.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/assisted/plot_b01model.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_assisted_plot_b01model.py: Investigation of several choice models ====================================== Investigate several choice models: - logit - nested logit with two nests: public and private transportation - nested logit with two nests existing and future modes for a total of 3 specifications. See `Bierlaire and Ortelli (2023) `_. Michel Bierlaire, EPFL Sun Apr 27 2025, 15:46:15 .. GENERATED FROM PYTHON SOURCE LINES 19-45 .. code-block:: Python from IPython.core.display_functions import display import biogeme.biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.catalog import Catalog from biogeme.data.swissmetro 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, read_data, ) from biogeme.expressions import Beta from biogeme.models import loglogit, lognested from biogeme.nests import NestsForNestedLogit, OneNestForNestedLogit from biogeme.results_processing import compile_estimation_results, pareto_optimal logger = blog.get_screen_logger(level=blog.INFO) .. GENERATED FROM PYTHON SOURCE LINES 46-47 Parameters to be estimated .. GENERATED FROM PYTHON SOURCE LINES 47-52 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_train = Beta('asc_train', 0, None, None, 0) b_time = Beta('b_time', 0, None, None, 0) b_cost = Beta('b_cost', 0, None, None, 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 = 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 67-69 Definition of the logit model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 69-71 .. code-block:: Python log_probability_logit = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 72-73 Nested logit model: nest with existing alternatives. .. GENERATED FROM PYTHON SOURCE LINES 73-81 .. code-block:: Python mu_existing = Beta('mu_existing', 1, 1, 10, 0) existing = OneNestForNestedLogit( nest_param=mu_existing, list_of_alternatives=[1, 3], name='Existing' ) nests_existing = NestsForNestedLogit(choice_set=list(v), tuple_of_nests=(existing,)) log_probability_nested_existing = lognested(v, av, nests_existing, CHOICE) .. 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 82-83 Nested logit model: nest with public transportation alternatives. .. GENERATED FROM PYTHON SOURCE LINES 83-91 .. code-block:: Python mu_public = Beta('mu_public', 1, 1, 10, 0) public = OneNestForNestedLogit( nest_param=mu_public, list_of_alternatives=[1, 2], name='Public' ) nests_public = NestsForNestedLogit(choice_set=list(v), tuple_of_nests=(public,)) log_probability_nested_public = lognested(v, av, nests_public, CHOICE) .. 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: {3}. If it is not the intention, check the assignment of alternatives to nests. .. GENERATED FROM PYTHON SOURCE LINES 92-93 Catalog. .. GENERATED FROM PYTHON SOURCE LINES 93-102 .. code-block:: Python model_catalog = Catalog.from_dict( catalog_name='model_catalog', dict_of_expressions={ 'logit': log_probability_logit, 'nested existing': log_probability_nested_existing, 'nested public': log_probability_nested_public, }, ) .. GENERATED FROM PYTHON SOURCE LINES 103-104 Read the data .. GENERATED FROM PYTHON SOURCE LINES 104-106 .. code-block:: Python database = read_data() .. GENERATED FROM PYTHON SOURCE LINES 107-108 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 108-111 .. code-block:: Python the_biogeme = BIOGEME(database, model_catalog, generate_html=False, generate_yaml=False) the_biogeme.model_name = 'b01model' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 112-113 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 113-115 .. code-block:: Python dict_of_results = the_biogeme.estimate_catalog() .. rst-class:: sphx-glr-script-out .. code-block:: none Estimating 3 models. Biogeme parameters provided by the user. No YAML file found at b01model_000000.yaml. Estimation is performed. *** Initial values of the parameters are obtained from the file __b01model_000000.iter Cannot read file __b01model_000000.iter. Statement is ignored. Starting values for the algorithm: {} Analytical Hessian method: full As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. 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 asc_car mu_existing Function Relgrad Radius Rho 0 0 0 0 0 1 1.1e+04 0.26 0.5 0.0044 - 1 -0.5 -0.5 -0.5 0.5 1.5 9.2e+03 0.14 0.5 0.51 + 2 -0.5 -1 1.1e-16 0 2 8.9e+03 0.094 0.5 0.25 + 3 -0.5 -1 1.1e-16 0 2 8.9e+03 0.094 0.25 -0.53 - 4 -0.25 -0.75 -0.25 0.009 1.9 8.7e+03 0.056 0.25 0.5 + 5 -0.5 -1 -0.5 0.21 2 8.7e+03 0.074 0.25 0.12 + 6 -0.32 -1 -0.6 -0.045 2 8.5e+03 0.027 0.25 0.65 + 7 -0.32 -1 -0.6 -0.045 2 8.5e+03 0.027 0.12 -0.64 - 8 -0.38 -0.97 -0.73 0.037 2 8.5e+03 0.011 0.12 0.32 + 9 -0.38 -0.97 -0.73 0.037 2 8.5e+03 0.011 0.062 -0.45 - 10 -0.39 -1 -0.67 -0.0094 2 8.5e+03 0.0041 0.062 0.74 + 11 -0.39 -1 -0.67 -0.0094 2 8.5e+03 0.0041 0.031 -0.33 - 12 -0.38 -0.98 -0.65 0.022 2 8.5e+03 0.0052 0.031 0.34 + 13 -0.38 -0.98 -0.65 0.022 2 8.5e+03 0.0052 0.016 -0.61 - 14 -0.37 -0.99 -0.64 0.0063 2 8.5e+03 0.0021 0.016 0.54 + 15 -0.37 -0.98 -0.64 0.0077 2 8.5e+03 0.0011 0.016 0.9 + 16 -0.37 -0.98 -0.64 0.0077 2 8.5e+03 0.0011 0.0078 -0.23 - 17 -0.38 -0.97 -0.63 -9.1e-05 2 8.5e+03 0.00085 0.0078 0.35 + 18 -0.38 -0.97 -0.64 0.0015 2 8.5e+03 0.0014 0.0078 0.29 + 19 -0.38 -0.97 -0.64 0.0019 2 8.5e+03 0.00048 0.0078 0.78 + 20 -0.37 -0.97 -0.63 0.00056 2 8.5e+03 0.00085 0.0078 0.69 + 21 -0.38 -0.97 -0.63 0.0021 2 8.5e+03 0.00051 0.0078 0.61 + 22 -0.37 -0.96 -0.63 -0.0007 2 8.5e+03 0.00038 0.0078 0.43 + 23 -0.37 -0.96 -0.63 -0.0007 2 8.5e+03 0.00038 0.0039 -0.039 - 24 -0.37 -0.96 -0.63 -0.00043 2 8.5e+03 0.00022 0.0039 0.74 + 25 -0.37 -0.96 -0.63 -0.00043 2 8.5e+03 0.00022 0.002 -0.053 - 26 -0.37 -0.96 -0.63 8.8e-05 2 8.5e+03 0.00036 0.002 0.43 + 27 -0.37 -0.96 -0.63 -0.00023 2 8.5e+03 0.00014 0.002 0.86 + 28 -0.37 -0.96 -0.63 -0.0013 2 8.5e+03 0.00032 0.002 0.18 + 29 -0.37 -0.96 -0.63 -0.00068 2 8.5e+03 0.00011 0.002 0.9 + 30 -0.37 -0.96 -0.63 -0.00083 2 8.5e+03 0.00017 0.002 0.69 + 31 -0.37 -0.96 -0.63 -0.0014 2 8.5e+03 0.00012 0.002 0.29 + 32 -0.37 -0.96 -0.63 -0.0014 2 8.5e+03 0.00011 0.002 0.31 + 33 -0.37 -0.96 -0.63 -0.0014 2 8.5e+03 0.00011 0.00098 0.048 - 34 -0.37 -0.96 -0.63 -0.0011 2 8.5e+03 4.9e-05 0.00098 0.79 + 35 -0.37 -0.96 -0.63 -0.0011 2 8.5e+03 4.9e-05 0.00049 -3.5 - 36 -0.37 -0.96 -0.63 -0.0011 2 8.5e+03 4.9e-05 0.00024 -0.69 - 37 -0.37 -0.96 -0.63 -0.0012 2 8.5e+03 4.9e-05 0.00024 0.16 + 38 -0.37 -0.96 -0.63 -0.0014 2.1 8.5e+03 3.9e-05 0.00024 0.22 + 39 -0.37 -0.96 -0.63 -0.0011 2.1 8.5e+03 5.1e-05 0.00024 0.26 + 40 -0.37 -0.96 -0.63 -0.0013 2.1 8.5e+03 1.4e-05 0.00024 0.87 + 41 -0.37 -0.96 -0.63 -0.0013 2.1 8.5e+03 4.9e-06 0.00024 0.87 + Optimization algorithm has converged. Relative gradient: 4.8911388627737665e-06 Cause of termination: Relative gradient = 4.9e-06 <= 6.1e-06 Number of function evaluations: 103 Number of gradient evaluations: 61 Number of hessian evaluations: 0 Algorithm: BFGS with trust region for simple bound constraints Number of iterations: 42 Proportion of Hessian calculation: 0/30 = 0.0% Optimization time: 0:00:00.214547 Calculate final gradient and BHHH Calculate second derivatives Biogeme parameters provided by the user. No YAML file found at b01model_000001.yaml. Estimation is performed. *** Initial values of the parameters are obtained from the file __b01model_000001.iter Cannot read file __b01model_000001.iter. Statement is ignored. Starting values for the algorithm: {} Analytical Hessian method: full As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. 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 asc_car mu_public Function Relgrad Radius Rho 0 0 0 0 0 1 1.1e+04 0.26 0.5 -0.063 - 1 -0.5 -0.5 -0.5 0.5 1.5 9.6e+03 0.15 0.5 0.53 + 2 -0.65 -1 0 0 1 9e+03 0.068 0.5 0.36 + 3 -0.65 -1 0 0 1 9e+03 0.068 0.25 -1.5 - 4 -0.65 -1 0 0 1 9e+03 0.068 0.12 -0.28 - 5 -0.77 -1.1 -0.12 0.076 1.1 8.9e+03 0.059 0.12 0.37 + 6 -0.65 -1.1 -0.25 0.068 1 8.8e+03 0.043 0.12 0.82 + 7 -0.52 -1.2 -0.38 0.034 1.1 8.7e+03 0.034 0.12 0.77 + 8 -0.45 -1.2 -0.5 0.16 1.2 8.7e+03 0.026 0.12 0.36 + 9 -0.4 -1.3 -0.62 0.034 1.1 8.7e+03 0.012 1.2 0.92 ++ 10 -0.4 -1.3 -0.62 0.034 1.1 8.7e+03 0.012 0.62 -3.9 - 11 -0.4 -1.3 -0.62 0.034 1.1 8.7e+03 0.012 0.31 -1.7 - 12 -0.4 -1.3 -0.62 0.034 1.1 8.7e+03 0.012 0.16 0.01 - 13 -0.49 -1.3 -0.78 0.017 1.1 8.7e+03 0.0043 0.16 0.75 + 14 -0.49 -1.3 -0.78 0.017 1.1 8.7e+03 0.0043 0.078 -1 - 15 -0.49 -1.3 -0.78 0.017 1.1 8.7e+03 0.0043 0.039 -0.04 - 16 -0.5 -1.3 -0.77 -0.022 1.1 8.7e+03 0.0019 0.039 0.64 + 17 -0.54 -1.2 -0.78 -0.017 1.1 8.7e+03 0.0022 0.039 0.25 + 18 -0.54 -1.2 -0.78 -0.017 1.1 8.7e+03 0.0022 0.02 -0.15 - 19 -0.56 -1.2 -0.77 -0.031 1.1 8.7e+03 0.0018 0.02 0.14 + 20 -0.56 -1.2 -0.78 -0.011 1.1 8.7e+03 0.0004 0.02 0.8 + 21 -0.56 -1.2 -0.78 -0.011 1.1 8.7e+03 0.0004 0.0098 -0.47 - 22 -0.56 -1.3 -0.78 -0.0094 1.1 8.7e+03 0.00055 0.0098 0.26 + 23 -0.57 -1.2 -0.78 -0.012 1.1 8.7e+03 0.0003 0.0098 0.12 + 24 -0.57 -1.2 -0.78 -0.012 1.1 8.7e+03 0.0003 0.0049 -1.5 - 25 -0.57 -1.3 -0.78 -0.0095 1.1 8.7e+03 8.4e-05 0.0049 0.88 + 26 -0.57 -1.3 -0.78 -0.0095 1.1 8.7e+03 8.4e-05 0.0024 -5.2 - 27 -0.57 -1.3 -0.78 -0.0095 1.1 8.7e+03 8.4e-05 0.0012 -3.5 - 28 -0.57 -1.3 -0.78 -0.0095 1.1 8.7e+03 8.4e-05 0.00061 -0.71 - 29 -0.57 -1.3 -0.78 -0.01 1.1 8.7e+03 7.5e-05 0.00061 0.46 + 30 -0.57 -1.3 -0.78 -0.0095 1.1 8.7e+03 6e-05 0.00061 0.53 + 31 -0.57 -1.3 -0.78 -0.0096 1.1 8.7e+03 1.2e-05 0.00061 0.84 + 32 -0.57 -1.3 -0.78 -0.0096 1.1 8.7e+03 1.2e-05 0.00031 -0.85 - 33 -0.57 -1.3 -0.78 -0.0096 1.1 8.7e+03 1.2e-05 0.00015 0.099 - 34 -0.57 -1.3 -0.78 -0.0096 1.1 8.7e+03 6e-06 0.00015 0.81 - Optimization algorithm has converged. Relative gradient: 6.018995530655885e-06 Cause of termination: Relative gradient = 6e-06 <= 6.1e-06 Number of function evaluations: 74 Number of gradient evaluations: 39 Number of hessian evaluations: 0 Algorithm: BFGS with trust region for simple bound constraints Number of iterations: 35 Proportion of Hessian calculation: 0/19 = 0.0% Optimization time: 0:00:00.182564 Calculate final gradient and BHHH Calculate second derivatives Biogeme parameters provided by the user. No YAML file found at b01model_000002.yaml. Estimation is performed. *** Initial values of the parameters are obtained from the file __b01model_000002.iter Cannot read file __b01model_000002.iter. Statement is ignored. Starting values for the algorithm: {} Analytical Hessian method: full As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho 0 -0.76 -0.77 -0.7 -0.29 8.8e+03 0.04 10 1.1 ++ 1 -0.66 -1.2 -0.77 -0.0015 8.7e+03 0.0064 1e+02 1.1 ++ 2 -0.65 -1.3 -0.79 0.016 8.7e+03 0.00012 1e+03 1 ++ 3 -0.65 -1.3 -0.79 0.016 8.7e+03 4e-08 1e+03 1 ++ Optimization algorithm has converged. Relative gradient: 3.954408090874478e-08 Cause of termination: Relative gradient = 4e-08 <= 6.1e-06 Number of function evaluations: 13 Number of gradient evaluations: 9 Number of hessian evaluations: 4 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 4 Proportion of Hessian calculation: 4/4 = 100.0% Optimization time: 0:00:00.302128 Calculate final gradient and BHHH Calculate second derivatives .. GENERATED FROM PYTHON SOURCE LINES 116-117 Number of estimated models. .. GENERATED FROM PYTHON SOURCE LINES 117-119 .. code-block:: Python print(f'A total of {len(dict_of_results)} models have been estimated') .. rst-class:: sphx-glr-script-out .. code-block:: none A total of 3 models have been estimated .. GENERATED FROM PYTHON SOURCE LINES 120-121 All estimation results .. GENERATED FROM PYTHON SOURCE LINES 121-124 .. code-block:: Python compiled_results, specs = compile_estimation_results( dict_of_results, use_short_names=True ) .. GENERATED FROM PYTHON SOURCE LINES 125-128 .. code-block:: Python display('All estimated models') display(compiled_results) .. rst-class:: sphx-glr-script-out .. code-block:: none All estimated models Model_000000 ... Model_000002 Number of estimated parameters 5 ... 4 Sample size 10719 ... 10719 Final log likelihood -8526.89 ... -8670.163 Akaike Information Criterion 17063.78 ... 17348.33 Bayesian Information Criterion 17100.18 ... 17377.45 asc_train (t-test) -0.373 (-7.17) ... -0.652 (-12) b_time (t-test) -0.958 (-14.7) ... -1.28 (-19.5) b_cost (t-test) -0.629 (-14.8) ... -0.79 (-15.5) asc_car (t-test) -0.00128 (-0.0375) ... 0.0162 (0.438) mu_existing (t-test) 2.05 (15.8) ... mu_public (t-test) ... [11 rows x 3 columns] .. GENERATED FROM PYTHON SOURCE LINES 129-130 Glossary .. GENERATED FROM PYTHON SOURCE LINES 130-133 .. code-block:: Python for short_name, spec in specs.items(): print(f'{short_name}\t{spec}') .. rst-class:: sphx-glr-script-out .. code-block:: none Model_000000 model_catalog:nested existing Model_000001 model_catalog:nested public Model_000002 model_catalog:logit .. GENERATED FROM PYTHON SOURCE LINES 134-135 Estimation results of the Pareto optimal models. .. GENERATED FROM PYTHON SOURCE LINES 135-140 .. code-block:: Python pareto_results = pareto_optimal(dict_of_results) compiled_pareto_results, pareto_specs = compile_estimation_results( pareto_results, use_short_names=True ) .. rst-class:: sphx-glr-script-out .. code-block:: none No Pareto file has been provided .. GENERATED FROM PYTHON SOURCE LINES 141-144 .. code-block:: Python display('Non dominated models') display(compiled_pareto_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Non dominated models Model_000000 Model_000001 Number of estimated parameters 4 5 Sample size 10719 10719 Final log likelihood -8670.163 -8526.89 Akaike Information Criterion 17348.33 17063.78 Bayesian Information Criterion 17377.45 17100.18 asc_train (t-test) -0.652 (-12) -0.373 (-7.17) b_time (t-test) -1.28 (-19.5) -0.958 (-14.7) b_cost (t-test) -0.79 (-15.5) -0.629 (-14.8) asc_car (t-test) 0.0162 (0.438) -0.00128 (-0.0375) mu_existing (t-test) 2.05 (15.8) .. GENERATED FROM PYTHON SOURCE LINES 145-146 Glossary. .. GENERATED FROM PYTHON SOURCE LINES 146-148 .. code-block:: Python for short_name, spec in pareto_specs.items(): print(f'{short_name}\t{spec}') .. rst-class:: sphx-glr-script-out .. code-block:: none Model_000000 model_catalog:logit Model_000001 model_catalog:nested existing .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.341 seconds) .. _sphx_glr_download_auto_examples_assisted_plot_b01model.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b01model.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b01model.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b01model.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_