.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b03_scale.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_b03_scale.py: 3. Moneymetric and heteroscedastic specification ================================================ Although normalizing the scale to 1 is a common practice in random utility models, it is sometimes preferable to normalize another parameter. For instance, normalizing the cost coefficient to -1 sets the units of the utility function as currency units (CHF here), and the estimated coefficients are easily interpreted as willingness to pay. In that case, the scale must be estimated. We also illustrate here a heteroscedastic specification, where 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 18-29 .. 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 30-31 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 31-46 .. 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 47-48 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 48-56 .. 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', -1, None, None, 1) scale_not_group3 = Beta('scale_not_group3', 1, 0.001, None, 0) scale_group3 = Beta('scale_group3', 1, 0.001, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 57-58 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 58-62 .. 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 63-64 The scale is defined based on the group membership of each individual. .. GENERATED FROM PYTHON SOURCE LINES 64-66 .. code-block:: Python scale = (GROUP != 3) * scale_not_group3 + (GROUP == 3) * scale_group3 .. GENERATED FROM PYTHON SOURCE LINES 67-69 Scale the utility functions, and associate them with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 69-71 .. code-block:: Python v = {1: scale * v_train, 2: scale * v_swissmetro, 3: scale * v_car} .. 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 76-78 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 78-80 .. code-block:: Python logprob = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 81-82 These notes will be included as such in the report file. .. GENERATED FROM PYTHON SOURCE LINES 82-87 .. code-block:: Python USER_NOTES = ( 'Illustrates a moneymetric and heteroscedastic specification. A different scale is' ' associated with different segments of the sample. The utility function is expressed in CHF.' ) .. GENERATED FROM PYTHON SOURCE LINES 88-89 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 89-92 .. code-block:: Python the_biogeme = BIOGEME(database, logprob, user_notes=USER_NOTES) the_biogeme.model_name = 'b03_scale' .. GENERATED FROM PYTHON SOURCE LINES 93-94 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 94-101 .. 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 102-104 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b03_scale 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 105-106 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 106-108 .. 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_not_group3 0.357350 0.038417 9.301929 0.000000 1 scale_group3 1.492976 0.075495 19.775879 0.000000 2 asc_train -1.251037 0.119768 -10.445471 0.000000 3 b_time -1.047820 0.080484 -13.018905 0.000000 4 asc_car -0.042907 0.050788 -0.844826 0.398208 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.016 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b03_scale.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b03_scale.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b03_scale.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b03_scale.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_