.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b18a_ordinal_logit.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_b18a_ordinal_logit.py: 18a. Ordinal logit model ======================== Example of an ordinal logit model. This is just to illustrate the syntax, as the data are not ordered. But the example assume, for the sake of it, that the alternatives are ordered as 1->2->3 Michel Bierlaire, EPFL Thu Jun 26 2025, 15:52:21 .. GENERATED FROM PYTHON SOURCE LINES 14-25 .. code-block:: Python from IPython.core.display_functions import display import biogeme.biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta, OrderedLogLogit from biogeme.results_processing import ( EstimationResults, get_pandas_estimated_parameters, ) .. GENERATED FROM PYTHON SOURCE LINES 26-27 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 27-32 .. code-block:: Python from swissmetro_data import CHOICE, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b18a_ordinal_logit.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b18a_ordinal_logit.py .. GENERATED FROM PYTHON SOURCE LINES 33-34 Parameters to be estimated .. GENERATED FROM PYTHON SOURCE LINES 34-37 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 38-39 Threshold parameters for the ordered logit. .. GENERATED FROM PYTHON SOURCE LINES 41-42 :math:`\tau_1 \leq 0`. .. GENERATED FROM PYTHON SOURCE LINES 42-44 .. code-block:: Python tau1 = Beta('tau1', -1, None, 0, 0) .. GENERATED FROM PYTHON SOURCE LINES 45-46 :math:`\delta_2 \geq 0`. .. GENERATED FROM PYTHON SOURCE LINES 46-48 .. code-block:: Python delta2 = Beta('delta2', 2, 0, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 49-50 :math:`\tau_2 = \tau_1 + \delta_2` .. GENERATED FROM PYTHON SOURCE LINES 50-52 .. code-block:: Python tau2 = tau1 + delta2 .. GENERATED FROM PYTHON SOURCE LINES 53-54 Utility. .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: Python utility = b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED .. GENERATED FROM PYTHON SOURCE LINES 57-62 Associate each discrete indicator with an interval. 1. :math:`-\infty \to \tau_1`, 2. :math:`\tau_1 \to \tau_2`, 3. :math:`\tau_2 \to +\infty`. .. GENERATED FROM PYTHON SOURCE LINES 62-71 .. code-block:: Python log_probability = OrderedLogLogit( eta=utility, cutpoints=[tau1, tau2], y=CHOICE, categories=[1, 2, 3], neutral_labels=[], ) .. GENERATED FROM PYTHON SOURCE LINES 72-73 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 73-76 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability) the_biogeme.model_name = 'b18a_ordinal_logit' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 77-78 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 78-85 .. 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 __b18a_ordinal_logit.iter Cannot read file __b18a_ordinal_logit.iter. Statement is ignored. Starting values for the algorithm: {} 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. b_time b_cost tau1 delta2 Function Relgrad Radius Rho 0 -0.0044 0.97 -0.91 2.7 5.9e+03 0.058 10 1.1 ++ 1 -0.022 1.2 -1 3.1 5.8e+03 0.0071 1e+02 1.1 ++ 2 -0.022 1.3 -1 3.2 5.8e+03 0.00013 1e+03 1 ++ 3 -0.022 1.3 -1 3.2 5.8e+03 4.6e-08 1e+03 1 ++ Optimization algorithm has converged. Relative gradient: 4.580772034607553e-08 Cause of termination: Relative gradient = 4.6e-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: 0:00:00.440946 Calculate second derivatives and BHHH File b18a_ordinal_logit.html has been generated. File b18a_ordinal_logit.yaml has been generated. .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b18a_ordinal_logit Nbr of parameters: 4 Sample size: 6768 Excluded data: 3960 Final log likelihood: -5789.309 Akaike Information Criterion: 11586.62 Bayesian Information Criterion: 11613.9 .. GENERATED FROM PYTHON SOURCE LINES 89-91 .. 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 b_time -0.022080 0.040060 -0.551179 0.581511 1 b_cost 1.262900 0.058542 21.572537 0.000000 2 tau1 -1.030101 0.067968 -15.155756 0.000000 3 delta2 3.193022 0.046336 68.909624 0.000000 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.002 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b18a_ordinal_logit.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b18a_ordinal_logit.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b18a_ordinal_logit.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b18a_ordinal_logit.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_