Mixture of logit with panel data

Example of a mixture of logit models, using Monte-Carlo integration.

The datafile is organized as panel data.

Michel Bierlaire, EPFL Sat Jun 21 2025, 16:54:51

import numpy as np
from IPython.core.display_functions import display

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

See the data processing script: Panel data preparation for Swissmetro.

from swissmetro_panel 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.results_processing import get_pandas_estimated_parameters

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b12panel.py')

Example b12panel.py

We set the seed so that the results are reproducible. This is not necessary in general.

np.random.seed(seed=90267)

Parameters to be estimated.

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

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

b_time = Beta('b_time', 0, None, None, 0)

It is advised not to use 0 as starting value for the following parameter.

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

We do the same for the constants, to address serial correlation.

asc_car = Beta('asc_car', 0, None, None, 0)
asc_car_s = Beta('asc_car_s', 1, None, None, 0)
asc_car_rnd = asc_car + asc_car_s * Draws('asc_car_rnd', 'NORMAL_ANTI')

asc_train = Beta('asc_train', 0, None, None, 0)
asc_train_s = Beta('asc_train_s', 1, None, None, 0)
asc_train_rnd = asc_train + asc_train_s * Draws('asc_train_rnd', 'NORMAL_ANTI')

asc_sm = Beta('asc_sm', 0, None, None, 0)
asc_sm_s = Beta('asc_sm_s', 1, None, None, 0)
asc_sm_rnd = asc_sm + asc_sm_s * Draws('asc_sm_rnd', 'NORMAL_ANTI')

Definition of the utility functions.

v_train = asc_train_rnd + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = asc_sm_rnd + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car_rnd + 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 the random parameters, the likelihood of one observation is given by the logit model (called the kernel).

choice_probability_one_observation = logit(v, av, CHOICE)

Conditional on the random parameters, the likelihood of all observations for one individual (the trajectory) is the product of the likelihood of each observation.

conditional_trajectory_probability = PanelLikelihoodTrajectory(
    choice_probability_one_observation
)

We integrate over the random parameters using Monte-Carlo

log_probability = log(MonteCarlo(conditional_trajectory_probability))

As the objective is to illustrate the syntax, we calculate the Monte-Carlo approximation with a small number of draws.

the_biogeme = BIOGEME(database, log_probability, number_of_draws=10000, seed=1223)
the_biogeme.model_name = 'b12panel'

Biogeme parameters read from biogeme.toml.
Flattening database [(6768, 38)].
Database flattened [(752, 362)]
Flattening database [(6768, 38)].
Database flattened [(752, 362)]
Flattening database [(6768, 38)].
Database flattened [(752, 362)]
Flattening database [(6768, 38)].
Database flattened [(752, 362)]

Estimate the parameters.

try:
    results = EstimationResults.from_yaml_file(filename='saved_results/b12panel.yaml')
except FileNotFoundError:
    results = the_biogeme.estimate()

print(results.short_summary())

Results for model b12panel
Nbr of parameters:              9
Sample size:                    752
Observations:                   6768
Excluded data:                  0
Final log likelihood:           -3578.671
Akaike Information Criterion:   7175.341
Bayesian Information Criterion: 7216.946

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  0.147614         0.147900        0.998068    3.182462e-01
1  asc_train_s  2.715929         0.259500       10.466003    0.000000e+00
2       b_time -6.016472         0.361328      -16.651000    0.000000e+00
3     b_time_s  3.510503         0.214154       16.392422    0.000000e+00
4       b_cost -3.606924         0.427857       -8.430201    0.000000e+00
5       asc_sm  0.594940         0.123182        4.829764    1.366947e-06
6     asc_sm_s -0.286424         0.283529       -1.010212    3.123938e-01
7      asc_car  0.935106         0.153905        6.075846    1.233354e-09
8    asc_car_s  4.057350         0.342115       11.859596    0.000000e+00