Illustration the quick_estimate of Biogeme

Same model as b01logit, estimated using the quick_estimate, that skips the calculation of the second orders statistics.

Michel Bierlaire, EPFL Wed Jun 18 2025, 11:19:12

import biogeme.biogeme_logging as blog
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.

from swissmetro_data 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,
    database,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b01logit_ter.py')

Example b01logit_ter.py

Parameters to be estimated.

asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)
asc_sm = Beta('asc_sm', 0, None, None, 1)
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 = asc_sm + 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.

logprob = loglogit(v, av, CHOICE)

Create the Biogeme object.

the_biogeme = BIOGEME(database, logprob)
the_biogeme.model_name = 'b01logit_ter'

Biogeme parameters read from biogeme.toml.

Calculate the null log likelihood for reporting.

the_biogeme.calculate_null_loglikelihood(av)

-6964.662979192191

Estimate the parameters.

results = the_biogeme.quick_estimate()

*** Initial values of the parameters are obtained from the file __b01logit_ter.iter
Parameter values restored from __b01logit_ter.iter
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds

print(results.short_summary())

Results for model b01logit_ter
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

Where quick_estimate is called, the initial log likelihood is not calculated. The derivatives of the loglikelihood function are not calculated either. It means that several statistics are missing in the report. This function is convenient when only the estimated values of the parameters are needed.

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 -0.701187              NaN             NaN             NaN
1     b_time -1.277859              NaN             NaN             NaN
2     b_cost -1.083790              NaN             NaN             NaN
3    asc_car -0.154633              NaN             NaN             NaN

Get general statistics.

print('General statistics')
print('------------------')
stats = results.get_general_statistics()
for description, value in stats.items():
    print(f'{description}: {value}')

General statistics
------------------
Number of estimated parameters: 4
Sample size: 6768
Excluded observations: 3960
Null log likelihood: -6964.663
Final log likelihood: -5331.252
Likelihood ratio test for the null model: 3266.822
Rho-square for the null model: 0.235
Rho-square-bar for the null model: 0.234
Likelihood ratio test for the init. model:
Rho-square for the init. model:
Rho-square-bar for the init. model:
Akaike Information Criterion: 10670.5
Bayesian Information Criterion: 10697.78
Final gradient norm:
Bootstrapping time: None

The YAML file is not automatically generated when quick_estimate is used. It can be done manually if needed.

results.dump_yaml_file(filename=f'{the_biogeme.model_name}.yaml')

File b01logit_ter.yaml has been generated.