1c. Illustration of the quick_estimate method in Biogeme

This example estimates the same logit model as in Example 1a, but uses quick_estimate, a lightweight estimation procedure designed for cases where only the estimated parameter values are required.

Unlike the standard estimation procedure, quick_estimate skips the calculation of second-order derivatives and several post-estimation statistics. As a result, the estimation is faster, but some indicators normally reported by Biogeme are not available.

The script illustrates:

• the specification of a logit model,

• the use of quick_estimate,

• the inspection of the estimation results,

• the extraction of the estimated parameters into a pandas DataFrame,

• the manual generation of a YAML output file.

The # %% markers are used to separate the script into notebook cells when the example gallery is converted into Jupyter notebooks.

Tested with Biogeme 3.3.3.

Michel Bierlaire, EPFL Tue Jun 09 2026, 14:45:00

from IPython.core.display_functions import display

Import the variables and the database prepared in the Swissmetro data-processing example.

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,
)

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import get_pandas_estimated_parameters

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

Example b01logit_ter.py

Define the model 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)

Define 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 each utility function with the corresponding alternative identifier.

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

Associate the availability conditions with each alternative.

av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

Define the log-likelihood contribution of each observation.

logprob = loglogit(v, av, CHOICE)

Create the Biogeme object.

the_biogeme = BIOGEME(database, logprob)
the_biogeme.model_name = 'b01c_logit'

Biogeme parameters read from biogeme.toml.

Calculate the null log likelihood used in the estimation report.

the_biogeme.calculate_null_loglikelihood(av)

-6964.662979192191

Estimate the parameters using the quick estimation procedure.

results = the_biogeme.quick_estimate()

*** Initial values of the parameters are obtained from the file __b01c_logit.iter
Cannot read file __b01c_logit.iter. Statement is ignored.
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
Iter.       asc_train          b_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.92           -0.67           -0.88           -0.49      5.4e+03      0.041       10      1.1   ++
    1           -0.73            -1.2              -1           -0.18      5.3e+03     0.0072    1e+02      1.1   ++
    2            -0.7            -1.3            -1.1           -0.16      5.3e+03    0.00018    1e+03        1   ++
    3            -0.7            -1.3            -1.1           -0.16      5.3e+03    1.1e-07    1e+03        1   ++

Display a short summary of the estimation results.

print(results.short_summary())

Results for model b01c_logit
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

The quick estimation procedure does not calculate the initial log likelihood, second derivatives, or several post-estimation statistics. It is useful when only the estimated parameter values are required.

Convert the estimated parameters into a pandas DataFrame.

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

{'Estimated parameters':         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}

Display the available general estimation 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 generated automatically when quick_estimate is used. Generate it manually if needed.

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

File b01c_logit.yaml has been generated.