Base model

Logit model.

author:

Michel Bierlaire, EPFL

date:

Thu Jul 13 16:18:10 2023

import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta

See 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)
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 = 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 = 'b00logit'
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False

File biogeme.toml has been created

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 b00logit
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()
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