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Nested logit model normalized from bottom
- Example of a nested logit model where the normalization is done at the
bottom level. The specification is using the original syntax for nests. Since biogeme 3.13, a new syntax, more explicit, has been adopted.
- author:
Michel Bierlaire, EPFL
- date:
Sun Apr 9 18:05:04 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 b10nested_bottom.py')
Example b10nested_bottom.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)
This is the scale parameter of the choice model. It is usually normalized to one. In this example, we normalize the nest parameter instead, and estimate the scale parameter for the model. If the lower bound is set to zero, the model cannot be evaluated. Therefore, we set the lower bound to a small number, strictly larger than zero.
MU = Beta('MU', 0.5, 0.000001, 1.0, 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 = 1.0, [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, where the scale parameter mu is explicitly involved.
logprob = models.lognestedMevMu(V, av, nests, CHOICE, MU)
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 = 'b10nested_bottom'
File biogeme.toml has been parsed.
Estimate the parameters.
results = the_biogeme.estimate()
*** Initial values of the parameters are obtained from the file __b10nested_bottom.iter
Parameter values restored from __b10nested_bottom.iter
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Results saved in file b10nested_bottom~00.html
Results saved in file b10nested_bottom~00.pickle
print(results.short_summary())
Results for model b10nested_bottom
Nbr of parameters: 5
Sample size: 6768
Excluded data: 3960
Final log likelihood: -5236.9
Akaike Information Criterion: 10483.8
Bayesian Information Criterion: 10517.9
pandas_results = results.getEstimatedParameters()
pandas_results
Total running time of the script: (0 minutes 0.197 seconds)