.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b09nested.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_b09nested.py: Nested logit model ================== Example of a nested logit model. :author: Michel Bierlaire, EPFL :date: Tue Oct 24 13:37:32 2023 .. GENERATED FROM PYTHON SOURCE LINES 12-19 .. code-block:: Python from biogeme import biogeme_logging as blog import biogeme.biogeme as bio from biogeme import models from biogeme.expressions import Beta from biogeme.nests import OneNestForNestedLogit, NestsForNestedLogit .. GENERATED FROM PYTHON SOURCE LINES 20-21 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 21-38 .. code-block:: Python from swissmetro_data import ( database, CHOICE, SM_AV, CAR_AV_SP, TRAIN_AV_SP, TRAIN_TT_SCALED, TRAIN_COST_SCALED, SM_TT_SCALED, SM_COST_SCALED, CAR_TT_SCALED, CAR_CO_SCALED, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b09nested') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b09nested .. GENERATED FROM PYTHON SOURCE LINES 39-40 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 40-47 .. 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) MU = Beta('MU', 1, 1, 10, 0) .. GENERATED FROM PYTHON SOURCE LINES 48-49 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 49-53 .. code-block:: Python V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED V2 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED V3 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 54-55 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 55-57 .. code-block:: Python V = {1: V1, 2: V2, 3: V3} .. GENERATED FROM PYTHON SOURCE LINES 58-59 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 59-61 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 62-66 Definition of nests. Only the non-trivial nests must be defined. A trivial nest is a nest containing exactly one alternative. In this example, we create a nest for the existing modes, that is train (1) and car (3). .. GENERATED FROM PYTHON SOURCE LINES 66-73 .. code-block:: Python existing = OneNestForNestedLogit( nest_param=MU, list_of_alternatives=[1, 3], name='existing' ) nests = NestsForNestedLogit(choice_set=list(V), tuple_of_nests=(existing,)) .. rst-class:: sphx-glr-script-out .. code-block:: none The following elements do not appear in any nest and are assumed each to be alone in a separate nest: {2}. If it is not the intention, check the assignment of alternatives to nests. .. GENERATED FROM PYTHON SOURCE LINES 74-77 Definition of the model. This is the contribution of each observation to the log likelihood function. The choice model is a nested logit, with availability conditions. .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. code-block:: Python logprob = models.lognested(V, av, nests, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 80-81 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 81-84 .. code-block:: Python the_biogeme = bio.BIOGEME(database, logprob) the_biogeme.modelName = "b09nested" .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 85-86 Calculate the null log likelihood for reporting. .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: Python the_biogeme.calculate_null_loglikelihood(av) .. rst-class:: sphx-glr-script-out .. code-block:: none np.float64(-6964.662979191462) .. GENERATED FROM PYTHON SOURCE LINES 89-90 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 90-92 .. code-block:: Python results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" *** Initial values of the parameters are obtained from the file __b09nested.iter Cannot read file __b09nested.iter. Statement is ignored. As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. ASC_CAR ASC_TRAIN B_COST B_TIME MU Function Relgrad Radius Rho 0 0.1 -0.75 -1 -0.8 1.5 5.4e+03 0.082 10 0.92 ++ 1 -0.22 -0.28 -0.82 -0.86 2.2 5.3e+03 0.076 10 0.44 + 2 -0.17 -0.52 -0.7 -0.7 2.7 5.3e+03 0.023 10 0.72 + 3 -0.17 -0.52 -0.7 -0.7 2.7 5.3e+03 0.023 0.84 -4.6 - 4 -0.14 -0.52 -0.87 -0.92 1.8 5.2e+03 0.006 0.84 0.63 + 5 -0.16 -0.51 -0.87 -0.91 2 5.2e+03 0.0014 8.4 1.1 ++ 6 -0.16 -0.51 -0.87 -0.91 2 5.2e+03 8.1e-05 8.4 1 ++ Results saved in file b09nested.html Results saved in file b09nested.pickle .. GENERATED FROM PYTHON SOURCE LINES 93-95 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b09nested Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Null log likelihood: -6964.663 Final log likelihood: -5236.9 Likelihood ratio test (null): 3455.525 Rho square (null): 0.248 Rho bar square (null): 0.247 Akaike Information Criterion: 10483.8 Bayesian Information Criterion: 10517.9 .. GENERATED FROM PYTHON SOURCE LINES 96-99 .. code-block:: Python pandas_results = results.get_estimated_parameters() pandas_results .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
ASC_CAR -0.166892 0.054518 -3.061193 2.204573e-03
ASC_TRAIN -0.512028 0.079123 -6.471258 9.719070e-11
B_COST -0.857133 0.060002 -14.285004 0.000000e+00
B_TIME -0.899360 0.107040 -8.402065 0.000000e+00
MU 2.051129 0.163477 12.546934 0.000000e+00


.. GENERATED FROM PYTHON SOURCE LINES 100-102 We calculate the correlation between the error terms of the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 102-107 .. code-block:: Python corr = nests.correlation( parameters=results.get_beta_values(), alternatives_names={1: 'Train', 2: 'Swissmetro', 3: 'Car'}, ) print(corr) .. rst-class:: sphx-glr-script-out .. code-block:: none Train Swissmetro Car Train 1.000000 0.0 0.762308 Swissmetro 0.000000 1.0 0.000000 Car 0.762308 0.0 1.000000 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.373 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b09nested.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b09nested.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b09nested.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b09nested.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_