statsmodels/statsmodels — comment on commit 17540867ef660d39bc19e15526adcf342ff2c44b
File:  line 0
By jseabold:

Added analytic score not Hessian yet obviously. The performance of the solvers is very odd. I'm taking it on faith that the results from Stata are "correct" for now. They use the null model for starting parameters. The other options are to use the starting values of the OLS with all the data divided by the number of nonlimit observations as an approximation (cf. Greene 19.3.3, 7th edition), or the OLS params using only the nonlimit observations.

The performance of the solvers shouldn't be driven by the (our) Hessian approximation, though it remains sensitive for bse to the epsilon, so the internal solver Hessian approximations, where done, may be bad.

he other option is to revert the Olsen reparameterization and use the score from the full likelihood, though it's slightly more complicated, and then test the performance with all the solvers. I'm going to do some systematic comparisons of the combination of these options and then decide on some sensible defaults. More test datasets may then be needed to gauge convergence. My intuition is that if our Hessian approximation is robust, then newton is going to be the way to go here.