Estimation of the hybrid choice model

Full information estimation of the model combining observed choice and Likert scale psychometric indicators.

Michel Bierlaire, EPFL Wed Sept 03 2025, 08:19:40

from choice_model import v
from IPython.core.display_functions import display
from measurement_equations_likert import generate_likert_measurement_equations
from optima import (
    Choice,
    read_data,
)
from read_or_estimate import read_or_estimate
from structural_equations import (
    LatentVariable,
    build_car_centric_attitude,
    build_urban_preference_attitude,
)

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Expression, MonteCarlo, log
from biogeme.models import logit
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

NUMBER_OF_DRAWS = 10_000

logger = blog.get_screen_logger(level=blog.INFO)

database = read_data()

Structural equation: car centric attitude

car_centric_attitude: LatentVariable = build_car_centric_attitude()

Structural equation: urban preference

urban_preference_attitude: LatentVariable = build_urban_preference_attitude()

Generate the measurement equations for the indicators

measurement_equations: Expression = generate_likert_measurement_equations(
    car_centric_attitude, urban_preference_attitude
)

Conditional likelihood for the choice model

choice_likelihood = logit(v, None, Choice)

conditional_likelihood = choice_likelihood * measurement_equations

Log likelihood

log_likelihood = log(MonteCarlo(conditional_likelihood))

Create the Biogeme object

print('Create the biogeme object')
the_biogeme = BIOGEME(
    database,
    log_likelihood,
    number_of_draws=NUMBER_OF_DRAWS,
    calculating_second_derivatives='never',
    numerically_safe=True,
    max_iterations=5000,
)
the_biogeme.model_name = 'b03_hybrid'

Create the biogeme object
Biogeme parameters read from biogeme.toml.

If estimation results are saved on file, we read them to speed up the process. If not, we estimate the parameters.

results: EstimationResults = read_or_estimate(
    the_biogeme=the_biogeme, directory='saved_results'
)

Results are read from the file saved_results/b03_hybrid.yaml.

print(f'Estimated betas: {results.number_of_parameters}')
print(f'final log likelihood: {results.final_log_likelihood:.3f}')
print(f'Output file: {the_biogeme.html_filename}')

Estimated betas: 84
final log likelihood: -17367.158
Output file: None

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

                                       Name  ...  BHHH p-value
0         log_scale_choice_model_short_dist  ...  0.000000e+00
1          log_scale_choice_model_long_dist  ...  0.000000e+00
2                  choice_asc_pt_short_dist  ...  5.652436e-04
3                   choice_asc_pt_long_dist  ...  2.272115e-01
4            choice_beta_time_pt_short_dist  ...  1.588512e-04
..                                      ...  ...           ...
79  meas_car_centric_attitude_coeff_Mobil08  ...  9.490186e-13
80                       meas_scale_Mobil08  ...  0.000000e+00
81                   meas_intercept_Mobil07  ...  0.000000e+00
82  meas_car_centric_attitude_coeff_Mobil07  ...  5.021534e-06
83                       meas_scale_Mobil07  ...  0.000000e+00

[84 rows x 5 columns]