.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b09_nested.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_b09_nested.py: 9. Nested logit model ===================== Example of a nested logit model. Michel Bierlaire, EPFL Sat Jun 21 2025, 15:33:00 .. GENERATED FROM PYTHON SOURCE LINES 11-24 .. code-block:: Python from IPython.core.display_functions import display from biogeme import biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta from biogeme.models import lognested from biogeme.nests import NestsForNestedLogit, OneNestForNestedLogit from biogeme.results_processing import ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 25-26 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 26-43 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b09_nested') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b09_nested .. GENERATED FROM PYTHON SOURCE LINES 44-45 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 45-52 .. 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) nest_parameter = Beta('nest_parameter', 1, 1, 3, 0) .. GENERATED FROM PYTHON SOURCE LINES 53-54 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 54-58 .. 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 59-60 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 60-62 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 63-64 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 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 71-78 .. code-block:: Python existing = OneNestForNestedLogit( nest_param=nest_parameter, 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 79-82 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 82-84 .. code-block:: Python log_probability = lognested(v, av, nests, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 85-86 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 86-91 .. code-block:: Python the_biogeme = BIOGEME( database, log_probability, optimization_algorithm='simple_bounds_BFGS' ) the_biogeme.modelName = "b09_nested" .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. /Users/bierlair/MyFiles/github/biogeme/docs/source/examples/swissmetro/plot_b09_nested.py:89: DeprecationWarning: 'modelName' is deprecated. Please use 'model_name' instead. the_biogeme.modelName = "b09_nested" .. GENERATED FROM PYTHON SOURCE LINES 92-93 Calculate the null log likelihood for reporting. .. GENERATED FROM PYTHON SOURCE LINES 93-95 .. code-block:: Python the_biogeme.calculate_null_loglikelihood(av) .. rst-class:: sphx-glr-script-out .. code-block:: none -6964.662979192191 .. GENERATED FROM PYTHON SOURCE LINES 96-97 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 97-104 .. code-block:: Python try: results = EstimationResults.from_yaml_file( filename=f'saved_results/{the_biogeme.model_name}.yaml' ) except FileNotFoundError: results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none *** Initial values of the parameters are obtained from the file __b09_nested.iter Cannot read file __b09_nested.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: BFGS with simple bounds [simple_bounds_BFGS]. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_cost nest_parameter asc_car Function Relgrad Radius Rho 0 -1 -1 -1 2 -1 5.7e+03 0.14 1 0.27 + 1 -1 -1 -1 2 -1 5.7e+03 0.14 0.5 -0.74 - 2 -1.1 -0.5 -1.2 1.9 -0.5 5.3e+03 0.038 0.5 0.6 + 3 -0.7 -0.85 -0.74 1.8 -0.35 5.3e+03 0.031 0.5 0.49 + 4 -0.7 -0.85 -0.74 1.8 -0.35 5.3e+03 0.031 0.25 -0.68 - 5 -0.7 -0.85 -0.74 1.8 -0.35 5.3e+03 0.031 0.12 -0.12 - 6 -0.68 -0.73 -0.87 1.9 -0.23 5.3e+03 0.018 0.12 0.52 + 7 -0.66 -0.85 -0.86 1.9 -0.27 5.2e+03 0.0097 0.12 0.7 + 8 -0.54 -0.89 -0.93 2 -0.15 5.2e+03 0.01 0.12 0.31 + 9 -0.54 -0.89 -0.93 2 -0.15 5.2e+03 0.01 0.062 -1.1 - 10 -0.54 -0.89 -0.93 2 -0.15 5.2e+03 0.01 0.031 -0.21 - 11 -0.51 -0.92 -0.9 2 -0.18 5.2e+03 0.0046 0.031 0.56 + 12 -0.51 -0.92 -0.9 2 -0.18 5.2e+03 0.0046 0.016 -0.85 - 13 -0.52 -0.93 -0.88 2 -0.16 5.2e+03 0.0042 0.016 0.16 + 14 -0.51 -0.92 -0.87 2 -0.16 5.2e+03 0.00098 0.016 0.81 + 15 -0.51 -0.92 -0.87 2 -0.16 5.2e+03 0.00098 0.0078 -0.46 - 16 -0.51 -0.92 -0.87 2 -0.16 5.2e+03 0.00098 0.0039 -0.006 - 17 -0.51 -0.92 -0.87 2 -0.16 5.2e+03 0.00095 0.0039 0.52 + 18 -0.51 -0.91 -0.87 2 -0.16 5.2e+03 0.0011 0.0039 0.39 + 19 -0.51 -0.91 -0.86 2 -0.16 5.2e+03 0.00046 0.0039 0.66 + 20 -0.51 -0.91 -0.86 2 -0.16 5.2e+03 0.00031 0.0039 0.81 + 21 -0.51 -0.91 -0.86 2 -0.16 5.2e+03 0.00035 0.0039 0.78 + 22 -0.51 -0.91 -0.86 2 -0.17 5.2e+03 0.00041 0.0039 0.66 + 23 -0.51 -0.9 -0.86 2 -0.16 5.2e+03 0.00048 0.0039 0.45 + 24 -0.51 -0.91 -0.86 2 -0.17 5.2e+03 0.00049 0.0039 0.27 + 25 -0.51 -0.91 -0.86 2 -0.17 5.2e+03 0.00049 0.002 -0.91 - 26 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00028 0.002 0.6 + 27 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00032 0.002 0.56 + 28 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00025 0.002 0.49 + 29 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00028 0.002 0.48 + 30 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00012 0.002 0.77 + 31 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00015 0.002 0.8 + 32 -0.51 -0.9 -0.86 2 -0.17 5.2e+03 0.00019 0.002 0.25 + 33 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 8.2e-05 0.002 0.61 + 34 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 8.2e-05 0.00098 -0.36 - 35 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 6.7e-05 0.00098 0.56 + 36 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 3.2e-05 0.00098 0.77 + 37 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 3.2e-05 0.00049 -2.2 - 38 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 3.2e-05 0.00024 -0.88 - 39 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 3.2e-05 0.00012 -0.33 - 40 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 2.4e-05 0.00012 0.52 + 41 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 1.5e-05 0.00012 0.69 + 42 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 9.6e-06 0.00012 0.9 + 43 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 1.2e-05 0.00012 0.82 + 44 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 8.5e-06 0.00012 0.5 + 45 -0.51 -0.9 -0.86 2.1 -0.17 5.2e+03 5.6e-06 0.00012 0.95 + Optimization algorithm has converged. Relative gradient: 5.5658938507214695e-06 Cause of termination: Relative gradient = 5.6e-06 <= 6.1e-06 Number of function evaluations: 113 Number of gradient evaluations: 67 Number of hessian evaluations: 0 Algorithm: BFGS with trust region for simple bound constraints Number of iterations: 46 Proportion of Hessian calculation: 0/33 = 0.0% Optimization time: 0:00:00.524550 Calculate second derivatives and BHHH File b09_nested.html has been generated. File b09_nested.yaml has been generated. .. GENERATED FROM PYTHON SOURCE LINES 105-107 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b09_nested Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Null log likelihood: -6964.663 Final log likelihood: -5236.9 Likelihood ratio test (null): 3455.526 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 108-111 .. 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 -0.511953 0.079114 -6.471051 9.732348e-11 1 b_time -0.898716 0.107108 -8.390749 0.000000e+00 2 b_cost -0.856701 0.060033 -14.270452 0.000000e+00 3 nest_parameter 2.053862 0.164154 12.511833 0.000000e+00 4 asc_car -0.167141 0.054528 -3.065218 2.175112e-03 .. GENERATED FROM PYTHON SOURCE LINES 112-114 We calculate the correlation between the error terms of the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 114-119 .. 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 1.00000 0.0 0.76294 Swissmetro 0.00000 1.0 0.00000 Car 0.76294 0.0 1.00000 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.930 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b09_nested.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b09_nested.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b09_nested.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b09_nested.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_