Mixtures of logit with Monte-Carlo 2000 antithetic MLHS draws

Estimation of a mixtures of logit models where the integral is approximated using MonteCarlo integration with antithetic MLHS draws.

author:

Michel Bierlaire, EPFL

date:

Thu Apr 13 23:38:58 2023

import biogeme.biogeme_logging as blog
from biogeme.expressions import bioDraws
from b07estimation_specification import get_biogeme

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b07estimation_specification_mlhs_anti.py')

Example b07estimation_specification_mlhs_anti.py

R = 2000

the_draws = bioDraws('B_TIME_RND', 'NORMAL_MLHS_ANTI')
the_biogeme = get_biogeme(the_draws=the_draws, number_of_draws=R)
the_biogeme.modelName = 'b07estimation_monte_carlo_mlhs_anti'

File /var/folders/rp/ppksq7xd6_x7p0jb0t73x7vw0000gq/T/tmp_a3zlk2w/117e337a-40fb-4cd9-b81f-2807d677101e has been parsed.

results = the_biogeme.estimate()

*** Initial values of the parameters are obtained from the file __b07estimation_monte_carlo_mlhs_anti.iter
Parameter values restored from __b07estimation_monte_carlo_mlhs_anti.iter
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.         asc_car       asc_train          b_cost          b_time        b_time_s     Function    Relgrad   Radius      Rho
    0          -0.082            -0.8           -0.32              -1            0.87      5.4e+03      0.046       10        1   ++
    1           0.018           -0.56           -0.99            -1.6            0.93      5.2e+03      0.009    1e+02      1.1   ++
    2             0.1           -0.42            -1.2            -2.1             1.4      5.2e+03     0.0053    1e+03      1.1   ++
    3            0.13            -0.4            -1.3            -2.2             1.6      5.2e+03    0.00079    1e+04      1.1   ++
    4            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    1.5e-05    1e+05        1   ++
    5            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    4.6e-09    1e+05        1   ++

print(results.shortSummary())

The syntax "shortSummary" is deprecated and is replaced by the syntax "short_summary".
Results for model b07estimation_monte_carlo_mlhs_anti
Nbr of parameters:              5
Sample size:                    6768
Excluded data:                  3960
Final log likelihood:           -5215.033
Akaike Information Criterion:   10440.07
Bayesian Information Criterion: 10474.17

pandas_results = results.getEstimatedParameters()
pandas_results

	Value	Rob. Std err	Rob. t-test	Rob. p-value
asc_car	0.136686	0.051675	2.645110	8.166426e-03
asc_train	-0.401673	0.065805	-6.103988	1.034538e-09
b_cost	-1.284093	0.086314	-14.876988	0.000000e+00
b_time	-2.258465	0.116803	-19.335631	0.000000e+00
b_time_s	1.654370	0.129659	12.759368	0.000000e+00