.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b12panel.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_b12panel.py: Mixture of logit with panel data ================================ Example of a mixture of logit models, using Monte-Carlo integration. The datafile is organized as panel data. :author: Michel Bierlaire, EPFL :date: Sun Apr 9 18:12:17 2023 .. GENERATED FROM PYTHON SOURCE LINES 13-27 .. code-block:: Python import numpy as np import biogeme.biogeme_logging as blog import biogeme.biogeme as bio from biogeme import models from biogeme.expressions import ( Beta, bioDraws, PanelLikelihoodTrajectory, MonteCarlo, log, ) from biogeme.parameters import Parameters .. GENERATED FROM PYTHON SOURCE LINES 28-29 See the data processing script: :ref:`swissmetro_panel`. .. GENERATED FROM PYTHON SOURCE LINES 29-46 .. code-block:: Python from swissmetro_panel import ( database, CHOICE, SM_AV, CAR_AV_SP, TRAIN_AV_SP, TRAIN_TT_SCALED, TRAIN_COST_SCALED, SM_TT_SCALED, SM_COST_SCALED, CAR_TT_SCALED, CAR_CO_SCALED, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b12panel.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b12panel.py .. GENERATED FROM PYTHON SOURCE LINES 47-48 We set the seed so that the results are reproducible. This is not necessary in general. .. GENERATED FROM PYTHON SOURCE LINES 48-50 .. code-block:: Python np.random.seed(seed=90267) .. GENERATED FROM PYTHON SOURCE LINES 51-52 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 52-54 .. code-block:: Python B_COST = Beta('B_COST', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 55-57 Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 57-59 .. code-block:: Python B_TIME = Beta('B_TIME', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 60-61 It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 61-64 .. code-block:: Python B_TIME_S = Beta('B_TIME_S', 1, None, None, 0) B_TIME_RND = B_TIME + B_TIME_S * bioDraws('b_time_rnd', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 65-66 We do the same for the constants, to address serial correlation. .. GENERATED FROM PYTHON SOURCE LINES 66-78 .. code-block:: Python ASC_CAR = Beta('ASC_CAR', 0, None, None, 0) ASC_CAR_S = Beta('ASC_CAR_S', 1, None, None, 0) ASC_CAR_RND = ASC_CAR + ASC_CAR_S * bioDraws('ASC_CAR_RND', 'NORMAL_ANTI') ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0) ASC_TRAIN_S = Beta('ASC_TRAIN_S', 1, None, None, 0) ASC_TRAIN_RND = ASC_TRAIN + ASC_TRAIN_S * bioDraws('ASC_TRAIN_RND', 'NORMAL_ANTI') ASC_SM = Beta('ASC_SM', 0, None, None, 1) ASC_SM_S = Beta('ASC_SM_S', 1, None, None, 0) ASC_SM_RND = ASC_SM + ASC_SM_S * bioDraws('ASC_SM_RND', 'NORMAL_ANTI') .. GENERATED FROM PYTHON SOURCE LINES 79-80 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 80-84 .. code-block:: Python V1 = ASC_TRAIN_RND + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED V2 = ASC_SM_RND + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED V3 = ASC_CAR_RND + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 85-86 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: Python V = {1: V1, 2: V2, 3: V3} .. GENERATED FROM PYTHON SOURCE LINES 89-90 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 90-92 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 93-95 Conditional on the random parameters, the likelihood of one observation is given by the logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 95-97 .. code-block:: Python obsprob = models.logit(V, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 98-101 Conditional on the random parameters, the likelihood of all observations for one individual (the trajectory) is the product of the likelihood of each observation. .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. code-block:: Python condprobIndiv = PanelLikelihoodTrajectory(obsprob) .. GENERATED FROM PYTHON SOURCE LINES 104-105 We integrate over the random parameters using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 105-107 .. code-block:: Python logprob = log(MonteCarlo(condprobIndiv)) .. GENERATED FROM PYTHON SOURCE LINES 108-111 As the objective is to illustrate the syntax, we calculate the Monte-Carlo approximation with a small number of draws. .. GENERATED FROM PYTHON SOURCE LINES 111-114 .. code-block:: Python the_biogeme = bio.BIOGEME(database, logprob, number_of_draws=100, seed=1223) the_biogeme.modelName = 'b12panel' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 115-116 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 116-118 .. code-block:: Python results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" *** Initial values of the parameters are obtained from the file __b12panel.iter Cannot read file __b12panel.iter. Statement is ignored. The number of draws (100) is low. The results may not be meaningful. As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. ASC_CAR ASC_CAR_S ASC_SM_S ASC_TRAIN ASC_TRAIN_S B_COST B_TIME B_TIME_S Function Relgrad Radius Rho 0 1 2 2 -1 2 -1 -1 2 4e+03 0.041 1 0.41 + 1 0 2.1 1.9 -1.6 1.7 -2 -2 2.9 3.8e+03 0.029 1 0.85 + 2 -1 3.1 0.85 -0.64 2.7 -3 -3 2.1 3.7e+03 0.046 1 0.35 + 3 -0.3 3.4 0.53 -1.6 2.5 -2.4 -4 2.5 3.7e+03 0.04 1 0.54 + 4 -0.3 3.4 0.53 -1.6 2.5 -2.4 -4 2.5 3.7e+03 0.04 0.5 -0.93 - 5 -0.3 3.4 0.53 -1.6 2.5 -2.4 -4 2.5 3.7e+03 0.04 0.25 -0.075 - 6 -0.34 3.1 0.78 -1.4 2.8 -2.6 -4.2 2.2 3.7e+03 0.032 0.25 0.37 + 7 -0.34 3.1 0.78 -1.4 2.8 -2.6 -4.2 2.2 3.7e+03 0.032 0.12 -0.00093 - 8 -0.22 3 0.65 -1.3 2.9 -2.8 -4.1 2.4 3.7e+03 0.013 0.12 0.72 + 9 -0.094 3.1 0.53 -1.1 2.8 -2.6 -4.2 2.5 3.7e+03 0.03 0.12 0.68 + 10 -0.091 3.1 0.52 -1.1 2.8 -2.6 -4.4 2.5 3.6e+03 0.024 0.12 0.4 + 11 -0.079 3.1 0.52 -1 2.8 -2.7 -4.4 2.6 3.6e+03 0.019 1.2 0.99 ++ 12 0.13 3.3 0.56 -0.39 2.8 -2.8 -5.7 3.2 3.6e+03 0.043 1.2 0.34 + 13 0.13 3.3 0.56 -0.39 2.8 -2.8 -5.7 3.2 3.6e+03 0.043 0.62 -0.55 - 14 0.46 3.9 0.75 -0.29 2.5 -2.9 -5.5 3.2 3.6e+03 0.017 0.62 0.23 + 15 0.46 3.9 0.75 -0.29 2.5 -2.9 -5.5 3.2 3.6e+03 0.017 0.31 -0.75 - 16 0.23 3.6 0.83 -0.17 2.4 -3 -5.6 3.3 3.6e+03 0.0079 3.1 1.1 ++ 17 0.23 3.6 0.83 -0.17 2.4 -3 -5.6 3.3 3.6e+03 0.0079 1.6 -12 - 18 0.23 3.6 0.83 -0.17 2.4 -3 -5.6 3.3 3.6e+03 0.0079 0.78 -12 - 19 0.23 3.6 0.83 -0.17 2.4 -3 -5.6 3.3 3.6e+03 0.0079 0.39 -2.7 - 20 0.23 3.6 0.83 -0.17 2.4 -3 -5.6 3.3 3.6e+03 0.0079 0.2 -0.17 - 21 0.3 3.6 0.79 -0.21 2.2 -3.1 -5.8 3.3 3.6e+03 0.025 0.2 0.31 + 22 0.3 3.6 0.79 -0.21 2.2 -3.1 -5.8 3.3 3.6e+03 0.025 0.098 -0.4 - 23 0.3 3.5 0.81 -0.17 2.2 -3.1 -5.8 3.4 3.6e+03 0.02 0.098 0.29 + 24 0.31 3.6 0.86 -0.074 2.1 -3 -5.8 3.4 3.6e+03 0.004 0.098 0.68 + 25 0.31 3.6 0.86 -0.074 2.1 -3 -5.8 3.4 3.6e+03 0.004 0.049 -2.8 - 26 0.31 3.6 0.86 -0.074 2.1 -3 -5.8 3.4 3.6e+03 0.004 0.024 -1 - 27 0.33 3.6 0.85 -0.05 2.2 -3.1 -5.9 3.4 3.6e+03 0.0095 0.024 0.22 + 28 0.34 3.6 0.85 -0.045 2.1 -3.1 -5.9 3.4 3.6e+03 0.005 0.024 0.8 + 29 0.34 3.6 0.86 -0.047 2.1 -3.1 -5.9 3.4 3.6e+03 0.002 0.24 0.91 ++ 30 0.34 3.6 0.86 -0.047 2.1 -3.1 -5.9 3.4 3.6e+03 0.002 0.12 0.093 - 31 0.38 3.6 0.91 -0.024 2.1 -3.1 -6 3.5 3.6e+03 0.0058 0.12 0.55 + 32 0.38 3.6 0.91 -0.024 2.1 -3.1 -6 3.5 3.6e+03 0.0058 0.061 -1.3 - 33 0.38 3.6 0.91 -0.024 2.1 -3.1 -6 3.5 3.6e+03 0.0058 0.031 -0.051 - 34 0.38 3.6 0.9 0.007 2.1 -3.1 -6 3.5 3.6e+03 0.0016 0.031 0.56 + 35 0.39 3.7 0.89 -0.0041 2.1 -3.1 -6.1 3.5 3.6e+03 0.00031 0.031 0.79 + 36 0.39 3.7 0.89 -0.0041 2.1 -3.1 -6.1 3.5 3.6e+03 0.00031 0.015 -0.04 - 37 0.38 3.7 0.9 0.011 2.1 -3.1 -6.1 3.5 3.6e+03 0.0011 0.015 0.46 + 38 0.38 3.7 0.9 0.0057 2.1 -3.1 -6.1 3.5 3.6e+03 0.00073 0.015 0.64 + 39 0.38 3.7 0.89 0.011 2.2 -3.1 -6.1 3.5 3.6e+03 0.00025 0.015 0.27 + 40 0.38 3.7 0.89 0.011 2.2 -3.1 -6.1 3.5 3.6e+03 0.00025 0.0076 -0.5 - 41 0.38 3.7 0.9 0.012 2.1 -3.1 -6.1 3.5 3.6e+03 0.00017 0.0076 0.85 + 42 0.38 3.7 0.9 0.012 2.1 -3.1 -6.1 3.5 3.6e+03 0.00017 0.0038 -0.96 - 43 0.38 3.7 0.9 0.014 2.1 -3.1 -6.1 3.5 3.6e+03 0.00017 0.0038 0.36 + 44 0.38 3.7 0.9 0.014 2.1 -3.1 -6.1 3.5 3.6e+03 0.00011 0.0038 0.26 + Results saved in file b12panel.html Results saved in file b12panel.pickle .. GENERATED FROM PYTHON SOURCE LINES 119-121 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b12panel Nbr of parameters: 8 Sample size: 752 Observations: 6768 Excluded data: 3960 Final log likelihood: -3621.455 Akaike Information Criterion: 7258.911 Bayesian Information Criterion: 7295.893 .. GENERATED FROM PYTHON SOURCE LINES 122-124 .. code-block:: Python pandas_results = results.get_estimated_parameters() pandas_results .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
ASC_CAR 0.385083 0.315764 1.219527 2.226441e-01
ASC_CAR_S 3.676024 0.298701 12.306718 0.000000e+00
ASC_SM_S 0.899167 0.380249 2.364683 1.804550e-02
ASC_TRAIN 0.012822 0.210955 0.060781 9.515336e-01
ASC_TRAIN_S 2.145739 0.202699 10.585829 0.000000e+00
B_COST -3.143861 0.443004 -7.096692 1.277867e-12
B_TIME -6.100106 0.358725 -17.004964 0.000000e+00
B_TIME_S 3.549978 0.208671 17.012312 0.000000e+00


.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 24.254 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b12panel.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b12panel.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b12panel.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b12panel.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_