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)

This illustrates the possibility to ignore all membership parameters that are 0.

author:

Michel Bierlaire, EPFL

date:

Sun Apr 9 18:06:44 2023

import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta
from biogeme.nests import OneNestForCrossNestedLogit, NestsForCrossNestedLogit

See the data processing script: Data preparation for Swissmetro.

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

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b11cnl.py')

Example b11cnl.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 = Beta('B_TIME', 0, None, None, 0)
B_COST = Beta('B_COST', 0, None, None, 0)

MU_EXISTING = Beta('MU_EXISTING', 1, 1, 10, 0)
MU_PUBLIC = Beta('MU_PUBLIC', 1, 1, 10, 0)

Nest membership parameters.

ALPHA_EXISTING = Beta('ALPHA_EXISTING', 0.5, 0, 1, 0)
ALPHA_PUBLIC = 1 - ALPHA_EXISTING

Definition of the utility functions

V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED

Associate utility functions with the numbering of alternatives

V = {1: V1, 2: V2, 3: V3}

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=MU_EXISTING,
    dict_of_alpha={1: ALPHA_EXISTING, 3: 1.0},
    name='existing',
)

nest_public = OneNestForCrossNestedLogit(
    nest_param=MU_PUBLIC, dict_of_alpha={1: ALPHA_PUBLIC, 2: 1.0}, 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.

logprob = models.logcnl_avail(V, av, nests, CHOICE)

/Users/bierlair/OnlineFiles/FilesOnGoogleDrive/github/biogeme/docs/examples/swissmetro/plot_b11cnl_sparse.py:93: DeprecationWarning: The function logcnl_avail is deprecated. It has been replaced by the function logcnl
  logprob = models.logcnl_avail(V, av, nests, CHOICE)

Create the Biogeme object

the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b11cnl'

File biogeme.toml has been parsed.

Estimate the parameters.

results = the_biogeme.estimate()

*** Initial values of the parameters are obtained from the file __b11cnl.iter
Parameter values restored from __b11cnl.iter
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Results saved in file b11cnl~01.html
Results saved in file b11cnl~01.pickle

print(results.short_summary())

Results for model b11cnl
Nbr of parameters:              7
Sample size:                    6768
Excluded data:                  3960
Final log likelihood:           -5214.049
Akaike Information Criterion:   10442.1
Bayesian Information Criterion: 10489.84

pandas_results = results.getEstimatedParameters()
pandas_results

	Value	Rob. Std err	Rob. t-test	Rob. p-value
ALPHA_EXISTING	0.495072	0.034752	14.246000	0.000000e+00
ASC_CAR	-0.240459	0.053450	-4.498764	6.834958e-06
ASC_TRAIN	0.098277	0.069978	1.404403	1.601989e-01
B_COST	-0.818885	0.058971	-13.886130	0.000000e+00
B_TIME	-0.776846	0.102380	-7.587854	3.241851e-14
MU_EXISTING	2.514876	0.248325	10.127363	0.000000e+00
MU_PUBLIC	4.113595	0.496722	8.281479	2.220446e-16