.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b06unif_mixture_integral.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_b06unif_mixture_integral.py: Mixture of logit models ======================= Example of a mixture of logit models, using numerical integration. The mixing distribution is uniform. :author: Michel Bierlaire, EPFL :date: Sun Apr 9 17:52:52 2023 .. GENERATED FROM PYTHON SOURCE LINES 13-25 .. code-block:: Python import biogeme.biogeme_logging as blog import biogeme.biogeme as bio from biogeme import models from biogeme.expressions import ( Beta, Integrate, RandomVariable, exp, log, ) .. GENERATED FROM PYTHON SOURCE LINES 26-27 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 27-44 .. code-block:: Python from swissmetro_data 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 b06unif_mixture_integral.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b06unif_mixture_integral.py .. GENERATED FROM PYTHON SOURCE LINES 45-46 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 46-51 .. 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_COST = Beta('B_COST', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 52-54 Define a random parameter, normally distributed, designed to be used for numerical integration .. GENERATED FROM PYTHON SOURCE LINES 54-58 .. code-block:: Python B_TIME = Beta('B_TIME', 0, None, None, 0) B_TIME_S = Beta('B_TIME_S', 1, None, None, 0) omega = RandomVariable('omega') .. GENERATED FROM PYTHON SOURCE LINES 59-65 .. |infinity| unicode:: U+221E :trim: As the numerical integration ranges from -|infinity| \ to + |infinity| , we need to perform a change of variable in order to integrate between -1 and 1. .. GENERATED FROM PYTHON SOURCE LINES 65-71 .. code-block:: Python LOWER_BND = -1 UPPER_BND = 1 x = LOWER_BND + (UPPER_BND - LOWER_BND) / (1 + exp(-omega)) dx = (UPPER_BND - LOWER_BND) * exp(-omega) * (1 + exp(-omega)) ** (-2) B_TIME_RND = B_TIME + B_TIME_S * x .. GENERATED FROM PYTHON SOURCE LINES 72-73 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 73-77 .. code-block:: Python V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 78-79 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 79-81 .. code-block:: Python V = {1: V1, 2: V2, 3: V3} .. GENERATED FROM PYTHON SOURCE LINES 82-83 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 83-85 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 86-87 Conditional on omega, we have a logit model (called the kernel). .. GENERATED FROM PYTHON SOURCE LINES 87-89 .. code-block:: Python condprob = models.logit(V, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 90-91 We integrate over omega using numerical integration. .. GENERATED FROM PYTHON SOURCE LINES 91-93 .. code-block:: Python logprob = log(Integrate(condprob * dx / (UPPER_BND - LOWER_BND), 'omega')) .. GENERATED FROM PYTHON SOURCE LINES 94-95 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 95-98 .. code-block:: Python the_biogeme = bio.BIOGEME(database, logprob) the_biogeme.modelName = '06unif_mixture_integral' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 99-100 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 100-102 .. 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 __06unif_mixture_integral.iter Cannot read file __06unif_mixture_integral.iter. Statement is ignored. 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_TRAIN B_COST B_TIME B_TIME_S Function Relgrad Radius Rho 0 -1 -1 -1 -1 2 5.6e+03 0.09 1 0.39 + 1 -1 -1 -1 -1 2 5.6e+03 0.09 0.5 -0.11 - 2 -0.5 -1.5 -1.5 -1.3 1.5 5.4e+03 0.074 0.5 0.32 + 3 -0.5 -1.5 -1.5 -1.3 1.5 5.4e+03 0.074 0.25 -0.18 - 4 -0.25 -1.2 -1.2 -1 1.8 5.3e+03 0.028 0.25 0.47 + 5 -0.5 -1 -1 -1.3 1.5 5.3e+03 0.04 0.25 0.16 + 6 -0.5 -1 -1 -1.3 1.5 5.3e+03 0.04 0.12 -0.058 - 7 -0.38 -0.88 -1.1 -1.2 1.5 5.3e+03 0.024 0.12 0.63 + 8 -0.25 -1 -1.2 -1.3 1.4 5.3e+03 0.017 0.12 0.33 + 9 -0.24 -0.88 -1.1 -1.4 1.5 5.3e+03 0.0093 0.12 0.88 + 10 -0.11 -0.75 -1.3 -1.5 1.7 5.2e+03 0.012 0.12 0.71 + 11 -0.079 -0.68 -1.1 -1.6 1.7 5.2e+03 0.0073 0.12 0.71 + 12 -0.043 -0.56 -1.2 -1.7 1.9 5.2e+03 0.0094 1.2 0.91 ++ 13 -0.043 -0.56 -1.2 -1.7 1.9 5.2e+03 0.0094 0.62 -2.1 - 14 -0.043 -0.56 -1.2 -1.7 1.9 5.2e+03 0.0094 0.31 -1.5 - 15 -0.043 -0.56 -1.2 -1.7 1.9 5.2e+03 0.0094 0.16 -0.15 - 16 0.05 -0.59 -1.2 -1.9 2 5.2e+03 0.01 0.16 0.38 + 17 -0.011 -0.52 -1.2 -1.9 2.2 5.2e+03 0.0047 0.16 0.81 + 18 -0.011 -0.52 -1.2 -1.9 2.2 5.2e+03 0.0047 0.078 -0.45 - 19 0.067 -0.51 -1.2 -1.9 2.2 5.2e+03 0.008 0.078 0.3 + 20 0.039 -0.48 -1.2 -2 2.3 5.2e+03 0.0038 0.78 0.94 ++ 21 0.039 -0.48 -1.2 -2 2.3 5.2e+03 0.0038 0.39 -1.4 - 22 0.039 -0.48 -1.2 -2 2.3 5.2e+03 0.0038 0.2 -0.89 - 23 0.039 -0.48 -1.2 -2 2.3 5.2e+03 0.0038 0.098 0.017 - 24 0.062 -0.5 -1.3 -2.1 2.4 5.2e+03 0.0066 0.098 0.47 + 25 0.095 -0.45 -1.2 -2.1 2.5 5.2e+03 0.0047 0.098 0.83 + 26 0.11 -0.44 -1.2 -2.2 2.6 5.2e+03 0.0032 0.98 0.94 ++ 27 0.11 -0.44 -1.2 -2.2 2.6 5.2e+03 0.0032 0.49 -22 - 28 0.11 -0.44 -1.2 -2.2 2.6 5.2e+03 0.0032 0.24 -3.8 - 29 0.11 -0.44 -1.2 -2.2 2.6 5.2e+03 0.0032 0.12 -0.74 - 30 0.098 -0.41 -1.3 -2.2 2.7 5.2e+03 0.0028 0.12 0.23 + 31 0.098 -0.41 -1.3 -2.2 2.7 5.2e+03 0.0028 0.061 -0.22 - 32 0.12 -0.41 -1.3 -2.2 2.7 5.2e+03 0.00093 0.061 0.77 + 33 0.12 -0.41 -1.3 -2.2 2.7 5.2e+03 0.00093 0.031 -0.029 - 34 0.13 -0.39 -1.3 -2.3 2.8 5.2e+03 0.0015 0.031 0.61 + 35 0.13 -0.4 -1.3 -2.3 2.8 5.2e+03 0.00073 0.31 1 ++ 36 0.13 -0.4 -1.3 -2.3 2.8 5.2e+03 0.00073 0.15 -4.9 - 37 0.13 -0.4 -1.3 -2.3 2.8 5.2e+03 0.00073 0.076 -0.56 - 38 0.13 -0.4 -1.3 -2.3 2.8 5.2e+03 0.00073 0.038 -0.47 - 39 0.13 -0.4 -1.3 -2.3 2.8 5.2e+03 0.00073 0.019 0.00081 - 40 0.14 -0.39 -1.3 -2.3 2.8 5.2e+03 0.0016 0.019 0.43 + 41 0.14 -0.39 -1.3 -2.3 2.8 5.2e+03 0.00058 0.19 0.92 ++ 42 0.14 -0.39 -1.3 -2.3 2.8 5.2e+03 0.00058 0.095 -3.4 - 43 0.14 -0.39 -1.3 -2.3 2.8 5.2e+03 0.00058 0.048 -0.51 - 44 0.14 -0.4 -1.3 -2.3 2.9 5.2e+03 0.00047 0.048 0.17 + 45 0.14 -0.4 -1.3 -2.3 2.9 5.2e+03 0.00047 0.015 -3.6 - 46 0.15 -0.38 -1.3 -2.3 2.9 5.2e+03 0.00032 0.015 0.73 + 47 0.15 -0.38 -1.3 -2.3 2.9 5.2e+03 0.00032 0.0076 -0.71 - 48 0.15 -0.38 -1.3 -2.3 2.9 5.2e+03 0.00032 0.0038 0.07 - 49 0.14 -0.38 -1.3 -2.3 2.9 5.2e+03 0.00032 0.0038 0.39 + 50 0.14 -0.39 -1.3 -2.3 2.9 5.2e+03 0.00019 0.0038 0.47 + 51 0.14 -0.39 -1.3 -2.3 2.9 5.2e+03 8.4e-05 0.0038 0.7 + Results saved in file 06unif_mixture_integral.html Results saved in file 06unif_mixture_integral.pickle .. GENERATED FROM PYTHON SOURCE LINES 103-105 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model 06unif_mixture_integral Nbr of parameters: 5 Sample size: 6768 Excluded data: 3960 Final log likelihood: -5215.073 Akaike Information Criterion: 10440.15 Bayesian Information Criterion: 10474.24 .. GENERATED FROM PYTHON SOURCE LINES 106-108 .. 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 0.144470 0.044780 3.226252 1.254230e-03
ASC_TRAIN -0.386013 0.056699 -6.808088 9.890533e-12
B_COST -1.275968 0.046472 -27.456929 0.000000e+00
B_TIME -2.317691 0.110960 -20.887666 0.000000e+00
B_TIME_S 2.871057 0.173325 16.564594 0.000000e+00


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