.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/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_swissmetro_plot_b26triangular_panel_mixture.py: Triangular mixture with panel data ================================== Example of a mixture of logit models, using Monte-Carlo integration. The mixing distribution is user-defined (triangular, here). The datafile is organized as panel data. Michel Bierlaire, EPFL .. GENERATED FROM PYTHON SOURCE LINES 13-33 .. 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, PanelLikelihoodTrajectory, log, ) from biogeme.models import logit from biogeme.results_processing import ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 34-35 See the data processing script: :ref:`swissmetro_panel`. .. GENERATED FROM PYTHON SOURCE LINES 35-53 .. 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 54-55 Function generating the draws. .. GENERATED FROM PYTHON SOURCE LINES 55-63 .. code-block:: Python def the_triangular_generator(sample_size: int, number_of_draws: int) -> np.ndarray: """ Provide my own 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 64-65 Associate the function with a name. .. GENERATED FROM PYTHON SOURCE LINES 65-72 .. code-block:: Python my_random_number_generators = { 'TRIANGULAR': RandomNumberGeneratorTuple( the_triangular_generator, 'Draws from a triangular distribution', ) } .. GENERATED FROM PYTHON SOURCE LINES 73-74 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 74-76 .. code-block:: Python b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 77-79 Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 81-82 Mean of the distribution. .. GENERATED FROM PYTHON SOURCE LINES 82-84 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 85-87 Scale of the distribution. It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 87-90 .. 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', 'TRIANGULAR') .. GENERATED FROM PYTHON SOURCE LINES 91-92 We do the same for the constants, to address serial correlation. .. GENERATED FROM PYTHON SOURCE LINES 92-104 .. 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', 'TRIANGULAR') 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', 'TRIANGULAR') asc_sm = Beta('asc_sm', 0, None, None, 1) asc_sm_s = Beta('asc_sm_s', 1, None, None, 0) asc_sm_rnd = asc_sm + asc_sm_s * Draws('asc_sm_rnd', 'TRIANGULAR') .. GENERATED FROM PYTHON SOURCE LINES 105-106 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 106-110 .. 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 111-112 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 112-114 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 115-116 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 116-118 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 119-121 Conditional to the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 121-123 .. code-block:: Python one_observation_conditional_probability = logit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 124-127 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 127-131 .. code-block:: Python trajectory_conditional_probability = PanelLikelihoodTrajectory( one_observation_conditional_probability ) .. GENERATED FROM PYTHON SOURCE LINES 132-133 We integrate over the random parameters using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 133-135 .. code-block:: Python log_probability = log(MonteCarlo(trajectory_conditional_probability)) .. GENERATED FROM PYTHON SOURCE LINES 136-145 .. code-block:: Python the_biogeme = BIOGEME( database, log_probability, random_number_generators=my_random_number_generators, number_of_draws=10_000, seed=1223, ) the_biogeme.model_name = 'b26triangular_panel_mixture' .. 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 146-147 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 147-154 .. code-block:: Python try: results = EstimationResults.from_yaml_file( filename='saved_results/b26triangular_panel_mixture.yaml' ) except FileNotFoundError: results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 155-157 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b26triangular_panel_mixture Nbr of parameters: 8 Sample size: 752 Observations: 6768 Excluded data: 0 Final log likelihood: -3593.921 Akaike Information Criterion: 7203.842 Bayesian Information Criterion: 7240.824 .. GENERATED FROM PYTHON SOURCE LINES 158-160 .. 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 -0.357907 0.232508 -1.539332 1.237234e-01 1 asc_train_s 5.672924 0.756461 7.499296 6.417089e-14 2 b_time -6.078874 0.359765 -16.896772 0.000000e+00 3 b_time_s 8.941038 0.538493 16.603824 0.000000e+00 4 b_cost -3.282904 0.426908 -7.689959 1.465494e-14 5 asc_sm_s 3.492176 0.666815 5.237095 1.631240e-07 6 asc_car 0.355111 0.245255 1.447926 1.476377e-01 7 asc_car_s 9.534559 0.836263 11.401385 0.000000e+00 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 11.087 seconds) .. _sphx_glr_download_auto_examples_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 `_