.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b02_weight.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_b02_weight.py: 2. Estimation with weights: 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 12-23 .. 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 ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 24-25 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 25-40 .. 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 41-43 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 43-49 .. 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 50-52 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 52-56 .. 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 57-59 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 59-61 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 62-64 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 64-66 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 67-71 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 71-73 .. code-block:: Python logprob = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 74-75 Definition of the weight. .. GENERATED FROM PYTHON SOURCE LINES 75-80 .. 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 81-82 These notes will be included as such in the report file. .. GENERATED FROM PYTHON SOURCE LINES 82-89 .. 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 90-95 Create the Biogeme object. Here, we need to provide both the formula for the log likelihood function, and the formula for the weights. This is done via a dict with keys `log_like` and `weight`. 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 95-101 .. 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 = 'b02_weight' .. GENERATED FROM PYTHON SOURCE LINES 102-103 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 103-110 .. code-block:: Python try: results = EstimationResults.from_yaml_file( filename=f'saved_results/{the_biogeme.model_name}.yaml' ) except FileNotFoundError: results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 112-114 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b02_weight 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 115-116 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 116-118 .. 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 0.675 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b02_weight.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b02_weight.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b02_weight.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b02_weight.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_