.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b12panel.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_b12panel.py: Mixture of logit with panel data ================================ Example of a mixture of logit models, using Monte-Carlo integration. The datafile is organized as panel data. Michel Bierlaire, EPFL Sat Jun 21 2025, 16:54:51 .. GENERATED FROM PYTHON SOURCE LINES 12-25 .. 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.expressions import Beta, Draws, MonteCarlo, PanelLikelihoodTrajectory, log from biogeme.models import logit from biogeme.results_processing import ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 26-27 See the data processing script: :ref:`swissmetro_panel`. .. GENERATED FROM PYTHON SOURCE LINES 27-46 .. code-block:: Python from swissmetro_panel 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, ) # from biogeme.results_processing import get_pandas_estimated_parameters logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b12panel.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b12panel.py .. GENERATED FROM PYTHON SOURCE LINES 47-48 We set the seed so that the results are reproducible. This is not necessary in general. .. GENERATED FROM PYTHON SOURCE LINES 48-50 .. code-block:: Python np.random.seed(seed=90267) .. GENERATED FROM PYTHON SOURCE LINES 51-52 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 52-54 .. code-block:: Python b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 55-57 Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 57-59 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 60-61 It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 61-64 .. code-block:: Python b_time_s = Beta('b_time_s', 1, None, None, 0) b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 65-66 We do the same for the constants, to address serial correlation. .. GENERATED FROM PYTHON SOURCE LINES 66-78 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_car_s = Beta('asc_car_s', 1, None, None, 0) asc_car_rnd = asc_car + asc_car_s * Draws('asc_car_rnd', 'NORMAL_ANTI') asc_train = Beta('asc_train', 0, None, None, 0) asc_train_s = Beta('asc_train_s', 1, None, None, 0) asc_train_rnd = asc_train + asc_train_s * Draws('asc_train_rnd', 'NORMAL_ANTI') asc_sm = Beta('asc_sm', 0, None, None, 0) asc_sm_s = Beta('asc_sm_s', 1, None, None, 0) asc_sm_rnd = asc_sm + asc_sm_s * Draws('asc_sm_rnd', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 79-80 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 80-84 .. code-block:: Python v_train = asc_train_rnd + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm_rnd + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car_rnd + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 85-86 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 89-90 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 90-92 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 93-95 Conditional on the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 95-97 .. code-block:: Python choice_probability_one_observation = logit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 98-101 Conditional on the random parameters, the likelihood of all observations for one individual (the trajectory) is the product of the likelihood of each observation. .. GENERATED FROM PYTHON SOURCE LINES 101-105 .. code-block:: Python conditional_trajectory_probability = PanelLikelihoodTrajectory( choice_probability_one_observation ) .. GENERATED FROM PYTHON SOURCE LINES 106-107 We integrate over the random parameters using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 107-109 .. code-block:: Python log_probability = log(MonteCarlo(conditional_trajectory_probability)) .. GENERATED FROM PYTHON SOURCE LINES 110-113 As the objective is to illustrate the syntax, we calculate the Monte-Carlo approximation with a small number of draws. .. GENERATED FROM PYTHON SOURCE LINES 113-116 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability, number_of_draws=10000, seed=1223) the_biogeme.model_name = 'b12panel' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. Flattening database [(6768, 38)]. Database flattened [(752, 362)] Flattening database [(6768, 38)]. Database flattened [(752, 362)] Flattening database [(6768, 38)]. Database flattened [(752, 362)] Flattening database [(6768, 38)]. Database flattened [(752, 362)] .. GENERATED FROM PYTHON SOURCE LINES 117-118 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 118-123 .. code-block:: Python try: results = EstimationResults.from_yaml_file(filename='saved_results/b12panel.yaml') except FileNotFoundError: results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 124-126 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b12panel Nbr of parameters: 9 Sample size: 752 Observations: 6768 Excluded data: 0 Final log likelihood: -3578.671 Akaike Information Criterion: 7175.341 Bayesian Information Criterion: 7216.946 .. GENERATED FROM PYTHON SOURCE LINES 127-129 .. code-block:: Python pandas_results = get_pandas_estimated_parameters(estimation_results=results) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value Robust std err. Robust t-stat. Robust p-value 0 asc_train 0.147614 0.147900 0.998068 3.182462e-01 1 asc_train_s 2.715929 0.259500 10.466003 0.000000e+00 2 b_time -6.016472 0.361328 -16.651000 0.000000e+00 3 b_time_s 3.510503 0.214154 16.392422 0.000000e+00 4 b_cost -3.606924 0.427857 -8.430201 0.000000e+00 5 asc_sm 0.594940 0.123182 4.829764 1.366947e-06 6 asc_sm_s -0.286424 0.283529 -1.010212 3.123938e-01 7 asc_car 0.935106 0.153905 6.075846 1.233354e-09 8 asc_car_s 4.057350 0.342115 11.859596 0.000000e+00 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 9.410 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b12panel.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b12panel.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b12panel.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b12panel.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_