.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/indicators/plot_b08arc_elasticities.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_indicators_plot_b08arc_elasticities.py: Arc elasticities ================ We use a previously estimated nested logit model and calculate arc elasticities. Details about this example are available in Section 3 of `Bierlaire (2018) Calculating indicators with PandasBiogeme `_ :author: Michel Bierlaire, EPFL :date: Wed Apr 12 21:00:10 2023 .. GENERATED FROM PYTHON SOURCE LINES 16-28 .. code-block:: Python import sys from IPython.core.display_functions import display import biogeme.biogeme as bio from biogeme.exceptions import BiogemeError from biogeme import models import biogeme.results as res from biogeme.data.optima import read_data, normalized_weight from scenarios import scenario .. GENERATED FROM PYTHON SOURCE LINES 29-31 Obtain the specification for the default scenario The definition of the scenarios is available in :ref:`scenarios`. .. GENERATED FROM PYTHON SOURCE LINES 31-33 .. code-block:: Python V, nests, _, MarginalCostPT = scenario() .. GENERATED FROM PYTHON SOURCE LINES 34-35 Obtain the expression for the choice probability of the public transportation. .. GENERATED FROM PYTHON SOURCE LINES 35-37 .. code-block:: Python prob_PT = models.nested(V, None, nests, 0) .. GENERATED FROM PYTHON SOURCE LINES 38-40 We investigate a scenario where the price for public transportation increases by 20%. We extract the corresponding scenario. .. GENERATED FROM PYTHON SOURCE LINES 40-43 .. code-block:: Python V_after, _, _, MarginalCostPT_after = scenario(factor=1.2) prob_PT_after = models.nested(V_after, None, nests, 0) .. GENERATED FROM PYTHON SOURCE LINES 44-45 Disaggregate elasticities .. GENERATED FROM PYTHON SOURCE LINES 45-51 .. code-block:: Python direct_elas_pt = ( (prob_PT_after - prob_PT) * MarginalCostPT / (prob_PT * (MarginalCostPT_after - MarginalCostPT)) ) .. GENERATED FROM PYTHON SOURCE LINES 52-53 Formulas to simulate. .. GENERATED FROM PYTHON SOURCE LINES 53-59 .. code-block:: Python simulate = { 'weight': normalized_weight, 'Prob. PT': prob_PT, 'direct_elas_pt': direct_elas_pt, } .. GENERATED FROM PYTHON SOURCE LINES 60-61 Read the data .. GENERATED FROM PYTHON SOURCE LINES 61-63 .. code-block:: Python database = read_data() .. GENERATED FROM PYTHON SOURCE LINES 64-65 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 65-67 .. code-block:: Python the_biogeme = bio.BIOGEME(database, simulate) .. GENERATED FROM PYTHON SOURCE LINES 68-69 Read the estimation results from the file .. GENERATED FROM PYTHON SOURCE LINES 69-77 .. code-block:: Python try: results = res.bioResults(pickle_file='saved_results/b02estimation.pickle') except BiogemeError: sys.exit( 'Run first the script b02estimation.py in order to generate ' 'the file b02estimation.pickle.' ) .. GENERATED FROM PYTHON SOURCE LINES 78-80 `simulated_values` is a Panda dataframe with the same number of rows as the database, and as many columns as formulas to simulate. .. GENERATED FROM PYTHON SOURCE LINES 80-83 .. code-block:: Python simulated_values = the_biogeme.simulate(results.get_beta_values()) display(simulated_values) .. rst-class:: sphx-glr-script-out .. code-block:: none weight Prob. PT direct_elas_pt 0 0.886023 0.490700 0.000000 2 0.861136 0.228886 -0.276116 3 0.861136 0.102446 -1.618974 4 0.957386 0.039047 -1.261659 5 0.861136 0.252618 -0.588057 ... ... ... ... 2259 2.036009 0.289274 -0.571994 2261 0.861136 0.148251 -0.920795 2262 0.861136 0.187894 -0.536265 2263 0.957386 0.205622 -0.830743 2264 0.957386 0.198499 -0.888497 [1906 rows x 3 columns] .. GENERATED FROM PYTHON SOURCE LINES 84-85 We calculate the aggregate elasticities. .. GENERATED FROM PYTHON SOURCE LINES 87-88 First, the weighted probabilities. .. GENERATED FROM PYTHON SOURCE LINES 88-92 .. code-block:: Python simulated_values['Weighted prob. PT'] = ( simulated_values['weight'] * simulated_values['Prob. PT'] ) .. GENERATED FROM PYTHON SOURCE LINES 93-94 Then the denominator of the aggregate elasticity expression. .. GENERATED FROM PYTHON SOURCE LINES 94-96 .. code-block:: Python denominator_pt = simulated_values['Weighted prob. PT'].sum() .. GENERATED FROM PYTHON SOURCE LINES 97-98 And finally the aggregate elasticities themselves. .. GENERATED FROM PYTHON SOURCE LINES 98-108 .. code-block:: Python direct_elas_pt = ( simulated_values['Weighted prob. PT'] * simulated_values['direct_elas_pt'] / denominator_pt ).sum() print( f'Aggregate direct arc elasticity of public transportation wrt cost: ' f'{direct_elas_pt:.3g}' ) .. rst-class:: sphx-glr-script-out .. code-block:: none Aggregate direct arc elasticity of public transportation wrt cost: -0.34 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.764 seconds) .. _sphx_glr_download_auto_examples_indicators_plot_b08arc_elasticities.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b08arc_elasticities.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b08arc_elasticities.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b08arc_elasticities.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_