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.

Michel Bierlaire, EPFL Sun Jun 29 2025, 02:12:06

from b07estimation_specification import get_biogeme
from IPython.core.display_functions import display

import biogeme.biogeme_logging as blog
from biogeme.expressions import Draws
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b07estimation_specification_mlhs_anti_500.py')

Example b07estimation_specification_mlhs_anti_500.py

R = 500
the_draws = Draws('b_time_rnd', 'NORMAL_MLHS_ANTI')
the_biogeme = get_biogeme(the_draws=the_draws, number_of_draws=R)
the_biogeme.model_name = 'b07estimation_monte_carlo_mlhs_anti_500'
results_file = f'saved_results/{the_biogeme.model_name}.yaml'

Biogeme parameters read from biogeme.toml.
The number of draws (500) is low. The results may not be meaningful.

try:
    results = EstimationResults.from_yaml_file(filename=results_file)
except FileNotFoundError:
    results = the_biogeme.estimate()

print(results.short_summary())

Results for model b07estimation_monte_carlo_mlhs_anti_500
Nbr of parameters:              5
Sample size:                    10719
Excluded data:                  9
Final log likelihood:           -8572.255
Akaike Information Criterion:   17154.51
Bayesian Information Criterion: 17190.91

Get the results in a pandas table

pandas_results = get_pandas_estimated_parameters(
    estimation_results=results,
)
display(pandas_results)

        Name     Value  Robust std err.  Robust t-stat.  Robust p-value
0  asc_train -0.467866         0.048022       -9.742735    0.000000e+00
1     b_time -1.861711         0.075532      -24.647839    0.000000e+00
2   b_time_s  1.207829         0.082474       14.645053    0.000000e+00
3     b_cost -0.845145         0.057626      -14.666004    0.000000e+00
4    asc_car  0.179738         0.035184        5.108470    3.247787e-07