.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b12_panel.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_b12_panel.py: 12. 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 12-23 .. code-block:: Python import biogeme.biogeme_logging as blog from IPython.core.display_functions import display 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 24-25 See the data processing script: :ref:`swissmetro_panel`. .. GENERATED FROM PYTHON SOURCE LINES 25-44 .. 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 b12_panel.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b12_panel.py .. GENERATED FROM PYTHON SOURCE LINES 45-46 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 46-48 .. code-block:: Python b_cost = Beta('b_cost', 0, None, 0, 0) .. GENERATED FROM PYTHON SOURCE LINES 49-51 Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 51-53 .. code-block:: Python b_time = Beta('b_time', 0, None, 0, 0) .. GENERATED FROM PYTHON SOURCE LINES 54-55 It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 55-58 .. code-block:: Python b_time_s = Beta('b_time_s', 1, 1.0e-5, None, 0) b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 59-60 We do the same for the constants, to address serial correlation. .. GENERATED FROM PYTHON SOURCE LINES 60-72 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_car_s = Beta('asc_car_s', 1, 1.0e-5, 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, 1.0e-5, 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, 1.0e-5, None, 0) asc_sm_rnd = asc_sm + asc_sm_s * Draws('asc_sm_rnd', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 73-74 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 74-78 .. 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 79-80 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 80-82 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 83-84 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 84-86 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 87-89 Conditional on the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 89-91 .. code-block:: Python choice_probability_one_observation = logit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 92-95 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 95-99 .. code-block:: Python conditional_trajectory_probability = PanelLikelihoodTrajectory( choice_probability_one_observation ) .. GENERATED FROM PYTHON SOURCE LINES 100-101 We integrate over the random parameters using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. code-block:: Python log_probability = log(MonteCarlo(conditional_trajectory_probability)) .. GENERATED FROM PYTHON SOURCE LINES 104-107 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 107-117 .. code-block:: Python the_biogeme = BIOGEME( database, log_probability, number_of_draws=5_000, seed=1223, calculating_second_derivatives='never', ) the_biogeme.model_name = 'b12_panel' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 118-119 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 119-126 .. 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 127-129 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b12_panel Nbr of parameters: 9 Sample size: 752 Observations: 6768 Excluded data: 0 Final log likelihood: -3574.944 Akaike Information Criterion: 7167.887 Bayesian Information Criterion: 7209.492 .. GENERATED FROM PYTHON SOURCE LINES 130-133 .. 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 ... BHHH p-value Active bound 0 asc_train -0.035216 ... 8.155440e-01 False 1 asc_train_s 2.763781 ... 0.000000e+00 False 2 b_time -6.045210 ... 0.000000e+00 False 3 b_time_s 3.547604 ... 0.000000e+00 False 4 b_cost -3.580028 ... 0.000000e+00 False 5 asc_sm 0.510528 ... 9.472799e-07 False 6 asc_sm_s 0.000010 ... 9.999822e-01 True 7 asc_car 0.904044 ... 2.848728e-10 False 8 asc_car_s 3.957354 ... 0.000000e+00 False [9 rows x 6 columns] .. GENERATED FROM PYTHON SOURCE LINES 134-135 Here is a list of the columns of the "flat" database fthat has been generated by Biogeme .. GENERATED FROM PYTHON SOURCE LINES 135-138 .. code-block:: Python for col in the_biogeme.model_elements.database.dataframe.columns: print(col) .. rst-class:: sphx-glr-script-out .. code-block:: none GROUP SURVEY SP ID PURPOSE FIRST TICKET WHO LUGGAGE AGE MALE INCOME GA ORIGIN DEST TRAIN_AV CAR_AV SM_AV TRAIN_TT TRAIN_CO TRAIN_HE SM_TT SM_CO SM_HE SM_SEATS CAR_TT CAR_CO CHOICE SM_COST TRAIN_COST CAR_AV_SP TRAIN_AV_SP TRAIN_TT_SCALED TRAIN_COST_SCALED SM_TT_SCALED SM_COST_SCALED CAR_TT_SCALED CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 139-140 And here is a list of the variables that have been renamed in the model specification. .. GENERATED FROM PYTHON SOURCE LINES 140-142 .. code-block:: Python for var in the_biogeme.model_elements.expressions_registry.variables: print(var) .. rst-class:: sphx-glr-script-out .. code-block:: none GROUP SURVEY SP ID PURPOSE FIRST TICKET WHO LUGGAGE AGE MALE INCOME GA ORIGIN DEST TRAIN_AV CAR_AV SM_AV TRAIN_TT TRAIN_CO TRAIN_HE SM_TT SM_CO SM_HE SM_SEATS CAR_TT CAR_CO CHOICE SM_COST TRAIN_COST CAR_AV_SP TRAIN_AV_SP TRAIN_TT_SCALED TRAIN_COST_SCALED SM_TT_SCALED SM_COST_SCALED CAR_TT_SCALED CAR_CO_SCALED .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.271 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b12_panel.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b12_panel.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b12_panel.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b12_panel.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_