Estimators for Discrete Choice models, collected as I go.

Please direct comments/questions about the code to me, not to the authors of the papers I am citing.

Revelt Train (1998)

This is a straightforward port of Kenneth Train's Mixed Logit Maximum Simulated Likelihood code as detailed in Revelt Train (1998; publisher version here, working paper here).

Modifications of note:

• Removed the possibility to use stored quasirandom draws;
• Removed the possibility to store in memory only a subset of random draws at a time;
• Added the possibility of not using analytical gradient in likelihood (though it is advisable to do so);
• The likelihood/gradient function is modified to run faster; more comments add context to commands.

To run: parameters are defined and data is imported by mxlmsl.jl. Note the data.txt called in the file is available from Train's original upload. loglik.jl and llgrad2.jl are included but the script only calls llg.jl, which supersedes the aforementioned files.

Train (2016)

This is a straightforward port of Kenneth Train's Mixed logit with a flexible mixing distribution code as detailed in Train (2016; publisher version here). This paper generalises ideas found in Section 6 of Train (2008; publisher version here).

Modifications of note:

• Removed the possibility to use GPU computing (could be added, I am not acquainted with Julia possibilities);
• Added the possibility to estimate the model in preference space;
• Added the possibility to not subset from S to S_r (see Train 2016, p. 42).

To run: parameters are defined and data is imported by FlexibleWtp.jl. Note the videodata100.mat called in the file is available from Train's original upload. Estimation is performed by doestimation.jl, and bootstrap is available via boot.jl.

Ackerberg (2009)

This is a quick Monte Carlo example of the Importance Sampling idea in Ackerberg (2009, QME) applied to discrete choice with random coefficients. I wrote this example to teach myself the basic idea behind the estimator, which I could not wrap my head around by reading the paper.

The benefits of the estimator clearly lie beyond this simple example, in which IS is outperformed by a simple simulated likelihood estimator.

However, the example is complex enough to illustrate general features of IS. Most importantly, the performance of the estimator depends heavily on a good proposal density. This seems to lead to a natural extension: iteratively updating the proposal distribution. The Julia script implements such iterative estimator: iterating delivers little improvement in this case, but it could be helpful in more complex models. For example, one could iteratively obtain better proposal distributions by optimization with lax convergence criteria, and pursue optimization with stricter convergence criteria once the parameters of the proposal distribution seem to have converged.