In [ ]:
#%%
"""File 07problem.py

 This file is the same as 02oneLatentOrdered.py, where The starting
 values for the sigma have been changed in order to illustrate a common
 issue with the estimation of such models.

 We set the starting value of a scale parameter (SIGMA_STAR_Envir02)
 to a small value: 0.01. The resulting likelihood is so close to zero
 that taking the log generates a numerical issue.

 Make sure to set large initial values for scale parameters.

:author: Michel Bierlaire, EPFL
:date: Wed Sep 11 15:40:43 2019

"""

import pandas as pd
import biogeme.database as db
import biogeme.biogeme as bio
import biogeme.models as models
import biogeme.messaging as msg
from biogeme.expressions import Beta, DefineVariable, log, Elem, bioNormalCdf

# Read the data
df = pd.read_csv('optima.dat', sep='\t')
database = db.Database('optima', df)

# The following statement allows you to use the names of the variable
# as Python variable.
globals().update(database.variables)

# Exclude observations such that the chosen alternative is -1
database.remove(Choice == -1.0)

# Piecewise linear definition of income
ScaledIncome = DefineVariable('ScaledIncome', CalculatedIncome / 1000, database)

thresholds = [None, 4, 6, 8, 10, None]
formulaIncome = models.piecewiseFormula(ScaledIncome,
                                        thresholds,
                                        [0.0, 0.0, 0.0, 0.0, 0.0])

# Definition of other variables
age_65_more = DefineVariable('age_65_more', age >= 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)

# Parameters to be estimated
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_age_unknown = Beta('coef_age_unknown', 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)

### 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 +\
            formulaIncome + \
            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, 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)

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)

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', 100, 1.0e-5, None, 0)
SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 0.01, 1.0e-5, None, 0)
SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 100, 1.0e-5, None, 0)
SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 100, 1.0e-5, None, 0)
SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 100, 1.0e-5, None, 0)
SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 100, 1.0e-5, None, 0)
SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 100, 1.0e-5, None, 0)


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

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)

# Define level of verbosity
logger = msg.bioMessage()
#logger.setSilent()
#logger.setWarning()
logger.setGeneral()
#logger.setDetailed()


# Create the Biogeme object
biogeme = bio.BIOGEME(database, loglike, numberOfDraws=20000)
biogeme.modelName = '07problem'

# Estimate the parameters
results = biogeme.estimate(saveIterations=True)

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}')