.. 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. Michel Bierlaire, EPFL Sat Jun 21 2025, 15:33:00 .. GENERATED FROM PYTHON SOURCE LINES 11-20 .. 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 get_pandas_estimated_parameters .. GENERATED FROM PYTHON SOURCE LINES 21-22 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 22-39 .. 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 b09nested') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b09nested .. GENERATED FROM PYTHON SOURCE LINES 40-41 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 41-48 .. 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 49-50 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 50-54 .. 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 55-56 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 59-60 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 60-62 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 63-67 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 67-74 .. 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 75-78 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 78-80 .. code-block:: Python log_probability = lognested(v, av, nests, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 81-82 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 82-87 .. code-block:: Python the_biogeme = BIOGEME( database, log_probability, optimization_algorithm='simple_bounds_BFGS' ) the_biogeme.modelName = "b09nested" .. 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_b09nested.py:85: DeprecationWarning: 'modelName' is deprecated. Please use 'model_name' instead. the_biogeme.modelName = "b09nested" .. GENERATED FROM PYTHON SOURCE LINES 88-89 Calculate the null log likelihood for reporting. .. GENERATED FROM PYTHON SOURCE LINES 89-91 .. 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 92-93 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 93-95 .. code-block:: Python results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none *** Initial values of the parameters are obtained from the file __b09nested.iter Parameter values restored from __b09nested.iter Starting values for the algorithm: {'asc_train': -0.5119573878979035, 'b_time': -0.8987202255038353, 'b_cost': -0.8566967912527499, 'nest_parameter': 2.053866579484938, 'asc_car': -0.16713665097004932} 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 Optimization algorithm has converged. Relative gradient: 5.681064121356373e-06 Cause of termination: Relative gradient = 5.7e-06 <= 6.1e-06 Number of function evaluations: 1 Number of gradient evaluations: 1 Number of hessian evaluations: 0 Algorithm: BFGS with trust region for simple bound constraints Number of iterations: 0 Optimization time: 0:00:00.398498 Calculate second derivatives and BHHH File b09nested~01.html has been generated. File b09nested~01.yaml has been generated. .. GENERATED FROM PYTHON SOURCE LINES 96-98 .. 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): 3455.526 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 99-102 .. 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 -0.511957 0.079115 -6.471071 9.731105e-11 1 b_time -0.898720 0.107109 -8.390695 0.000000e+00 2 b_cost -0.856697 0.060033 -14.270350 0.000000e+00 3 nest_parameter 2.053867 0.164162 12.511219 0.000000e+00 4 asc_car -0.167137 0.054529 -3.065110 2.175902e-03 .. GENERATED FROM PYTHON SOURCE LINES 103-105 We calculate the correlation between the error terms of the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 105-110 .. 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 0.762941 Swissmetro 0.000000 1.0 0.000000 Car 0.762941 0.0 1.000000 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.002 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 `_