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Nested logit model
Example of a nested logit model, using the original syntax for nests. Since biogeme 3.13, a new syntax, more explicit, has been adopted.
- author:
Michel Bierlaire, EPFL
- date:
Tue Oct 24 13:37:27 2023
import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta
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 b09nested')
Example b09nested
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 = Beta('MU', 1, 1, 10, 0)
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. In this example, we create a nest for the existing modes, that is train (1) and car (3). Each nest is associated with a tuple containing (i) the nest parameter and (ii) the list of alternatives.
existing = MU, [1, 3]
future = 1.0, [2]
nests = existing, future
Definition of the model. This is the contribution of each observation to the log likelihood function. The choice model is a nested logit, with availability conditions.
logprob = models.lognested(V, av, nests, CHOICE)
It is recommended to define the nests of the nested logit model using the objects OneNestForNestedLogit and NestsForNestedLogit defined in biogeme.nests.
Create the Biogeme object.
the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = "b09nested"
File biogeme.toml has been parsed.
Calculate the null log likelihood for reporting.
the_biogeme.calculateNullLoglikelihood(av)
-6964.662979191462
Estimate the parameters.
results = the_biogeme.estimate()
*** Initial values of the parameters are obtained from the file __b09nested.iter
Parameter values restored from __b09nested.iter
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Results saved in file b09nested~00.html
Results saved in file b09nested~00.pickle
print(results.short_summary())
Results for model b09nested
Nbr of parameters: 5
Sample size: 6768
Excluded data: 3960
Null log likelihood: -6964.663
Final log likelihood: -5236.9
Likelihood ratio test (null): 3455.526
Rho square (null): 0.248
Rho bar square (null): 0.247
Akaike Information Criterion: 10483.8
Bayesian Information Criterion: 10517.9
pandas_results = results.getEstimatedParameters()
pandas_results
Total running time of the script: (0 minutes 0.213 seconds)