Binary logit model

Example of a binary logit model. Two alternatives: Train and Car.

author:

Michel Bierlaire, EPFL

date:

Wed Apr 12 17:58:18 2023

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

See the data processing script: Data preparation for Swissmetro (binary choice).

from swissmetro_binary import (
    database,
    CHOICE,
    TRAIN_AV_SP,
    CAR_AV_SP,
    TRAIN_TT_SCALED,
    TRAIN_COST_SCALED,
    CAR_TT_SCALED,
    CAR_CO_SCALED,
)

Parameters to be estimated.

ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
B_TIME_CAR = Beta('B_TIME_CAR', 0, None, None, 0)
B_TIME_TRAIN = Beta('B_TIME_TRAIN', 0, None, None, 0)
B_COST_CAR = Beta('B_COST_CAR', 0, None, None, 0)
B_COST_TRAIN = Beta('B_COST_TRAIN', 0, None, None, 0)

Definition of the utility functions. We estimate a binary logit model. There are only two alternatives.

V1 = B_TIME_TRAIN * TRAIN_TT_SCALED + B_COST_TRAIN * TRAIN_COST_SCALED
V3 = ASC_CAR + B_TIME_CAR * CAR_TT_SCALED + B_COST_CAR * CAR_CO_SCALED

Associate utility functions with the numbering of alternatives.

V = {1: V1, 3: V3}

Associate the availability conditions with the alternatives.

av = {1: TRAIN_AV_SP, 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 = 'b23logit'

Estimate the parameters

results = the_biogeme.estimate()

print(results.short_summary())

Results for model b23logit
Nbr of parameters:              5
Sample size:                    2678
Excluded data:                  8050
Final log likelihood:           -872.9052
Akaike Information Criterion:   1755.81
Bayesian Information Criterion: 1785.274

pandas_results = results.getEstimatedParameters()
pandas_results

	Value	Rob. Std err	Rob. t-test	Rob. p-value
ASC_CAR	-0.896101	0.178268	-5.026696	4.990013e-07
B_COST_CAR	-1.088054	0.295942	-3.676576	2.363851e-04
B_COST_TRAIN	-2.393364	0.272021	-8.798468	0.000000e+00
B_TIME_CAR	-0.383847	0.310672	-1.235537	2.166306e-01
B_TIME_TRAIN	-1.134867	0.210637	-5.387777	7.133434e-08