Calculation of individual level parameters

Calculation of the individual level parameters for the model defined in Mixture of logit models.

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

from IPython.core.display_functions import display
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, Draws, MonteCarlo
from biogeme.models import logit
from biogeme.results_processing import EstimationResults
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,
)

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/b05normal_mixture.yaml'
the_estimation_results = EstimationResults.from_yaml_file(filename=result_file_name)

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     -1.707874     0.636167     2.0                    -2.684631
1     -1.773128     0.664323     2.0                    -2.669074
2     -1.683020     0.612995     2.0                    -2.745569
3     -1.100413     0.439222     2.0                    -2.505368
4     -1.669049     0.635251     2.0                    -2.627386
...         ...          ...     ...                          ...
6763  -0.219694     0.159857     1.0                    -1.374321
6764  -0.201488     0.160500     1.0                    -1.255380
6765  -0.172924     0.144651     1.0                    -1.195458
6766  -0.115916     0.135797     1.0                    -0.853596
6767  -0.228873     0.171126     1.0                    -1.337450

[6768 rows x 4 columns]