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
}
MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS
SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, 0, None, 0)
SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, 0, None, 0)
SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, 0, None, 0)
SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, 0, None, 0)
SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, 0, None, 0)
SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, 0, None, 0)
SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, 0, None, 0)
# We build a dict with each contribution to the loglikelihood if
# (var > 0) and (var < 6). If not, 0 is returned.
F = {}
F['Envir01'] = Elem({0: 0,
1: ll.loglikelihoodregression(Envir01,
MODEL_Envir01,
SIGMA_STAR_Envir01)},
(Envir01 > 0)*(Envir01 < 6))
F['Envir02'] = Elem({0: 0,
1: ll.loglikelihoodregression(Envir02,
MODEL_Envir02,
SIGMA_STAR_Envir02)},
(Envir02 > 0)*(Envir02 < 6))
F['Envir03'] = Elem({0: 0,
1: ll.loglikelihoodregression(Envir03,
MODEL_Envir03,
SIGMA_STAR_Envir03)},
(Envir03 > 0)*(Envir03 < 6))
F['Mobil11'] = Elem({0: 0,
1: ll.loglikelihoodregression(Mobil11,
MODEL_Mobil11,
U = B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
# Associate each discrete indicator with an interval.
# 1: -infinity -> tau1
# 2: tau1 -> tau2
# 3: tau2 -> +infinity
ChoiceProba = {
1: 1 - dist.logisticcdf(U - tau1),
2: dist.logisticcdf(U - tau1) - dist.logisticcdf(U - tau2),
3: dist.logisticcdf(U - tau2)
}
# Definition of the model. This is the contribution of each
# observation to the log likelihood function.
logprob = log(Elem(ChoiceProba, CHOICE))
# Define level of verbosity
logger = msg.bioMessage()
logger.setSilent()
#logger.setWarning()
#logger.setGeneral()
#logger.setDetailed()
# Create the Biogeme object
biogeme = bio.BIOGEME(database, logprob)
biogeme.modelName = '18ordinalLogit'
# Estimate the parameters
results = biogeme.estimate()
pandasResults = results.getEstimatedParameters()
TRAIN_COST_SCALED = DefineVariable('TRAIN_COST_SCALED',\
TRAIN_COST / 100,database)
SM_TT_SCALED = DefineVariable('SM_TT_SCALED', SM_TT / 100.0, database)
SM_COST_SCALED = DefineVariable('SM_COST_SCALED', SM_COST / 100, database)
CAR_TT_SCALED = DefineVariable('CAR_TT_SCALED', CAR_TT / 100, database)
CAR_CO_SCALED = DefineVariable('CAR_CO_SCALED', CAR_CO / 100, database)
# We estimate a binary probit model. There are only two alternatives.
V1 = B_TIME * TRAIN_TT_SCALED + \
B_COST * TRAIN_COST_SCALED
V3 = ASC_CAR + \
B_TIME * CAR_TT_SCALED + \
B_COST * CAR_CO_SCALED
# Associate choice probability with the numbering of alternatives
P = {1: bioNormalCdf(V1 - V3), 3: bioNormalCdf(V3 - V1)}
prob = Elem(P, CHOICE)
class test_02(unittest.TestCase):
def testEstimation(self):
biogeme = bio.BIOGEME(database, log(prob))
results = biogeme.estimate()
self.assertAlmostEqual(results.data.logLike, -986.1888, 2)
if __name__ == '__main__':
unittest.main()
CAR_CO_SCALED = DefineVariable('CAR_CO_SCALED', CAR_CO / 100, database)
# Definition of the utility functions
# We estimate a binary probit model. There are only two alternatives.
V1 = B_TIME * TRAIN_TT_SCALED + \
B_COST * TRAIN_COST_SCALED
V3 = ASC_CAR + \
B_TIME * CAR_TT_SCALED + \
B_COST * CAR_CO_SCALED
# Associate choice probability with the numbering of alternatives
P = {1: bioNormalCdf(V1 - V3), 3: bioNormalCdf(V3 - V1)}
# Definition of the model. This is the contribution of each
# observation to the log likelihood function.
logprob = log(Elem(P, CHOICE))
# Define level of verbosity
logger = msg.bioMessage()
logger.setSilent()
#logger.setWarning()
#logger.setGeneral()
#logger.setDetailed()
# Create the Biogeme object
biogeme = bio.BIOGEME(database, logprob)
biogeme.modelName = '21probit'
# Estimate the parameters
results = biogeme.estimate()
pandasResults = results.getEstimatedParameters()
# Associate utility functions with the numbering of alternatives
V = {1: V1,
2: V2,
3: V3}
# Associate the availability conditions with the alternatives
CAR_AV_SP = DefineVariable('CAR_AV_SP',CAR_AV * ( SP != 0 ),database)
TRAIN_AV_SP = DefineVariable('TRAIN_AV_SP',TRAIN_AV * ( SP != 0 ),database)
av = {1: TRAIN_AV_SP,
2: SM_AV,
3: CAR_AV_SP}
# The choice model is a logit, with availability conditions
prob1 = Elem({0:0,1:models.logit(V,av,1)},av[1])
# Elasticities can be computed. We illustrate below two
# formulas. Check in the output file that they produce the same
# result.
# First, the general definition of elasticities. This illustrates the
# use of the Derive expression, and can be used with any model,
# however complicated it is. Note the quotes in the Derive opertor.
genelas1 = Derive(prob1,'TRAIN_TT') * TRAIN_TT / prob1
# Second, the elasticity of logit models. See Ben-Akiva and Lerman for
# the formula
logitelas1 = TRAIN_AV_SP * (1.0 - prob1) * TRAIN_TT_SCALED * B_TIME