.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b02weight.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_b02weight.py: WESML ===== Example of a logit model with Weighted Exogenous Sample Maximum Likelihood (WESML). Michel Bierlaire, EPFL Wed Jun 18 2025, 11:20:51 .. GENERATED FROM PYTHON SOURCE LINES 12-19 .. code-block:: Python from IPython.core.display_functions import display from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta from biogeme.models import loglogit from biogeme.results_processing import get_pandas_estimated_parameters .. GENERATED FROM PYTHON SOURCE LINES 20-21 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 21-36 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, GROUP, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) .. GENERATED FROM PYTHON SOURCE LINES 37-39 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 39-45 .. 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 46-48 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 48-52 .. code-block:: Python v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 53-55 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 55-57 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 58-60 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 60-62 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 63-67 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 67-69 .. code-block:: Python logprob = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 70-71 Definition of the weight. .. GENERATED FROM PYTHON SOURCE LINES 71-76 .. code-block:: Python WEIGHT_GROUP_2 = 8.890991e-01 WEIGHT_GROUP_3 = 1.2 weight = WEIGHT_GROUP_2 * (GROUP == 2) + WEIGHT_GROUP_3 * (GROUP == 3) .. GENERATED FROM PYTHON SOURCE LINES 77-78 These notes will be included as such in the report file. .. GENERATED FROM PYTHON SOURCE LINES 78-85 .. code-block:: Python USER_NOTES = ( 'Example of a logit model with three alternatives: ' 'Train, Car and Swissmetro.' ' Weighted Exogenous Sample Maximum Likelihood estimator (WESML)' ) .. GENERATED FROM PYTHON SOURCE LINES 86-90 Create the Biogeme object. It is possible to control the generation of the HTML and the yaml files. Note that these parameters can also be modified in the .TOML configuration file. .. GENERATED FROM PYTHON SOURCE LINES 90-96 .. code-block:: Python formulas = {'log_like': logprob, 'weight': weight} the_biogeme = BIOGEME( database, formulas, user_notes=USER_NOTES, generate_html=True, generate_yaml=False ) the_biogeme.model_name = 'b02weight' .. GENERATED FROM PYTHON SOURCE LINES 97-98 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 98-101 .. code-block:: Python results = the_biogeme.estimate() print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b02weight Nbr of parameters: 4 Sample size: 6768 Excluded data: 3960 Final log likelihood: -5669.069 Akaike Information Criterion: 11346.14 Bayesian Information Criterion: 11373.42 .. GENERATED FROM PYTHON SOURCE LINES 102-103 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 103-105 .. 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 -0.795330 0.079430 -10.012971 0.000000 1 b_time -1.347405 0.096642 -13.942173 0.000000 2 b_cost -1.141353 0.064112 -17.802360 0.000000 3 asc_car -0.091280 0.053915 -1.693050 0.090446 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.064 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b02weight.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b02weight.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b02weight.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b02weight.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_