Base model

Logit model.

Michel Bierlaire, EPFL Fri Jul 25 2025, 16:51:33

from IPython.core.display_functions import display

from biogeme.biogeme import BIOGEME
from biogeme.data.swissmetro import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    read_data,
)
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import get_pandas_estimated_parameters

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.

v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED

Associate utility functions with the numbering of alternatives.

v = {1: v_train, 2: v_swissmetro, 3: v_car}

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.

log_probability = loglogit(v, av, CHOICE)

Read the data

database = read_data()

Create the Biogeme object.

the_biogeme = BIOGEME(
    database, log_probability, generate_html=False, generate_yaml=False
)
the_biogeme.model_name = 'b00logit'

Calculate the null log likelihood for reporting.

the_biogeme.calculate_null_loglikelihood(av)

-11093.627345287434

Estimate the parameters

results = the_biogeme.estimate()

print(results.short_summary())

Results for model b00logit
Nbr of parameters:              4
Sample size:                    10719
Excluded data:                  9
Null log likelihood:            -11093.63
Final log likelihood:           -8670.163
Likelihood ratio test (null):           4846.928
Rho square (null):                      0.218
Rho bar square (null):                  0.218
Akaike Information Criterion:   17348.33
Bayesian Information Criterion: 17377.45

Get the results in a pandas table

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

        Name     Value  Robust std err.  Robust t-stat.  Robust p-value
0  asc_train -0.652239         0.054394      -11.991022        0.000000
1     b_time -1.278941         0.065598      -19.496759        0.000000
2     b_cost -0.789790         0.050965      -15.496743        0.000000
3    asc_car  0.016228         0.037088        0.437556        0.661708