.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b07discrete_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_b07discrete_mixture.py: Latent class model ================== Example of a discrete mixture of logit (or latent_old class model). Michel Bierlaire, EPFL Sat Jun 21 2025, 15:11:24 .. GENERATED FROM PYTHON SOURCE LINES 12-15 .. code-block:: Python from IPython.core.display_functions import display .. GENERATED FROM PYTHON SOURCE LINES 16-17 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 17-36 .. code-block:: Python from swissmetro_data 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.biogeme import BIOGEME from biogeme.expressions import Beta, log from biogeme.models import logit from biogeme.results_processing import get_pandas_estimated_parameters .. GENERATED FROM PYTHON SOURCE LINES 37-38 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 38-44 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_train = Beta('asc_train', 0, None, None, 0) asc_sm = Beta('asc_sm', 0, None, None, 1) b_time = Beta('b_time', 0, None, None, 0) b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 45-46 Class membership probability. .. GENERATED FROM PYTHON SOURCE LINES 46-49 .. code-block:: Python prob_class1 = Beta('prob_class1', 0.5, 0, 1, 0) prob_class2 = 1 - prob_class1 .. GENERATED FROM PYTHON SOURCE LINES 50-52 Definition of the utility functions for latent_old class 1, where the time coefficient is zero. .. GENERATED FROM PYTHON SOURCE LINES 52-56 .. code-block:: Python v_train_class_1 = asc_train + b_cost * TRAIN_COST_SCALED v_swissmetro_class_1 = asc_sm + b_cost * SM_COST_SCALED v_car_class_1 = asc_car + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 57-58 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 58-60 .. code-block:: Python v_class_1 = {1: v_train_class_1, 2: v_swissmetro_class_1, 3: v_car_class_1} .. GENERATED FROM PYTHON SOURCE LINES 61-63 Definition of the utility functions for latent_old class 2, whete the time coefficient is estimated. .. GENERATED FROM PYTHON SOURCE LINES 63-67 .. code-block:: Python v_train_class_2 = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro_class_2 = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car_class_2 = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 68-69 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 69-71 .. code-block:: Python v_class_2 = {1: v_train_class_2, 2: v_swissmetro_class_2, 3: v_car_class_2} .. GENERATED FROM PYTHON SOURCE LINES 72-73 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 73-75 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 76-77 The choice model is a discrete mixture of logit, with availability conditions .. GENERATED FROM PYTHON SOURCE LINES 77-84 .. code-block:: Python choice_probability_class_1 = logit(v_class_1, av, CHOICE) choice_probability_class_2 = logit(v_class_2, av, CHOICE) prob = ( prob_class1 * choice_probability_class_1 + prob_class2 * choice_probability_class_2 ) log_probability = log(prob) .. GENERATED FROM PYTHON SOURCE LINES 85-86 Create the Biogeme object .. GENERATED FROM PYTHON SOURCE LINES 86-89 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability) the_biogeme.model_name = 'b07discrete_mixture' .. GENERATED FROM PYTHON SOURCE LINES 90-91 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 91-93 .. code-block:: Python results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 94-96 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b07discrete_mixture Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Final log likelihood: -5208.498 Akaike Information Criterion: 10427 Bayesian Information Criterion: 10461.1 .. GENERATED FROM PYTHON SOURCE LINES 97-99 .. 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 prob_class1 0.250792 0.021741 11.535649 0.000000e+00 1 asc_train -0.397586 0.062033 -6.409281 1.462079e-10 2 b_cost -1.264065 0.085606 -14.766051 0.000000e+00 3 asc_car 0.124605 0.050735 2.455992 1.404965e-02 4 b_time -2.797932 0.171663 -16.298949 0.000000e+00 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.411 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b07discrete_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_b07discrete_mixture.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b07discrete_mixture.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b07discrete_mixture.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_