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Estimation of a logit model
Three alternatives:
train,
car and,
Swissmetro.
Stated preferences data.
- author:
Michel Bierlaire, EPFL
- date:
Sun Apr 9 17:02:18 2023
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta
See the data processing script: Data preparation for Swissmetro.
from swissmetro_data import (
database,
CHOICE,
SM_AV,
CAR_AV_SP,
TRAIN_AV_SP,
TRAIN_TT_SCALED,
TRAIN_COST_SCALED,
SM_TT_SCALED,
SM_COST_SCALED,
CAR_TT_SCALED,
CAR_CO_SCALED,
)
Parameters to be estimated.
ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
ASC_SM = Beta('ASC_SM', 0, None, None, 1)
B_TIME = Beta('B_TIME', 0, None, None, 0)
B_COST = Beta('B_COST', 0, None, None, 0)
Definition of the utility functions.
V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED
Associate utility functions with the numbering of alternatives.
V = {1: V1, 2: V2, 3: V3}
Associate the availability conditions with the alternatives.
av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}
Definition of the model. This is the contribution of each observation to the log likelihood function.
logprob = models.loglogit(V, av, CHOICE)
Create the Biogeme object.
the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b01logit'
Calculate the null log likelihood for reporting.
the_biogeme.calculateNullLoglikelihood(av)
-6964.662979191462
Estimate the parameters.
results = the_biogeme.estimate()
print(results.short_summary())
Results for model b01logit
Nbr of parameters: 4
Sample size: 6768
Excluded data: 3960
Null log likelihood: -6964.663
Final log likelihood: -5331.252
Likelihood ratio test (null): 3266.822
Rho square (null): 0.235
Rho bar square (null): 0.234
Akaike Information Criterion: 10670.5
Bayesian Information Criterion: 10697.78
Get the results in a pandas table
pandas_results = results.getEstimatedParameters()
print(pandas_results)
Value Rob. Std err Rob. t-test Rob. p-value
ASC_CAR -0.154633 0.058163 -2.658590 0.007847
ASC_TRAIN -0.701187 0.082562 -8.492857 0.000000
B_COST -1.083790 0.068225 -15.885521 0.000000
B_TIME -1.277859 0.104254 -12.257120 0.000000
Total running time of the script: (0 minutes 0.660 seconds)