.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b07_discrete_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_b07_discrete_mixture.py: 7. Latent class model ===================== Bayesian estimation of a discrete mixture of logit (or latent class model). Michel Bierlaire, EPFL Mon Nov 03 2025, 13:36:51 .. GENERATED FROM PYTHON SOURCE LINES 12-19 .. code-block:: Python 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, log from biogeme.models import logit .. GENERATED FROM PYTHON SOURCE LINES 20-21 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 21-35 .. 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, ) .. GENERATED FROM PYTHON SOURCE LINES 36-37 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 37-43 .. 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 44-45 Class membership probability. .. GENERATED FROM PYTHON SOURCE LINES 45-48 .. code-block:: Python prob_class1 = Beta('prob_class1', 0.5, 0, 1, 0) prob_class2 = 1 - prob_class1 .. GENERATED FROM PYTHON SOURCE LINES 49-51 Definition of the utility functions for latent_old class 1, where the time coefficient is zero. .. GENERATED FROM PYTHON SOURCE LINES 51-55 .. 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 56-57 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 57-59 .. 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 60-62 Definition of the utility functions for latent_old class 2, whete the time coefficient is estimated. .. GENERATED FROM PYTHON SOURCE LINES 62-66 .. 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 67-68 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 68-70 .. 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 71-72 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 72-74 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 75-76 The choice model is a discrete mixture of logit, with availability conditions .. GENERATED FROM PYTHON SOURCE LINES 76-83 .. 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 84-85 Create the Biogeme object .. GENERATED FROM PYTHON SOURCE LINES 85-88 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability) the_biogeme.model_name = 'b07_discrete_mixture' .. GENERATED FROM PYTHON SOURCE LINES 89-90 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 90-97 .. 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 load finished in 4350 ms (4.35 s) .. GENERATED FROM PYTHON SOURCE LINES 98-100 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none posterior_predictive_loglike finished in 248 ms expected_log_likelihood finished in 11 ms best_draw_log_likelihood finished in 11 ms waic_res finished in 618 ms waic finished in 618 ms loo_res finished in 7493 ms (7.49 s) loo finished in 7493 ms (7.49 s) 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 0:01:20.750559 Posterior predictive log-likelihood (sum of log mean p) -5208.04 Expected log-likelihood E[log L(Y|θ)] -5211.01 Best-draw log-likelihood (posterior upper bound) -5208.55 WAIC (Widely Applicable Information Criterion) -5213.98 WAIC Standard Error 53.21 Effective number of parameters (p_WAIC) 5.94 LOO (Leave-One-Out Cross-Validation) -5213.98 LOO Standard Error 53.21 Effective number of parameters (p_LOO) 5.94 .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. 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 (mean) ... ESS (bulk) ESS (tail) 0 asc_train -0.399679 ... 4426.559689 5037.338577 1 b_cost -1.265343 ... 5089.817814 4912.904953 2 asc_car 0.123068 ... 4415.769041 4980.176025 3 b_time -2.807006 ... 4300.831069 4195.683113 4 prob_class1 0.251723 ... 4565.556656 4841.224547 [5 rows x 12 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 35.683 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b07_discrete_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_b07_discrete_mixture.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b07_discrete_mixture.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b07_discrete_mixture.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_