Binary logit model

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

Michel Bierlaire, EPFL Sat Jun 28 2025, 12:42:27

from IPython.core.display_functions import display
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import get_pandas_estimated_parameters

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

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

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.

v_train = b_time_train * TRAIN_TT_SCALED + b_cost_train * TRAIN_COST_SCALED
v_car = asc_car + b_time_car * CAR_TT_SCALED + b_cost_car * CAR_CO_SCALED

Associate utility functions with the numbering of alternatives.

v = {1: v_train, 3: v_car}

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.

log_probability = loglogit(v, av, CHOICE)

Create the Biogeme object

the_biogeme = BIOGEME(database, log_probability)
the_biogeme.model_name = 'b23logit'

Estimate the parameters

results = the_biogeme.estimate()

print(results.short_summary())

Results for model b23logit
Nbr of parameters:              5
Sample size:                    2232
Excluded data:                  8496
Final log likelihood:           -872.9052
Akaike Information Criterion:   1755.81
Bayesian Information Criterion: 1784.364

pandas_results = get_pandas_estimated_parameters(estimation_results=results)
display(pandas_results)

           Name     Value  Robust std err.  Robust t-stat.  Robust p-value
0  b_time_train -1.134867         0.210637       -5.387777    7.133434e-08
1  b_cost_train -2.393364         0.272021       -8.798468    0.000000e+00
2       asc_car -0.896101         0.178268       -5.026696    4.990013e-07
3    b_time_car -0.383847         0.310672       -1.235537    2.166306e-01
4    b_cost_car -1.088054         0.295942       -3.676576    2.363851e-04