok? I mean, is it ok if the estimated parameter is negative and then the mean of distribution is positive when the positive log-normal transformation was used? Or should the estimated parameter be also positive?
My second concern regards the calculation of mean WTA using delta method. In hybrid choice model for each level I obtain the mean of parameter and its SD but also the coefficient for interaction of a given level with latent variable. Should I just calculate two WTA (for mu and for interaction) and then sum it up?
For example, in the vector for expression of deltaMethod should I put:
deltaMethod_settings[['expression']] <- c(zero_till ="mu_b_zero_till/b_subsidies" , zero_till_interaction ="mu_b_zero_till_LV/b_subsidies")
The interpretation would then be, for example, that the farmers would accept to introduce zero-till practices for 100 EUR but for those with higher value of latent variable 70 EUR is enough (assuming that "first" WTA is -100 and for interaction is 30).
Best regards,
Łukasz