.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b03scale.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_b03scale.py: Heteroscedastic specification ============================= Illustrates a heteroscedastic specification. A different scale is associated with different segments of the sample. Michel Bierlaire, EPFL Wed Jun 18 2025, 11:25:26 .. GENERATED FROM PYTHON SOURCE LINES 13-20 .. 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 21-22 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 22-37 .. 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 38-39 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 39-46 .. 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) scale_group3 = Beta('scale_group3', 1, 0.001, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 47-48 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 53-54 Scale associated with group 3 is estimated. .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: Python scale = (GROUP != 3) + (GROUP == 3) * scale_group3 .. GENERATED FROM PYTHON SOURCE LINES 57-59 Scale the utility functions, and associate them with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 59-61 .. code-block:: Python v = {1: scale * v_train, 2: scale * v_swissmetro, 3: scale * v_car} .. GENERATED FROM PYTHON SOURCE LINES 62-63 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 63-65 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 66-68 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 68-70 .. code-block:: Python logprob = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 71-72 These notes will be included as such in the report file. .. GENERATED FROM PYTHON SOURCE LINES 72-77 .. code-block:: Python USER_NOTES = ( 'Illustrates heteroscedastic specification. A different scale is' ' associated with different segments of the sample.' ) .. GENERATED FROM PYTHON SOURCE LINES 78-79 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 79-82 .. code-block:: Python the_biogeme = BIOGEME(database, logprob, user_notes=USER_NOTES) the_biogeme.model_name = 'b03scale' .. GENERATED FROM PYTHON SOURCE LINES 83-84 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 84-86 .. code-block:: Python results = the_biogeme.estimate() .. GENERATED FROM PYTHON SOURCE LINES 87-89 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b03scale Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Final log likelihood: -4976.691 Akaike Information Criterion: 9963.381 Bayesian Information Criterion: 9997.481 .. GENERATED FROM PYTHON SOURCE LINES 90-91 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 91-93 .. 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 scale_group3 4.177737 0.370552 11.274371 0.000000 1 asc_train -0.447096 0.041146 -10.866099 0.000000 2 b_time -0.374455 0.044514 -8.412151 0.000000 3 b_cost -0.357349 0.038418 -9.301647 0.000000 4 asc_car -0.015332 0.018508 -0.828415 0.407435 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.020 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b03scale.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b03scale.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b03scale.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b03scale.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_