19. Calculation of individual level parameters

Calculation of the individual level parameters for the model defined in 5a. Mixture of logit models with Monte-Carlo integration.

Michel Bierlaire, EPFL Thu Jun 26 2025, 15:55:41

import sys

from IPython.core.display_functions import display
from pandas.core.interchange.dataframe_protocol import DataFrame

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,
)

from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, Draws, MonteCarlo
from biogeme.models import logit
from biogeme.results_processing import EstimationResults

Parameters. The initial value is irrelevant.

asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)
b_cost = Beta('b_cost', 0, None, None, 0)

Define a random parameter, normally distributed, designed to be used for Monte-Carlo simulation.

b_time = Beta('b_time', 0, None, None, 0)
b_time_s = Beta('b_time_s', 1, None, None, 0)
b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'NORMAL')

Retrieve estimation results

result_file_name = 'saved_results/b05a_normal_mixture.yaml'
try:
    the_estimation_results = EstimationResults.from_yaml_file(filename=result_file_name)
except FileNotFoundError:
    print(f'File {result_file_name} is not available.')
    sys.exit()

Definition of the utility functions.

v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time_rnd * 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}

Conditional on b_time_rnd, we have a logit model (called the kernel).

prob_chosen = logit(v, av, CHOICE)

Numerator and denominator of the formula for individual parameters.

numerator = MonteCarlo(b_time_rnd * prob_chosen)
denominator = MonteCarlo(prob_chosen)

simulate = {
    'Numerator': numerator,
    'Denominator': denominator,
    'Choice': CHOICE,
}

biosim = BIOGEME(database, simulate, number_of_draws=10_000)
sim: DataFrame = biosim.simulate(the_estimation_results.get_beta_values())
sim['Individual-level parameters'] = sim['Numerator'] / sim['Denominator']

display(sim)

      Numerator  Denominator  Choice  Individual-level parameters
0     -1.705448     0.635634     2.0                    -2.683065
1     -1.768477     0.664534     2.0                    -2.661227
2     -1.676652     0.612113     2.0                    -2.739120
3     -1.108634     0.439598     2.0                    -2.521925
4     -1.675129     0.636846     2.0                    -2.630352
...         ...          ...     ...                          ...
6763  -0.216145     0.160185     1.0                    -1.349349
6764  -0.201003     0.159907     1.0                    -1.257000
6765  -0.172317     0.143357     1.0                    -1.202009
6766  -0.113092     0.135417     1.0                    -0.835139
6767  -0.227678     0.171373     1.0                    -1.328556

[6768 rows x 4 columns]