.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/latent/plot_b02one_latent_ordered.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_latent_plot_b02one_latent_ordered.py: Measurement equations: discrete indicators ========================================== Ordered probit. :author: Michel Bierlaire, EPFL :date: Thu Apr 13 16:48:55 2023 .. GENERATED FROM PYTHON SOURCE LINES 11-40 .. code-block:: default import biogeme.biogeme_logging as blog from biogeme.models import piecewiseFormula import biogeme.biogeme as bio from biogeme.expressions import Beta, log, Elem, bioNormalCdf from optima import ( database, age_65_more, ScaledIncome, moreThanOneCar, moreThanOneBike, individualHouse, male, haveChildren, haveGA, highEducation, Envir01, Envir02, Envir03, Mobil11, Mobil14, Mobil16, Mobil17, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b02one_latent_ordered.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b02one_latent_ordered.py .. GENERATED FROM PYTHON SOURCE LINES 41-42 Parameters to be estimated .. GENERATED FROM PYTHON SOURCE LINES 42-55 .. code-block:: default coef_intercept = Beta('coef_intercept', 0.0, None, None, 0) coef_age_65_more = Beta('coef_age_65_more', 0.0, None, None, 0) coef_haveGA = Beta('coef_haveGA', 0.0, None, None, 0) coef_moreThanOneCar = Beta('coef_moreThanOneCar', 0.0, None, None, 0) coef_moreThanOneBike = Beta('coef_moreThanOneBike', 0.0, None, None, 0) coef_individualHouse = Beta('coef_individualHouse', 0.0, None, None, 0) coef_male = Beta('coef_male', 0.0, None, None, 0) coef_haveChildren = Beta('coef_haveChildren', 0.0, None, None, 0) coef_highEducation = Beta('coef_highEducation', 0.0, None, None, 0) thresholds = [None, 4, 6, 8, 10, None] formulaIncome = piecewiseFormula(variable=ScaledIncome, thresholds=thresholds) .. GENERATED FROM PYTHON SOURCE LINES 56-57 Latent variable: structural equation. .. GENERATED FROM PYTHON SOURCE LINES 57-70 .. code-block:: default CARLOVERS = ( coef_intercept + coef_age_65_more * age_65_more + formulaIncome + coef_moreThanOneCar * moreThanOneCar + coef_moreThanOneBike * moreThanOneBike + coef_individualHouse * individualHouse + coef_male * male + coef_haveChildren * haveChildren + coef_haveGA * haveGA + coef_highEducation * highEducation ) .. GENERATED FROM PYTHON SOURCE LINES 71-72 Measurement equations .. GENERATED FROM PYTHON SOURCE LINES 74-75 Intercepts. .. GENERATED FROM PYTHON SOURCE LINES 75-83 .. code-block:: default INTER_Envir01 = Beta('INTER_Envir01', 0, None, None, 1) INTER_Envir02 = Beta('INTER_Envir02', 0, None, None, 0) INTER_Envir03 = Beta('INTER_Envir03', 0, None, None, 0) INTER_Mobil11 = Beta('INTER_Mobil11', 0, None, None, 0) INTER_Mobil14 = Beta('INTER_Mobil14', 0, None, None, 0) INTER_Mobil16 = Beta('INTER_Mobil16', 0, None, None, 0) INTER_Mobil17 = Beta('INTER_Mobil17', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 84-85 Coefficients. .. GENERATED FROM PYTHON SOURCE LINES 85-93 .. code-block:: default B_Envir01_F1 = Beta('B_Envir01_F1', -1, None, None, 1) B_Envir02_F1 = Beta('B_Envir02_F1', -1, None, None, 0) B_Envir03_F1 = Beta('B_Envir03_F1', 1, None, None, 0) B_Mobil11_F1 = Beta('B_Mobil11_F1', 1, None, None, 0) B_Mobil14_F1 = Beta('B_Mobil14_F1', 1, None, None, 0) B_Mobil16_F1 = Beta('B_Mobil16_F1', 1, None, None, 0) B_Mobil17_F1 = Beta('B_Mobil17_F1', 1, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 94-95 Linear models. .. GENERATED FROM PYTHON SOURCE LINES 95-103 .. code-block:: default MODEL_Envir01 = INTER_Envir01 + B_Envir01_F1 * CARLOVERS MODEL_Envir02 = INTER_Envir02 + B_Envir02_F1 * CARLOVERS MODEL_Envir03 = INTER_Envir03 + B_Envir03_F1 * CARLOVERS MODEL_Mobil11 = INTER_Mobil11 + B_Mobil11_F1 * CARLOVERS MODEL_Mobil14 = INTER_Mobil14 + B_Mobil14_F1 * CARLOVERS MODEL_Mobil16 = INTER_Mobil16 + B_Mobil16_F1 * CARLOVERS MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS .. GENERATED FROM PYTHON SOURCE LINES 104-105 Scale parameters. .. GENERATED FROM PYTHON SOURCE LINES 105-113 .. code-block:: default SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, 1.0e-5, None, 1) SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, 1.0e-5, None, 0) SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, 1.0e-5, None, 0) SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, 1.0e-5, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 114-115 Symmetric thresholds. .. GENERATED FROM PYTHON SOURCE LINES 115-122 .. code-block:: default delta_1 = Beta('delta_1', 0.1, 1.0e-5, None, 0) delta_2 = Beta('delta_2', 0.2, 1.0e-5, None, 0) tau_1 = -delta_1 - delta_2 tau_2 = -delta_1 tau_3 = delta_1 tau_4 = delta_1 + delta_2 .. GENERATED FROM PYTHON SOURCE LINES 123-124 Ordered probit models. .. GENERATED FROM PYTHON SOURCE LINES 124-254 .. code-block:: default Envir01_tau_1 = (tau_1 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_2 = (tau_2 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_3 = (tau_3 - MODEL_Envir01) / SIGMA_STAR_Envir01 Envir01_tau_4 = (tau_4 - MODEL_Envir01) / SIGMA_STAR_Envir01 IndEnvir01 = { 1: bioNormalCdf(Envir01_tau_1), 2: bioNormalCdf(Envir01_tau_2) - bioNormalCdf(Envir01_tau_1), 3: bioNormalCdf(Envir01_tau_3) - bioNormalCdf(Envir01_tau_2), 4: bioNormalCdf(Envir01_tau_4) - bioNormalCdf(Envir01_tau_3), 5: 1 - bioNormalCdf(Envir01_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir01 = Elem(IndEnvir01, Envir01) Envir02_tau_1 = (tau_1 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_2 = (tau_2 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_3 = (tau_3 - MODEL_Envir02) / SIGMA_STAR_Envir02 Envir02_tau_4 = (tau_4 - MODEL_Envir02) / SIGMA_STAR_Envir02 IndEnvir02 = { 1: bioNormalCdf(Envir02_tau_1), 2: bioNormalCdf(Envir02_tau_2) - bioNormalCdf(Envir02_tau_1), 3: bioNormalCdf(Envir02_tau_3) - bioNormalCdf(Envir02_tau_2), 4: bioNormalCdf(Envir02_tau_4) - bioNormalCdf(Envir02_tau_3), 5: 1 - bioNormalCdf(Envir02_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir02 = Elem(IndEnvir02, Envir02) Envir03_tau_1 = (tau_1 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_2 = (tau_2 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_3 = (tau_3 - MODEL_Envir03) / SIGMA_STAR_Envir03 Envir03_tau_4 = (tau_4 - MODEL_Envir03) / SIGMA_STAR_Envir03 IndEnvir03 = { 1: bioNormalCdf(Envir03_tau_1), 2: bioNormalCdf(Envir03_tau_2) - bioNormalCdf(Envir03_tau_1), 3: bioNormalCdf(Envir03_tau_3) - bioNormalCdf(Envir03_tau_2), 4: bioNormalCdf(Envir03_tau_4) - bioNormalCdf(Envir03_tau_3), 5: 1 - bioNormalCdf(Envir03_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Envir03 = Elem(IndEnvir03, Envir03) Mobil11_tau_1 = (tau_1 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_2 = (tau_2 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_3 = (tau_3 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 Mobil11_tau_4 = (tau_4 - MODEL_Mobil11) / SIGMA_STAR_Mobil11 IndMobil11 = { 1: bioNormalCdf(Mobil11_tau_1), 2: bioNormalCdf(Mobil11_tau_2) - bioNormalCdf(Mobil11_tau_1), 3: bioNormalCdf(Mobil11_tau_3) - bioNormalCdf(Mobil11_tau_2), 4: bioNormalCdf(Mobil11_tau_4) - bioNormalCdf(Mobil11_tau_3), 5: 1 - bioNormalCdf(Mobil11_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil11 = Elem(IndMobil11, Mobil11) Mobil14_tau_1 = (tau_1 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_2 = (tau_2 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_3 = (tau_3 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 Mobil14_tau_4 = (tau_4 - MODEL_Mobil14) / SIGMA_STAR_Mobil14 IndMobil14 = { 1: bioNormalCdf(Mobil14_tau_1), 2: bioNormalCdf(Mobil14_tau_2) - bioNormalCdf(Mobil14_tau_1), 3: bioNormalCdf(Mobil14_tau_3) - bioNormalCdf(Mobil14_tau_2), 4: bioNormalCdf(Mobil14_tau_4) - bioNormalCdf(Mobil14_tau_3), 5: 1 - bioNormalCdf(Mobil14_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil14 = Elem(IndMobil14, Mobil14) Mobil16_tau_1 = (tau_1 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_2 = (tau_2 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_3 = (tau_3 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 Mobil16_tau_4 = (tau_4 - MODEL_Mobil16) / SIGMA_STAR_Mobil16 IndMobil16 = { 1: bioNormalCdf(Mobil16_tau_1), 2: bioNormalCdf(Mobil16_tau_2) - bioNormalCdf(Mobil16_tau_1), 3: bioNormalCdf(Mobil16_tau_3) - bioNormalCdf(Mobil16_tau_2), 4: bioNormalCdf(Mobil16_tau_4) - bioNormalCdf(Mobil16_tau_3), 5: 1 - bioNormalCdf(Mobil16_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil16 = Elem(IndMobil16, Mobil16) Mobil17_tau_1 = (tau_1 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_2 = (tau_2 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_3 = (tau_3 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 Mobil17_tau_4 = (tau_4 - MODEL_Mobil17) / SIGMA_STAR_Mobil17 IndMobil17 = { 1: bioNormalCdf(Mobil17_tau_1), 2: bioNormalCdf(Mobil17_tau_2) - bioNormalCdf(Mobil17_tau_1), 3: bioNormalCdf(Mobil17_tau_3) - bioNormalCdf(Mobil17_tau_2), 4: bioNormalCdf(Mobil17_tau_4) - bioNormalCdf(Mobil17_tau_3), 5: 1 - bioNormalCdf(Mobil17_tau_4), 6: 1.0, -1: 1.0, -2: 1.0, } P_Mobil17 = Elem(IndMobil17, Mobil17) loglike = ( log(P_Envir01) + log(P_Envir02) + log(P_Envir03) + log(P_Mobil11) + log(P_Mobil14) + log(P_Mobil16) + log(P_Mobil17) ) .. GENERATED FROM PYTHON SOURCE LINES 255-256 Create the Biogeme object .. GENERATED FROM PYTHON SOURCE LINES 256-259 .. code-block:: default the_biogeme = bio.BIOGEME(database, loglike) the_biogeme.modelName = 'b02one_latent_ordered' .. rst-class:: sphx-glr-script-out .. code-block:: none File biogeme.toml has been parsed. .. GENERATED FROM PYTHON SOURCE LINES 260-261 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 261-263 .. code-block:: default results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none *** Initial values of the parameters are obtained from the file __b02one_latent_ordered.iter Cannot read file __b02one_latent_ordered.iter. Statement is ignored. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 2.7e+04 1.1 0.5 -1.8e+304 - 1 2.4e+04 1.2 0.5 0.41 + 2 2.4e+04 1.2 0.25 -1.2e+304 - 3 1.9e+04 0.33 0.25 0.76 + 4 1.9e+04 0.33 0.12 -1.6 - 5 1.8e+04 0.22 0.12 0.51 + 6 1.8e+04 0.089 1.2 1.3 ++ 7 1.8e+04 0.089 0.62 -6.6 - 8 1.8e+04 0.089 0.31 -0.2 - 9 1.8e+04 0.017 3.1 0.91 ++ 10 1.8e+04 0.017 1.6 -1.6e+306 - 11 1.8e+04 0.017 0.78 -19 - 12 1.8e+04 0.017 0.39 -1.5 - 13 1.8e+04 0.031 0.39 0.63 + 14 1.8e+04 0.017 0.39 0.19 + 15 1.8e+04 0.013 0.39 0.39 + 16 1.8e+04 0.0023 3.9 1.1 ++ 17 1.8e+04 0.00071 39 1.1 ++ 18 1.8e+04 6e-06 39 1 ++ .. GENERATED FROM PYTHON SOURCE LINES 264-270 .. code-block:: default print(f'Estimated betas: {len(results.data.betaValues)}') print(f'final log likelihood: {results.data.logLike:.3f}') print(f'Output file: {results.data.htmlFileName}') results.writeLaTeX() print(f'LaTeX file: {results.data.latexFileName}') .. rst-class:: sphx-glr-script-out .. code-block:: none Estimated betas: 34 final log likelihood: -17794.883 Output file: None Results saved in file b02one_latent_ordered.tex LaTeX file: b02one_latent_ordered.tex .. GENERATED FROM PYTHON SOURCE LINES 271-272 .. code-block:: default results.getEstimatedParameters() .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
B_Envir02_F1 -0.431256 0.052248 -8.254044 2.220446e-16
B_Envir03_F1 0.565659 0.053072 10.658425 0.000000e+00
B_Mobil11_F1 0.483760 0.053233 9.087651 0.000000e+00
B_Mobil14_F1 0.581952 0.051309 11.342184 0.000000e+00
B_Mobil16_F1 0.462931 0.054263 8.531184 0.000000e+00
B_Mobil17_F1 0.368087 0.051859 7.097890 1.266764e-12
INTER_Envir02 0.348558 0.026108 13.350394 0.000000e+00
INTER_Envir03 -0.308910 0.027037 -11.425607 0.000000e+00
INTER_Mobil11 0.337810 0.028963 11.663335 0.000000e+00
INTER_Mobil14 -0.130447 0.025057 -5.206045 1.929078e-07
INTER_Mobil16 0.128385 0.027590 4.653287 3.266848e-06
INTER_Mobil17 0.145949 0.026022 5.608649 2.039125e-08
SIGMA_STAR_Envir02 0.767048 0.022155 34.621915 0.000000e+00
SIGMA_STAR_Envir03 0.717822 0.020577 34.884877 0.000000e+00
SIGMA_STAR_Mobil11 0.783344 0.024009 32.626525 0.000000e+00
SIGMA_STAR_Mobil14 0.688251 0.020869 32.979985 0.000000e+00
SIGMA_STAR_Mobil16 0.754406 0.022572 33.422764 0.000000e+00
SIGMA_STAR_Mobil17 0.760091 0.023519 32.317495 0.000000e+00
beta_ScaledIncome_10_inf 0.084377 0.030289 2.785757 5.340293e-03
beta_ScaledIncome_4_6 -0.221357 0.091792 -2.411499 1.588709e-02
beta_ScaledIncome_6_8 0.259546 0.109479 2.370747 1.775219e-02
beta_ScaledIncome_8_10 -0.523204 0.127566 -4.101439 4.105895e-05
beta_ScaledIncome_minus_inf_4 0.090312 0.052822 1.709750 8.731211e-02
coef_age_65_more 0.071665 0.061368 1.167793 2.428905e-01
coef_haveChildren -0.037612 0.045884 -0.819703 4.123855e-01
coef_haveGA -0.578162 0.075047 -7.703954 1.310063e-14
coef_highEducation -0.246772 0.052155 -4.731496 2.228717e-06
coef_individualHouse -0.088597 0.045559 -1.944666 5.181517e-02
coef_intercept 0.398118 0.152823 2.605092 9.184955e-03
coef_male 0.066365 0.043292 1.532948 1.252888e-01
coef_moreThanOneBike -0.277211 0.053816 -5.151134 2.589165e-07
coef_moreThanOneCar 0.533173 0.051548 10.343211 0.000000e+00
delta_1 0.251979 0.007261 34.703883 0.000000e+00
delta_2 0.759197 0.019319 39.298622 0.000000e+00


.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.966 seconds) .. _sphx_glr_download_auto_examples_latent_plot_b02one_latent_ordered.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b02one_latent_ordered.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b02one_latent_ordered.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_