## This file is the same as 02oneLatentOrdered.py, where ## The starting values for the sigma have been change in ## order to illustrate a common issue with the estimation of ## such models. import pandas as pd import numpy as np import biogeme.database as db import biogeme.biogeme as bio #import biogeme.models as models import biogeme.loglikelihood as ll pandas = pd.read_table("optima.dat") database = db.Database("optima",pandas) from headers import * exclude = (Choice == -1.0) database.remove(exclude) ### Variables ScaledIncome = DefineVariable('ScaledIncome',\ CalculatedIncome / 1000,database) ContIncome_0_4000 = DefineVariable('ContIncome_0_4000',\ bioMin(ScaledIncome,4),database) ContIncome_4000_6000 = DefineVariable('ContIncome_4000_6000',\ bioMax(0,bioMin(ScaledIncome-4,2)),database) ContIncome_6000_8000 = DefineVariable('ContIncome_6000_8000',\ bioMax(0,bioMin(ScaledIncome-6,2)),database) ContIncome_8000_10000 = DefineVariable('ContIncome_8000_10000',\ bioMax(0,bioMin(ScaledIncome-8,2)),database) ContIncome_10000_more = DefineVariable('ContIncome_10000_more',\ bioMax(0,ScaledIncome-10),database) age_65_more = DefineVariable('age_65_more',age >= Numeric(65),database) moreThanOneCar = DefineVariable('moreThanOneCar',NbCar > 1,database) moreThanOneBike = DefineVariable('moreThanOneBike',NbBicy > 1,database) individualHouse = DefineVariable('individualHouse',\ HouseType == 1,database) male = DefineVariable('male',Gender == 1,database) haveChildren = DefineVariable('haveChildren',\ ((FamilSitu == 3)+(FamilSitu == 4)) > 0,database) haveGA = DefineVariable('haveGA',GenAbST == 1,database) highEducation = DefineVariable('highEducation', Education >= 6,database) ### Coefficients 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_ContIncome_0_4000 = \ Beta('coef_ContIncome_0_4000',0.0,None,None,0 ) coef_ContIncome_4000_6000 = \ Beta('coef_ContIncome_4000_6000',0.0,None,None,0 ) coef_ContIncome_6000_8000 = \ Beta('coef_ContIncome_6000_8000',0.0,None,None,0 ) coef_ContIncome_8000_10000 = \ Beta('coef_ContIncome_8000_10000',0.0,None,None,0 ) coef_ContIncome_10000_more = \ Beta('coef_ContIncome_10000_more',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 ) ### Latent variable: structural equation # Note that the expression must be on a single line. In order to # write it across several lines, each line must terminate with # the \ symbol CARLOVERS = \ coef_intercept +\ coef_age_65_more * age_65_more +\ coef_ContIncome_0_4000 * ContIncome_0_4000 +\ coef_ContIncome_4000_6000 * ContIncome_4000_6000 +\ coef_ContIncome_6000_8000 * ContIncome_6000_8000 +\ coef_ContIncome_8000_10000 * ContIncome_8000_10000 +\ coef_ContIncome_10000_more * ContIncome_10000_more +\ coef_moreThanOneCar * moreThanOneCar +\ coef_moreThanOneBike * moreThanOneBike +\ coef_individualHouse * individualHouse +\ coef_male * male +\ coef_haveChildren * haveChildren +\ coef_haveGA * haveGA +\ coef_highEducation * highEducation ### Measurement equations INTER_Envir01 = Beta('INTER_Envir01',0,None,None,1) INTER_Envir02 = Beta('INTER_Envir02',0.0,None,None,0 ) INTER_Envir03 = Beta('INTER_Envir03',0.0,None,None,0 ) INTER_Mobil11 = Beta('INTER_Mobil11',0.0,None,None,0 ) INTER_Mobil14 = Beta('INTER_Mobil14',0.0,None,None,0 ) INTER_Mobil16 = Beta('INTER_Mobil16',0.0,None,None,0 ) INTER_Mobil17 = Beta('INTER_Mobil17',0.0,None,None,0 ) B_Envir01_F1 = Beta('B_Envir01_F1',-1,None,None,1) B_Envir02_F1 = Beta('B_Envir02_F1',0.0,None,None,0 ) B_Envir03_F1 = Beta('B_Envir03_F1',0.0,None,None,0 ) B_Mobil11_F1 = Beta('B_Mobil11_F1',0.0,None,None,0 ) B_Mobil14_F1 = Beta('B_Mobil14_F1',0.0,None,None,0 ) B_Mobil16_F1 = Beta('B_Mobil16_F1',0.0,None,None,0 ) B_Mobil17_F1 = Beta('B_Mobil17_F1',0.0,None,None,0 ) 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 SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01',1,None,None,1) SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02',0.01,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 ) delta_1 = Beta('delta_1',0.1,0,10,0 ) delta_2 = Beta('delta_2',0.2,0,10,0 ) tau_1 = -delta_1 - delta_2 tau_2 = -delta_1 tau_3 = delta_1 tau_4 = delta_1 + delta_2 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) biogeme = bio.BIOGEME(database,loglike) biogeme.modelName = "07problem" results = biogeme.estimate() 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}")