Catalog for segmented parameters

Investigate the segmentations of parameters.

We consider 4 specifications for the constants:

• Not segmented

• Segmented by GA (yearly subscription to public transport)

• Segmented by luggage

• Segmented both by GA and luggage

We consider 3 specifications for the time coefficients:

• Not Segmented

• Segmented with first class

• Segmented with trip purpose

We obtain a total of 12 specifications. See Bierlaire and Ortelli (2023).

Michel Bierlaire, EPFL Sun Apr 27 2025, 15:52:48

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

from biogeme.biogeme import BIOGEME
from biogeme.catalog import segmentation_catalogs
from biogeme.data.swissmetro 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,
    read_data,
)
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import compile_estimation_results, pareto_optimal

Read the data

database = read_data()

Definition of the segmentations.

segmentation_ga = database.generate_segmentation(
    variable='GA', mapping={0: 'noGA', 1: 'GA'}
)

segmentation_luggage = database.generate_segmentation(
    variable='LUGGAGE', mapping={0: 'no_lugg', 1: 'one_lugg', 3: 'several_lugg'}
)

segmentation_first = database.generate_segmentation(
    variable='FIRST', mapping={0: '2nd_class', 1: '1st_class'}
)

We consider two trip purposes: ‘commuters’ and anything else. We need to define a binary variable first.

database.dataframe['COMMUTERS'] = np.where(database.dataframe['PURPOSE'] == 1, 1, 0)

segmentation_purpose = database.generate_segmentation(
    variable='COMMUTERS', mapping={0: 'non_commuters', 1: 'commuters'}
)

Parameters to be estimated.

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

Catalogs for the alternative specific constants.

asc_train_catalog, asc_car_catalog = segmentation_catalogs(
    generic_name='asc',
    beta_parameters=[asc_train, asc_car],
    potential_segmentations=(
        segmentation_ga,
        segmentation_luggage,
    ),
    maximum_number=2,
)

Catalog for the travel time coefficient. Note that the function returns a list of catalogs. Here, the list contains only one of them. This is why there is a comma after “B_TIME_catalog”.

(b_time_catalog,) = segmentation_catalogs(
    generic_name='b_time',
    beta_parameters=[b_time],
    potential_segmentations=(
        segmentation_first,
        segmentation_purpose,
    ),
    maximum_number=1,
)

Definition of the utility functions.

v_train = (
    asc_train_catalog + b_time_catalog * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
)
v_swissmetro = b_time_catalog * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car_catalog + b_time_catalog * 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}

Definition of the model. This is the contribution of each observation to the log likelihood function.

log_probability = loglogit(v, av, CHOICE)

Create the Biogeme object.

the_biogeme = BIOGEME(
    database, log_probability, generate_html=False, generate_yaml=False
)
the_biogeme.model_name = 'b04segmentation'

Estimate the parameters

dict_of_results = the_biogeme.estimate_catalog()

Number of estimated models.

print(f'A total of {len(dict_of_results)} models have been estimated')

A total of 12 models have been estimated

All estimation results

compiled_results, specs = compile_estimation_results(
    dict_of_results, use_short_names=True
)

display('All estimated models')
display(compiled_results)

All estimated models
                                         Model_000000  ...      Model_000011
Number of estimated parameters                      9  ...                 8
Sample size                                     10719  ...             10719
Final log likelihood                         -8500.62  ...         -8562.781
Akaike Information Criterion                 17019.24  ...          17141.56
Bayesian Information Criterion               17084.76  ...           17199.8
asc_train_ref (t-test)                 -1.39  (-16.6)  ...    -1.37  (-16.5)
asc_train_diff_one_lugg (t-test)        0.901  (11.9)  ...     0.955  (12.6)
asc_train_diff_several_lugg (t-test)    0.858  (4.96)  ...     0.949  (5.42)
b_time_ref (t-test)                   -0.915  (-10.7)  ...
b_time_diff_1st_class (t-test)        -0.645  (-8.89)  ...
b_cost (t-test)                       -0.856  (-15.5)  ...   -0.783  (-15.5)
asc_car_ref (t-test)                    0.0539  (1.1)  ...     0.0443  (0.9)
asc_car_diff_one_lugg (t-test)        -0.104  (-2.05)  ...  -0.0791  (-1.56)
asc_car_diff_several_lugg (t-test)    -0.616  (-2.96)  ...   -0.534  (-2.56)
b_time_diff_commuters (t-test)                         ...
asc_train (t-test)                                     ...
asc_car (t-test)                                       ...
asc_train_diff_GA (t-test)                             ...
b_time (t-test)                                        ...    -1.26  (-19.1)
asc_car_diff_GA (t-test)                               ...

[20 rows x 12 columns]

Glossary

for short_name, spec in specs.items():
    print(f'{short_name}\t{spec}')

Model_000000    asc:LUGGAGE;b_time:FIRST
Model_000001    asc:LUGGAGE;b_time:COMMUTERS
Model_000002    asc:no_seg;b_time:COMMUTERS
Model_000003    asc:GA;b_time:no_seg
Model_000004    asc:GA;b_time:FIRST
Model_000005    asc:GA;b_time:COMMUTERS
Model_000006    asc:GA-LUGGAGE;b_time:FIRST
Model_000007    asc:GA-LUGGAGE;b_time:no_seg
Model_000008    asc:GA-LUGGAGE;b_time:COMMUTERS
Model_000009    asc:no_seg;b_time:no_seg
Model_000010    asc:no_seg;b_time:FIRST
Model_000011    asc:LUGGAGE;b_time:no_seg

Estimation results of the Pareto optimal models.

pareto_results = pareto_optimal(dict_of_results)
compiled_pareto_results, pareto_specs = compile_estimation_results(
    pareto_results, use_short_names=True
)

display('Non dominated models')
display(compiled_pareto_results)

Non dominated models
                                         Model_000000  ...      Model_000004
Number of estimated parameters                      6  ...                11
Sample size                                     10719  ...             10719
Final log likelihood                        -8313.613  ...         -8228.457
Akaike Information Criterion                 16639.23  ...          16478.91
Bayesian Information Criterion                16682.9  ...          16558.99
asc_train_ref (t-test)                 -1.12  (-18.2)  ...      -1.52  (-18)
asc_train_diff_GA (t-test)               1.52  (22.1)  ...      1.35  (18.8)
b_time (t-test)                        -1.19  (-18.3)  ...
b_cost (t-test)                       -0.704  (-13.3)  ...    -0.78  (-13.5)
asc_car_ref (t-test)                  0.0143  (0.361)  ...   0.0346  (0.702)
asc_car_diff_GA (t-test)               -1.26  (-8.18)  ...    -1.19  (-7.61)
asc_train (t-test)                                     ...
asc_car (t-test)                                       ...
b_time_ref (t-test)                                    ...   -0.868  (-10.2)
b_time_diff_1st_class (t-test)                         ...    -0.604  (-8.2)
asc_train_diff_one_lugg (t-test)                       ...     0.517  (6.47)
asc_train_diff_several_lugg (t-test)                   ...     0.561  (3.28)
asc_car_diff_one_lugg (t-test)                         ...  -0.0562  (-1.11)
asc_car_diff_several_lugg (t-test)                     ...   -0.538  (-2.47)

[19 rows x 5 columns]

Glossary.

for short_name, spec in pareto_specs.items():
    print(f'{short_name}\t{spec}')

Model_000000    asc:GA;b_time:no_seg
Model_000001    asc:no_seg;b_time:no_seg
Model_000002    asc:no_seg;b_time:FIRST
Model_000003    asc:GA;b_time:FIRST
Model_000004    asc:GA-LUGGAGE;b_time:FIRST