.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b10_nested_bottom.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_bayesian_swissmetro_plot_b10_nested_bottom.py: 10. Nested logit model normalized from bottom ============================================= Bayesian estimation of a nested logit model where the normalization is done at the bottom level. Michel Bierlaire, EPFL Mon Nov 03 2025, 20:07:02 .. GENERATED FROM PYTHON SOURCE LINES 12-21 .. code-block:: Python from IPython.core.display_functions import display import biogeme.biogeme_logging as blog from biogeme.bayesian_estimation import BayesianResults, get_pandas_estimated_parameters from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta from biogeme.models import lognested_mev_mu from biogeme.nests import NestsForNestedLogit, OneNestForNestedLogit .. GENERATED FROM PYTHON SOURCE LINES 22-23 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 23-40 .. 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 b10nested_bottom.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b10nested_bottom.py .. GENERATED FROM PYTHON SOURCE LINES 41-42 The scale parameters must stay away from zero. We define a small but positive lower bound .. GENERATED FROM PYTHON SOURCE LINES 42-44 .. code-block:: Python POSITIVE_LOWER_BOUND = 1.0e-5 .. GENERATED FROM PYTHON SOURCE LINES 45-46 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 46-52 .. 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, 0, 0) b_cost = Beta('b_cost', 0, None, 0, 0) .. GENERATED FROM PYTHON SOURCE LINES 53-56 This is the scale parameter of the choice model. It is usually normalized to one. In this example, we normalize the nest parameter instead, and estimate the scale parameter for the model. .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: Python scale_parameter = Beta('scale_parameter', 0.5, POSITIVE_LOWER_BOUND, 1.0, 0) .. GENERATED FROM PYTHON SOURCE LINES 59-60 Definition of the utility functions .. GENERATED FROM PYTHON SOURCE LINES 60-64 .. 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 65-66 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 66-68 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 69-70 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 70-72 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 73-75 Definition of nests. Only the non trivial nests must be defined. A trivial nest is a nest containing exactly one alternative. The nest parameter is normalized to 1. .. GENERATED FROM PYTHON SOURCE LINES 75-82 .. code-block:: Python nest_parameter = 1.0 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 83-87 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, where the scale parameter mu is explicitly involved. .. GENERATED FROM PYTHON SOURCE LINES 87-89 .. code-block:: Python log_probability = lognested_mev_mu(v, av, nests, CHOICE, scale_parameter) .. GENERATED FROM PYTHON SOURCE LINES 90-91 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 91-94 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability) the_biogeme.model_name = 'b10_nested_bottom' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 95-96 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 96-103 .. code-block:: Python try: results = BayesianResults.from_netcdf( filename=f'saved_results/{the_biogeme.model_name}.nc' ) except FileNotFoundError: results = the_biogeme.bayesian_estimation() .. rst-class:: sphx-glr-script-out .. code-block:: none Loaded NetCDF file size: 855.7 MB load finished in 4356 ms (4.36 s) .. GENERATED FROM PYTHON SOURCE LINES 104-106 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none posterior_predictive_loglike finished in 234 ms expected_log_likelihood finished in 11 ms best_draw_log_likelihood finished in 11 ms /Users/bierlair/python_envs/venv313/lib/python3.13/site-packages/arviz/stats/stats.py:1667: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. See http://arxiv.org/abs/1507.04544 for details warnings.warn( waic_res finished in 618 ms waic finished in 618 ms loo_res finished in 7234 ms (7.23 s) loo finished in 7234 ms (7.23 s) Sample size 6768 Sampler NUTS Number of chains 4 Number of draws per chain 2000 Total number of draws 8000 Acceptance rate target 0.9 Run time 0:01:06.198744 Posterior predictive log-likelihood (sum of log mean p) -5234.16 Expected log-likelihood E[log L(Y|θ)] -5239.36 Best-draw log-likelihood (posterior upper bound) -5236.94 WAIC (Widely Applicable Information Criterion) -5244.61 WAIC Standard Error 62.44 Effective number of parameters (p_WAIC) 10.44 LOO (Leave-One-Out Cross-Validation) -5244.66 LOO Standard Error 62.46 Effective number of parameters (p_LOO) 10.49 .. GENERATED FROM PYTHON SOURCE LINES 107-109 .. code-block:: Python pandas_results = get_pandas_estimated_parameters(estimation_results=results) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Diagnostics computation took 22.8 seconds (cached). Name Value (mean) ... ESS (bulk) ESS (tail) 0 asc_train -1.057208 ... 3217.971743 4084.104963 1 asc_car -0.347291 ... 3342.393391 4167.286220 2 b_time -1.850609 ... 4085.167014 5166.466353 3 b_cost -1.765100 ... 4048.977940 4850.762497 4 scale_parameter 0.485079 ... 3691.634650 4293.053828 [5 rows x 12 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 35.340 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b10_nested_bottom.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b10_nested_bottom.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b10_nested_bottom.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b10_nested_bottom.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_