.. 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 14-21 .. code-block:: Python from functools import partial from pathlib import Path import pymc as pm from IPython.core.display_functions import display .. GENERATED FROM PYTHON SOURCE LINES 22-23 See the data processing script ``swissmetro_panel.py``. .. GENERATED FROM PYTHON SOURCE LINES 23-54 .. 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, ) import biogeme.biogeme_logging as blog from biogeme.bayesian_estimation import ( BayesianResults, BayesianResultsSummary, get_pandas_estimated_parameters, ) from biogeme.biogeme import BIOGEME from biogeme.expressions import ( Beta, DistributedParameter, Draws, ) from biogeme.models import loglogit 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 55-56 The scale parameters must stay away from zero. We define a small but positive lower bound .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: Python POSITIVE_LOWER_BOUND = 1.0e-5 .. GENERATED FROM PYTHON SOURCE LINES 59-65 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 67-68 Mean of the distribution. .. GENERATED FROM PYTHON SOURCE LINES 68-70 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 71-73 Scale of the distribution. It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 73-75 .. code-block:: Python b_time_s = Beta('b_time_s', 1, POSITIVE_LOWER_BOUND, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 76-77 Distribution of the draws .. GENERATED FROM PYTHON SOURCE LINES 77-84 .. code-block:: Python TriangularFactory = partial( pm.Triangular, lower=-1.0, c=0.0, upper=1.0, ) .. GENERATED FROM PYTHON SOURCE LINES 85-86 Associate the function with a name .. GENERATED FROM PYTHON SOURCE LINES 86-89 .. code-block:: Python DISTRIBUTIONS = {'TRIANGULAR': TriangularFactory} .. GENERATED FROM PYTHON SOURCE LINES 90-92 Define a random parameter with a triangular distribution, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 92-99 .. 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 100-101 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. code-block:: Python b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 104-108 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 108-134 .. 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 135-136 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 136-140 .. 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 141-142 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 142-144 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 145-146 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 146-148 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 149-151 Conditional to the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 151-153 .. code-block:: Python conditional_log_probability = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 154-155 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 155-161 .. 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 162-164 Estimate the posterior distribution of the parameters, or read the results if already available. .. GENERATED FROM PYTHON SOURCE LINES 164-171 .. code-block:: Python yaml_file = Path('saved_results') / f'{the_biogeme.model_name}.yaml' try: summary_results = BayesianResultsSummary.from_yaml_file(filename=yaml_file) except FileNotFoundError: results: BayesianResults = the_biogeme.bayesian_estimation() summary_results = results.to_summary() .. GENERATED FROM PYTHON SOURCE LINES 172-174 .. code-block:: Python print(summary_results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Sample size 6768 Sampler NUTS Number of chains 4 Number of draws per chain 2000 Total number of draws 8000 Acceptance rate target 0.9 Run time 0:13:53.106328 Posterior predictive log-likelihood (sum of log mean p) -2184.16 Expected log-likelihood E[log L(Y|θ)] -2365.45 Best-draw log-likelihood (posterior upper bound) -2250.81 LOO (Leave-One-Out Cross-Validation) -3021.60 LOO Standard Error 79.83 Effective number of parameters (p_LOO) 837.44 .. GENERATED FROM PYTHON SOURCE LINES 175-176 Present the parameter estimates in a pandas table. .. GENERATED FROM PYTHON SOURCE LINES 176-181 .. code-block:: Python pandas_results = get_pandas_estimated_parameters( estimation_results=summary_results, ) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value (mean) ... ESS (bulk) ESS (tail) 0 asc_train -0.416632 ... 3087.780794 4622.181303 1 asc_train_s 2.916961 ... 7.169148 11.063783 2 b_time -6.002655 ... 3409.633082 4819.948740 3 b_cost -3.296642 ... 3907.539480 4491.505722 4 asc_sm_s 1.842478 ... 7.599521 11.490153 5 asc_car 0.372910 ... 2813.779023 4025.026943 6 asc_car_s 0.006289 ... 6.133544 37.932271 7 b_time_s 8.759371 ... 1641.720680 2904.758463 [8 rows x 12 columns] .. GENERATED FROM PYTHON SOURCE LINES 182-183 Report the variables stored in the Bayesian estimation results. .. GENERATED FROM PYTHON SOURCE LINES 183-184 .. code-block:: Python display(summary_results.report_stored_variables()) .. rst-class:: sphx-glr-script-out .. code-block:: none group ... shape 0 constant_data ... [6768] 1 constant_data ... [6768] 2 constant_data ... [6768] 3 constant_data ... [6768] 4 constant_data ... [6768] 5 constant_data ... [6768] 6 constant_data ... [6768] 7 constant_data ... [6768] 8 constant_data ... [6768] 9 constant_data ... [6768] 10 log_likelihood ... [4, 2000, 752] 11 posterior ... [4, 2000] 12 posterior ... [4, 2000, 752] 13 posterior ... [4, 2000, 6768] 14 posterior ... [4, 2000, 752] 15 posterior ... [4, 2000] 16 posterior ... [4, 2000, 752] 17 posterior ... [4, 2000, 6768] 18 posterior ... [4, 2000, 752] 19 posterior ... [4, 2000] 20 posterior ... [4, 2000] 21 posterior ... [4, 2000, 752] 22 posterior ... [4, 2000, 6768] 23 posterior ... [4, 2000, 752] 24 posterior ... [4, 2000] 25 posterior ... [4, 2000] 26 posterior ... [4, 2000] 27 posterior ... [4, 2000, 6768] 28 posterior ... [4, 2000, 752] 29 posterior ... [4, 2000, 752] 30 posterior ... [4, 2000] 31 posterior ... [4, 2000, 752] 32 prior ... [1, 2000] 33 prior ... [1, 2000, 752] 34 prior ... [1, 2000, 6768] 35 prior ... [1, 2000, 752] 36 prior ... [1, 2000] 37 prior ... [1, 2000, 752] 38 prior ... [1, 2000, 6768] 39 prior ... [1, 2000, 752] 40 prior ... [1, 2000] 41 prior ... [1, 2000] 42 prior ... [1, 2000, 752] 43 prior ... [1, 2000, 6768] 44 prior ... [1, 2000, 752] 45 prior ... [1, 2000] 46 prior ... [1, 2000] 47 prior ... [1, 2000] 48 prior ... [1, 2000, 6768] 49 prior ... [1, 2000, 752] 50 prior ... [1, 2000, 752] 51 prior ... [1, 2000] 52 prior ... [1, 2000, 752] 53 sample_stats ... [4, 2000] 54 sample_stats ... [4, 2000] 55 sample_stats ... [4, 2000] 56 sample_stats ... [4, 2000] 57 sample_stats ... [4, 2000] 58 sample_stats ... [4, 2000] 59 sample_stats ... [4, 2000] [60 rows x 4 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.045 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 `_