.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b25_triangular_mixture.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_swissmetro_plot_b25_triangular_mixture.py: 25. Triangular mixture of logit =============================== Example of a mixture of logit models, using Monte-Carlo integration. The mixing distribution is specified by the user. Here, a triangular distribution. Michel Bierlaire, EPFL Sat Jun 28 2025, 12:49:10 .. GENERATED FROM PYTHON SOURCE LINES 15-29 .. code-block:: Python import numpy as np from IPython.core.display_functions import display import biogeme.biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.draws import RandomNumberGeneratorTuple from biogeme.expressions import Beta, Draws, MonteCarlo, log from biogeme.models import logit from biogeme.results_processing import ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 30-31 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 31-48 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b25_triangular_mixture.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b25_triangular_mixture.py .. GENERATED FROM PYTHON SOURCE LINES 49-50 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 50-55 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_train = Beta('asc_train', 0, None, None, 0) asc_sm = Beta('asc_sm', 0, None, None, 1) b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 56-60 Define a random parameter with a triangular distribution, designed to be used for Monte-Carlo simulation. The triangular distribution is not directly available from Biogeme. The draws have to be generated by a function provided by the user. .. GENERATED FROM PYTHON SOURCE LINES 62-63 Mean of the distribution. .. GENERATED FROM PYTHON SOURCE LINES 63-65 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 66-68 Scale of the distribution. It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 68-71 .. code-block:: Python b_time_s = Beta('b_time_s', 1, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 72-73 Function generating the draws. .. GENERATED FROM PYTHON SOURCE LINES 73-81 .. code-block:: Python def the_triangular_generator(sample_size: int, number_of_draws: int) -> np.ndarray: """ User-defined random number generator to the database. See the `numpy.random` documentation to obtain a list of other distributions. """ return np.random.triangular(-1, 0, 1, (sample_size, number_of_draws)) .. GENERATED FROM PYTHON SOURCE LINES 82-83 Associate the function with a name. .. GENERATED FROM PYTHON SOURCE LINES 83-91 .. code-block:: Python my_random_number_generators = { 'TRIANGULAR': RandomNumberGeneratorTuple( generator=the_triangular_generator, description='Draws from a triangular distribution', ) } .. GENERATED FROM PYTHON SOURCE LINES 92-94 Define a random parameter with a triangular distribution, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 94-96 .. code-block:: Python b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'TRIANGULAR') .. GENERATED FROM PYTHON SOURCE LINES 97-98 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 98-102 .. code-block:: Python v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 103-104 Associate utility functions with the numbering of alternatives .. GENERATED FROM PYTHON SOURCE LINES 104-106 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 107-108 Associate the availability conditions with the alternatives .. GENERATED FROM PYTHON SOURCE LINES 108-110 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 111-112 Conditional to b_time_rnd, we have a logit model (called the kernel) .. GENERATED FROM PYTHON SOURCE LINES 112-114 .. code-block:: Python conditional_probability = logit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 115-116 We integrate over b_time_rnd using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 116-118 .. code-block:: Python log_probability = log(MonteCarlo(conditional_probability)) .. GENERATED FROM PYTHON SOURCE LINES 119-129 .. code-block:: Python the_biogeme = BIOGEME( database, log_probability, random_number_generators=my_random_number_generators, number_of_draws=10_000, seed=1223, analytical_hessian_mode='automatic', ) the_biogeme.model_name = 'b25_triangular_mixture' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 130-131 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 131-138 .. code-block:: Python try: results = EstimationResults.from_yaml_file( filename=f'saved_results/{the_biogeme.model_name}.yaml' ) except FileNotFoundError: results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 139-141 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b25_triangular_mixture Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Final log likelihood: -5214.972 Akaike Information Criterion: 10439.94 Bayesian Information Criterion: 10474.04 .. GENERATED FROM PYTHON SOURCE LINES 142-144 .. code-block:: Python pandas_results = get_pandas_estimated_parameters(estimation_results=results) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none {'Estimated parameters': Name Value Robust std err. Robust t-stat. Robust p-value 0 asc_train -0.393970 0.065698 -5.996645 2.014361e-09 1 b_time -2.272662 0.119136 -19.076255 0.000000e+00 2 b_time_s 3.983067 0.306149 13.010235 0.000000e+00 3 b_cost -1.280404 0.086226 -14.849390 0.000000e+00 4 asc_car 0.140253 0.052139 2.689983 7.145576e-03} .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.031 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b25_triangular_mixture.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b25_triangular_mixture.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b25_triangular_mixture.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b25_triangular_mixture.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_