11a. Cross-nested logit

Example of a cross-nested logit model with two nests:

• one with existing alternatives (car and train),

• one with public transportation alternatives (train and Swissmetro)

Michel Bierlaire, EPFL Sat Jun 21 2025, 16:33:38

from IPython.core.display_functions import display

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta
from biogeme.models import logcnl
from biogeme.nests import NestsForCrossNestedLogit, OneNestForCrossNestedLogit
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

See the data processing script: Data preparation for Swissmetro.

from swissmetro_data import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    GA,
    SM_AV,
    SM_COST_SCALED,
    SM_HE,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_HE,
    TRAIN_TT_SCALED,
    database,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b11a_cnl.py')

Example b11a_cnl.py

Parameters to be estimated.

asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)
asc_sm = Beta('asc_sm', 0, None, None, 1)
b_time_swissmetro = Beta('b_time_swissmetro', 0, None, None, 0)
b_time_train = Beta('b_time_train', 0, None, None, 0)
b_time_car = Beta('b_time_car', 0, None, None, 0)
b_cost = Beta('b_cost', 0, None, None, 0)
b_headway_swissmetro = Beta('b_headway_swissmetro', 0, None, None, 0)
b_headway_train = Beta('b_headway_train', 0, None, None, 0)
ga_train = Beta('ga_train', 0, None, None, 0)
ga_swissmetro = Beta('ga_swissmetro', 0, None, None, 0)

existing_nest_parameter = Beta('existing_nest_parameter', 1, 1, 5, 0)
public_nest_parameter = Beta('public_nest_parameter', 1, 1, 5, 0)

Nest membership parameters.

alpha_existing = Beta('alpha_existing', 0.5, 0, 1, 0)
alpha_public = 1 - alpha_existing

Definition of the utility functions

v_train = (
    asc_train
    + b_time_train * TRAIN_TT_SCALED
    + b_cost * TRAIN_COST_SCALED
    + b_headway_train * TRAIN_HE
    + ga_train * GA
)
v_swissmetro = (
    asc_sm
    + b_time_swissmetro * SM_TT_SCALED
    + b_cost * SM_COST_SCALED
    + b_headway_swissmetro * SM_HE
    + ga_swissmetro * GA
)
v_car = asc_car + b_time_car * 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 nests.

nest_existing = OneNestForCrossNestedLogit(
    nest_param=existing_nest_parameter,
    dict_of_alpha={1: alpha_existing, 2: 0.0, 3: 1.0},
    name='existing',
)

nest_public = OneNestForCrossNestedLogit(
    nest_param=public_nest_parameter,
    dict_of_alpha={1: alpha_public, 2: 1.0, 3: 0.0},
    name='public',
)

nests = NestsForCrossNestedLogit(
    choice_set=[1, 2, 3], tuple_of_nests=(nest_existing, nest_public)
)

The choice model is a cross-nested logit, with availability conditions.

log_probability = logcnl(v, av, nests, CHOICE)

Create the Biogeme object

the_biogeme = BIOGEME(database, log_probability)
the_biogeme.model_name = 'b11a_cnl'

Biogeme parameters read from biogeme.toml.

Estimate the parameters.

try:
    results = EstimationResults.from_yaml_file(
        filename=f'saved_results/{the_biogeme.model_name}.yaml'
    )
except FileNotFoundError:
    results = the_biogeme.estimate()

print(results.short_summary())

Results for model b11a_cnl
Nbr of parameters:              13
Sample size:                    6768
Excluded data:                  3960
Final log likelihood:           -4997.865
Akaike Information Criterion:   10021.73
Bayesian Information Criterion: 10110.39

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

{'Estimated parameters':                        Name     Value  ...  Robust t-stat.  Robust p-value
0                 asc_train -0.308632  ...       -1.541996    1.230745e-01
1              b_time_train -1.073972  ...       -7.579594    3.463896e-14
2                    b_cost -0.973743  ...      -14.711588    0.000000e+00
3           b_headway_train -0.004367  ...       -4.491675    7.066515e-06
4                  ga_train  1.143139  ...        4.934137    8.050575e-07
5            alpha_existing  0.644834  ...        3.743363    1.815738e-04
6   existing_nest_parameter  1.771090  ...        7.695250    1.421085e-14
7         b_time_swissmetro -0.991558  ...       -5.574204    2.486645e-08
8      b_headway_swissmetro -0.007724  ...       -2.601077    9.293148e-03
9             ga_swissmetro -0.138906  ...       -0.861887    3.887494e-01
10                  asc_car -0.606250  ...       -4.885821    1.029990e-06
11               b_time_car -0.857061  ...       -6.761085    1.369616e-11
12    public_nest_parameter  1.839302  ...        3.952286    7.740803e-05

[13 rows x 5 columns]}