Note
Go to the end to download the full example code.
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)
- 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, 5, 0)
MU_PUBLIC = Beta('MU_PUBLIC', 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
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, 2: 0.0, 3: 1.0},
name='existing',
)
nest_public = OneNestForCrossNestedLogit(
nest_param=MU_PUBLIC, 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.
logprob = models.logcnl(V, av, nests, CHOICE)
Create the Biogeme object
the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b11cnl'
Biogeme parameters read from biogeme.toml.
Estimate the parameters.
results = the_biogeme.estimate()
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b11cnl.iter
Cannot read file __b11cnl.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ALPHA_EXISTING ASC_CAR ASC_TRAIN B_COST B_TIME MU_EXISTING MU_PUBLIC Function Relgrad Radius Rho
0 0.57 -0.088 -0.83 -0.27 -1 1.5 1.5 5.6e+03 0.081 1 0.61 +
1 0.86 -0.29 -0.32 -1.3 -0.93 1.8 1.7 5.3e+03 0.049 1 0.63 +
2 0.86 -0.29 -0.32 -1.3 -0.93 1.8 1.7 5.3e+03 0.049 0.5 0.013 -
3 0.79 -0.12 -0.34 -0.77 -0.9 2 1.8 5.2e+03 0.012 0.5 0.79 +
4 0.56 -0.25 -0.1 -0.88 -0.8 2.5 2.2 5.2e+03 0.013 0.5 0.69 +
5 0.55 -0.25 -0.057 -0.86 -0.8 2.5 2.6 5.2e+03 0.0039 5 1.3 ++
6 0.51 -0.25 0.049 -0.84 -0.79 2.5 3.3 5.2e+03 0.0054 50 1.2 ++
7 0.5 -0.24 0.077 -0.83 -0.78 2.5 3.7 5.2e+03 0.0017 5e+02 1.2 ++
8 0.5 -0.24 0.095 -0.82 -0.78 2.5 4 5.2e+03 0.00053 5e+03 1.1 ++
9 0.5 -0.24 0.095 -0.82 -0.78 2.5 4 5.2e+03 3.3e-05 5e+03 1 ++
Results saved in file b11cnl.html
Results saved in file b11cnl.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.get_estimated_parameters()
pandas_results
Total running time of the script: (0 minutes 1.955 seconds)