.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/latent/plot_b01one_latent_regression.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_b01one_latent_regression.py: Measurement equations: continuous indicators ============================================ It is actually a simple linear regression. :author: Michel Bierlaire, EPFL :date: Thu Apr 13 16:42:02 2023 .. GENERATED FROM PYTHON SOURCE LINES 11-40 .. code-block:: Python import biogeme.biogeme_logging as blog import biogeme.biogeme as bio from biogeme.models import piecewise_formula import biogeme.loglikelihood as ll from biogeme.expressions import Beta, Elem, bioMultSum from biogeme.data.optima import ( read_data, 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 b01one_latent_regression.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b01one_latent_regression.py .. GENERATED FROM PYTHON SOURCE LINES 41-42 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 42-55 .. code-block:: Python 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] formula_income = piecewise_formula(variable=ScaledIncome, thresholds=thresholds) .. GENERATED FROM PYTHON SOURCE LINES 56-57 Latent variable: structural equation. .. GENERATED FROM PYTHON SOURCE LINES 57-71 .. code-block:: Python CARLOVERS = ( coef_intercept + coef_age_65_more * age_65_more + formula_income + 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 72-73 Measurement equations. .. GENERATED FROM PYTHON SOURCE LINES 75-76 Intercepts. .. GENERATED FROM PYTHON SOURCE LINES 76-84 .. code-block:: Python 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 85-86 Coefficients. .. GENERATED FROM PYTHON SOURCE LINES 86-94 .. code-block:: Python 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 95-96 Linear models. .. GENERATED FROM PYTHON SOURCE LINES 96-104 .. code-block:: Python 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 105-106 Scale parameters. .. GENERATED FROM PYTHON SOURCE LINES 106-114 .. code-block:: Python SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, None, None, 0) SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, None, None, 0) SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, None, None, 0) SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, None, None, 0) SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, None, None, 0) SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, None, None, 0) SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 115-117 We build a dict with each contribution to the loglikelihood if (var > 0) and (var < 6). If not, 0 is returned. .. GENERATED FROM PYTHON SOURCE LINES 117-169 .. code-block:: Python F = { 'Envir01': Elem( { 0: 0, 1: ll.loglikelihoodregression(Envir01, MODEL_Envir01, SIGMA_STAR_Envir01), }, (Envir01 > 0) * (Envir01 < 6), ), 'Envir02': Elem( { 0: 0, 1: ll.loglikelihoodregression(Envir02, MODEL_Envir02, SIGMA_STAR_Envir02), }, (Envir02 > 0) * (Envir02 < 6), ), 'Envir03': Elem( { 0: 0, 1: ll.loglikelihoodregression(Envir03, MODEL_Envir03, SIGMA_STAR_Envir03), }, (Envir03 > 0) * (Envir03 < 6), ), 'Mobil11': Elem( { 0: 0, 1: ll.loglikelihoodregression(Mobil11, MODEL_Mobil11, SIGMA_STAR_Mobil11), }, (Mobil11 > 0) * (Mobil11 < 6), ), 'Mobil14': Elem( { 0: 0, 1: ll.loglikelihoodregression(Mobil14, MODEL_Mobil14, SIGMA_STAR_Mobil14), }, (Mobil14 > 0) * (Mobil14 < 6), ), 'Mobil16': Elem( { 0: 0, 1: ll.loglikelihoodregression(Mobil16, MODEL_Mobil16, SIGMA_STAR_Mobil16), }, (Mobil16 > 0) * (Mobil16 < 6), ), 'Mobil17': Elem( { 0: 0, 1: ll.loglikelihoodregression(Mobil17, MODEL_Mobil17, SIGMA_STAR_Mobil17), }, (Mobil17 > 0) * (Mobil17 < 6), ), } .. GENERATED FROM PYTHON SOURCE LINES 170-171 The log likelihood is the sum of the elements of the above dict .. GENERATED FROM PYTHON SOURCE LINES 171-173 .. code-block:: Python loglike = bioMultSum(F) .. GENERATED FROM PYTHON SOURCE LINES 174-175 Read the data .. GENERATED FROM PYTHON SOURCE LINES 175-177 .. code-block:: Python database = read_data() .. GENERATED FROM PYTHON SOURCE LINES 178-179 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 179-182 .. code-block:: Python the_biogeme = bio.BIOGEME(database, loglike) the_biogeme.modelName = 'b01one_latent_regression' .. rst-class:: sphx-glr-script-out .. code-block:: none Default values of the Biogeme parameters are used. File biogeme.toml has been created .. GENERATED FROM PYTHON SOURCE LINES 183-184 Estimate the parameters .. GENERATED FROM PYTHON SOURCE LINES 184-186 .. code-block:: Python results = the_biogeme.estimate() .. rst-class:: sphx-glr-script-out .. code-block:: none As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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 __b01one_latent_regression.iter Cannot read file __b01one_latent_regression.iter. Statement is ignored. As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 3.2e+04 0.13 10 1 ++ 1 3.2e+04 0.13 5 -7 - 2 3.2e+04 0.13 2.5 -3.9 - 3 3.2e+04 0.13 1.2 -4.8e+04 - 4 3.2e+04 0.13 0.62 -0.018 - 5 2.6e+04 0.15 0.62 0.82 + 6 2.3e+04 0.025 6.2 0.95 ++ 7 2.3e+04 0.025 3.1 -6.9e+02 - 8 2.3e+04 0.025 1.6 -80 - 9 2.3e+04 0.025 0.78 -17 - 10 2.3e+04 0.025 0.39 -1.9 - 11 2.3e+04 0.025 0.2 0.011 - 12 2.3e+04 0.075 0.2 0.61 + 13 2.2e+04 0.015 2 1 ++ 14 2.2e+04 0.015 0.98 -49 - 15 2.2e+04 0.015 0.49 -2.7 - 16 2.2e+04 0.015 0.24 0.027 - 17 2.2e+04 0.064 0.24 0.65 + 18 2.2e+04 0.014 0.24 0.73 + 19 2.2e+04 0.076 0.24 0.24 + 20 2.1e+04 0.042 0.24 0.45 + 21 2.1e+04 0.042 0.12 -0.62 - 22 2.1e+04 0.042 0.061 0.0064 - 23 2.1e+04 0.049 0.061 0.24 + 24 2.1e+04 0.0098 0.61 1 ++ 25 2.1e+04 0.0098 0.31 -4.9 - 26 2.1e+04 0.0098 0.15 -0.86 - 27 2.1e+04 0.068 0.15 0.29 + 28 2.1e+04 0.068 0.076 -0.15 - 29 2.1e+04 0.031 0.076 0.31 + 30 2.1e+04 0.031 0.038 -0.76 - 31 2.1e+04 0.037 0.038 0.26 + 32 2.1e+04 0.0068 0.38 1.1 ++ 33 2.1e+04 0.0068 0.19 -10 - 34 2.1e+04 0.0068 0.095 -3.1 - 35 2.1e+04 0.0068 0.048 -0.78 - 36 2.1e+04 0.037 0.048 0.46 + 37 2.1e+04 0.022 0.048 0.27 + 38 2.1e+04 0.022 0.024 -0.1 - 39 2.1e+04 0.023 0.024 0.46 + 40 2.1e+04 0.0049 0.24 1.2 ++ 41 2.1e+04 0.0049 0.12 -5.3 - 42 2.1e+04 0.0049 0.06 -1.3 - 43 2.1e+04 0.0049 0.03 0.046 - 44 2.1e+04 0.025 0.03 0.64 + 45 2.1e+04 0.013 0.03 0.44 + 46 2.1e+04 0.013 0.015 -0.14 - 47 2.1e+04 0.017 0.015 0.35 + 48 2.1e+04 0.0024 0.15 1.1 ++ 49 2.1e+04 0.0024 0.075 -2.4 - 50 2.1e+04 0.0024 0.037 -0.23 - 51 2.1e+04 0.029 0.037 0.49 + 52 2.1e+04 0.029 0.019 0.073 - 53 2.1e+04 0.0093 0.019 0.54 + 54 2.1e+04 0.0056 0.019 0.84 + 55 2.1e+04 0.0031 0.19 1.3 ++ 56 2.1e+04 0.0031 0.093 -0.93 - 57 2.1e+04 0.035 0.093 0.53 + 58 2.1e+04 0.035 0.047 -0.27 - 59 2.1e+04 0.028 0.047 0.15 + 60 2.1e+04 0.028 0.023 0.016 - 61 2.1e+04 0.022 0.023 0.43 + 62 2.1e+04 0.013 0.023 0.22 + 63 2.1e+04 0.016 0.023 0.49 + 64 2.1e+04 0.0065 0.023 0.69 + 65 2.1e+04 0.023 0.023 0.15 + 66 2.1e+04 0.011 0.023 0.41 + 67 2.1e+04 0.011 0.012 0.075 - 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Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. Results saved in file b01one_latent_regression.html Results saved in file b01one_latent_regression.pickle .. GENERATED FROM PYTHON SOURCE LINES 187-193 .. code-block:: Python 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.write_latex() print(f'LaTeX file: {results.data.latexFileName}') .. rst-class:: sphx-glr-script-out .. code-block:: none Estimated betas: 33 final log likelihood: -18669.552 Output file: b01one_latent_regression.html Results saved in file b01one_latent_regression.tex LaTeX file: b01one_latent_regression.tex .. GENERATED FROM PYTHON SOURCE LINES 194-195 .. code-block:: Python results.get_estimated_parameters() .. raw:: html
Value Rob. Std err Rob. t-test Rob. p-value
B_Envir02_F1 -0.671273 0.097669 -6.872966 6.288081e-12
B_Envir03_F1 0.989374 0.371295 2.664655 7.706735e-03
B_Mobil11_F1 0.835982 0.353844 2.362571 1.814866e-02
B_Mobil14_F1 1.035533 0.376805 2.748193 5.992477e-03
B_Mobil16_F1 0.800743 0.345501 2.317629 2.046947e-02
B_Mobil17_F1 0.653985 0.348497 1.876585 6.057501e-02
INTER_Envir02 1.543392 0.269465 5.727611 1.018550e-08
INTER_Envir03 5.404574 0.956086 5.652809 1.578466e-08
INTER_Mobil11 5.863455 0.910094 6.442695 1.173703e-10
INTER_Mobil14 5.784569 0.964224 5.999197 1.982951e-09
INTER_Mobil16 5.484541 0.887010 6.183182 6.282233e-10
INTER_Mobil17 5.086870 0.899083 5.657842 1.532880e-08
SIGMA_STAR_Envir01 1.256476 2.608340 0.481715 6.300087e-01
SIGMA_STAR_Envir02 1.120950 0.043925 25.519377 0.000000e+00
SIGMA_STAR_Envir03 1.068524 0.038331 27.876393 0.000000e+00
SIGMA_STAR_Mobil11 1.082617 0.050021 21.643369 0.000000e+00
SIGMA_STAR_Mobil14 1.049818 0.038435 27.313768 0.000000e+00
SIGMA_STAR_Mobil16 1.095804 0.044687 24.521819 0.000000e+00
SIGMA_STAR_Mobil17 1.109011 0.046279 23.963362 0.000000e+00
beta_ScaledIncome_10_inf 0.073692 0.027507 2.679056 7.383009e-03
beta_ScaledIncome_4_6 -0.176435 0.080479 -2.192297 2.835807e-02
beta_ScaledIncome_6_8 0.214425 0.098746 2.171480 2.989489e-02
beta_ScaledIncome_8_10 -0.448493 0.131220 -3.417877 6.311158e-04
beta_ScaledIncome_minus_inf_4 0.068610 0.045134 1.520139 1.284761e-01
coef_age_65_more 0.086783 0.085731 1.012268 3.114100e-01
coef_haveChildren -0.035896 0.051929 -0.691246 4.894107e-01
coef_haveGA -0.512347 0.175536 -2.918752 3.514358e-03
coef_highEducation -0.206542 0.041936 -4.925128 8.430509e-07
coef_individualHouse -0.074936 0.041909 -1.788075 7.376396e-02
coef_intercept -2.524363 0.128951 -19.576169 0.000000e+00
coef_male 0.053167 0.042191 1.260146 2.076166e-01
coef_moreThanOneBike -0.238825 0.056510 -4.226223 2.376462e-05
coef_moreThanOneCar 0.454595 0.082717 5.495754 3.890451e-08


.. rst-class:: sphx-glr-timing **Total running time of the script:** (2 minutes 46.429 seconds) .. _sphx_glr_download_auto_examples_latent_plot_b01one_latent_regression.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b01one_latent_regression.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b01one_latent_regression.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b01one_latent_regression.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_