23b. Binary probit model

Bayesian estimation of a binary probit model. Two alternatives: Train and Car. All observations such that the Swissmetro was chosen haven been removed from the sample.

Michel Bierlaire, EPFL Sat Jun 28 2025, 12:43:40

from pathlib import Path

from IPython.core.display_functions import display

See the data processing script swissmetro_binary.py.

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

from biogeme.bayesian_estimation import (
    BayesianResults,
    BayesianResultsSummary,
    get_pandas_estimated_parameters,
)
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, Elem, NormalCdf, log

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 probit 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 choice probability with the numbering of alternatives.

log_probability_dict = {
    1: log(NormalCdf(v_train - v_car)),
    3: log(NormalCdf(v_car - v_train)),
}

Definition of the model. This is the contribution of each observation to the log likelihood function.

log_probability = Elem(log_probability_dict, CHOICE)

Create the Biogeme object

the_biogeme = BIOGEME(database, log_probability)
the_biogeme.model_name = 'b23b_binary_probit'

Estimate the posterior distribution of the parameters, or read the results if already available.

yaml_file = Path('saved_results') / f'{the_biogeme.model_name}.yaml'
try:
    summary_results = BayesianResultsSummary.from_yaml_file(filename=yaml_file)
except FileNotFoundError:
    results: BayesianResults = the_biogeme.bayesian_estimation()
    summary_results = results.to_summary()

print(summary_results.short_summary())

Present the parameter estimates in a pandas table.

pandas_results = get_pandas_estimated_parameters(
    estimation_results=summary_results,
)
display(pandas_results)

Report the variables stored in the Bayesian estimation results.

display(summary_results.report_stored_variables())