.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b26triangular_panel_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_bayesian_swissmetro_plot_b26triangular_panel_mixture.py: 26. Triangular mixture with panel data ====================================== Bayesian estimation of a mixture of logit models. The mixing distribution is user-defined (triangular, here). The datafile is organized as panel data. Michel Bierlaire, EPFL Tue Nov 18 2025, 18:31:04 .. GENERATED FROM PYTHON SOURCE LINES 14-29 .. code-block:: Python from functools import partial import biogeme.biogeme_logging as blog import pymc as pm from IPython.core.display_functions import display from biogeme.bayesian_estimation import BayesianResults, get_pandas_estimated_parameters from biogeme.biogeme import BIOGEME from biogeme.expressions import ( Beta, DistributedParameter, Draws, ) from biogeme.models import loglogit .. GENERATED FROM PYTHON SOURCE LINES 30-31 See the data processing script: :ref:`swissmetro_panel`. .. GENERATED FROM PYTHON SOURCE LINES 31-48 .. 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, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b26triangular_panel_mixture.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b26triangular_panel_mixture.py .. GENERATED FROM PYTHON SOURCE LINES 49-50 The scale parameters must stay away from zero. We define a small but positive lower bound .. GENERATED FROM PYTHON SOURCE LINES 50-52 .. code-block:: Python POSITIVE_LOWER_BOUND = 1.0e-5 .. GENERATED FROM PYTHON SOURCE LINES 53-59 Define a random parameter with a triangular distribution. The triangular distribution is not directly available from Biogeme. It has to be generated by a function provided by the user, based on PyMC available distributions. See the PyMC documentation: https://www.pymc.io/projects/docs/en/stable/api/distributions.html .. GENERATED FROM PYTHON SOURCE LINES 61-62 Mean of the distribution. .. GENERATED FROM PYTHON SOURCE LINES 62-64 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 65-67 Scale of the distribution. It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 67-69 .. code-block:: Python b_time_s = Beta('b_time_s', 1, POSITIVE_LOWER_BOUND, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 70-71 Distribution of the draws .. GENERATED FROM PYTHON SOURCE LINES 71-78 .. code-block:: Python TriangularFactory = partial( pm.Triangular, lower=-1.0, c=0.0, upper=1.0, ) .. GENERATED FROM PYTHON SOURCE LINES 79-80 Associate the function with a name .. GENERATED FROM PYTHON SOURCE LINES 80-83 .. code-block:: Python DISTRIBUTIONS = {'TRIANGULAR': TriangularFactory} .. GENERATED FROM PYTHON SOURCE LINES 84-86 Define a random parameter with a triangular distribution, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 86-93 .. code-block:: Python b_time_rnd = DistributedParameter( 'b_time_rnd', b_time + b_time_s * Draws('b_time_rnd_err_term', 'TRIANGULAR', dict_of_distributions=DISTRIBUTIONS), ) .. GENERATED FROM PYTHON SOURCE LINES 94-95 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 95-97 .. code-block:: Python b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 98-102 The constants are distributed across individuals, to address serial correlation. In a panel setting, the corresponding draws are generated at the individual level. Wrapping them in `DistributedParameter` ensures they are expanded consistently when combined with observation-level variables. .. GENERATED FROM PYTHON SOURCE LINES 102-128 .. 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 = DistributedParameter( 'asc_car_rnd', asc_car + asc_car_s * Draws('asc_car_eps', 'TRIANGULAR', dict_of_distributions=DISTRIBUTIONS), ) asc_train = Beta('asc_train', 0, None, None, 0) asc_train_s = Beta('asc_train_s', 1, None, None, 0) asc_train_rnd = DistributedParameter( 'asc_train_rnd', asc_train + asc_train_s * Draws('asc_train_eps', 'TRIANGULAR', dict_of_distributions=DISTRIBUTIONS), ) asc_sm = Beta('asc_sm', 0, None, None, 1) asc_sm_s = Beta('asc_sm_s', 1, None, None, 0) asc_sm_rnd = DistributedParameter( 'asc_sm_rnd', asc_sm + asc_sm_s * Draws('asc_sm_eps', 'TRIANGULAR', dict_of_distributions=DISTRIBUTIONS), ) .. GENERATED FROM PYTHON SOURCE LINES 129-130 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 130-134 .. 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 135-136 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 136-138 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 139-140 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 140-142 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 143-145 Conditional to the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 145-147 .. code-block:: Python conditional_log_probability = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 148-149 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 149-155 .. code-block:: Python the_biogeme = BIOGEME( database, conditional_log_probability, ) the_biogeme.model_name = 'b26triangular_panel' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 156-157 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 157-164 .. code-block:: Python try: results = BayesianResults.from_netcdf( filename=f'saved_results/{the_biogeme.model_name}.nc' ) except FileNotFoundError: results = the_biogeme.bayesian_estimation() .. rst-class:: sphx-glr-script-out .. code-block:: none Loaded NetCDF file size: 792.7 MB load finished in 5931 ms (5.93 s) .. GENERATED FROM PYTHON SOURCE LINES 165-166 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 166-170 .. code-block:: Python pandas_results = get_pandas_estimated_parameters( estimation_results=results, ) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Diagnostics computation took 129.5 seconds (cached). Name Value (mean) ... ESS (bulk) ESS (tail) 0 asc_train -0.414175 ... 2648.124949 4360.839781 1 asc_train_s 2.886533 ... 7.255061 30.937272 2 b_time -6.008143 ... 3308.074825 4800.624422 3 b_cost -3.298295 ... 3908.323051 4962.608849 4 asc_sm_s 1.776373 ... 7.299923 31.449565 5 asc_car 0.378078 ... 3099.587106 4795.332576 6 asc_car_s 4.658081 ... 7.184546 29.290536 7 b_time_s 8.766247 ... 1946.618142 3405.072801 [8 rows x 12 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (2 minutes 15.616 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b26triangular_panel_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_b26triangular_panel_mixture.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b26triangular_panel_mixture.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b26triangular_panel_mixture.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_