Dear Prof. Bierlaire,
- the starting value for estimation is too close to zero, and the algorithm is trapped in a local optimum, (=> I set the starting value of the sigma parameter to 1, which seemed reasonable, given that the mu paramter was estimated ~2.1 by the Logit model)
- not enough draws, (=> I estimated the model with up to 100k draws as well as by calculating the integral)
- the normal distribution is not appropriate. (=> I also implemented the log-normal model which runs into the same problem.)
I am attaching a copy of the results (Normal.html), B_OC is the parameter of interest.
Naturally, I became sceptical of whether my assumption about the paramter being distributed within the sample would hold. Therefore, I estimated a Logit model with an interaction between the parameter and a time dummy variable (B_OC_Before2020) that I expected to explain some variation in the parameter (see attached Logit_Interaction.html). As shown, including the interaction and improves Log-Likelihood, which I interpret as evidence for the parameter to be in fact distributed within the sample, i.e., the sigma parameter in the mixed-logit should be significantly different from zero.
Could you please advice me on what I might be overlooking?
Thanks in advance,
Moritz