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