Note
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Investigation of several choice models
Investigate several choice models:
logit
nested logit with two nests: public and private transportation
nested logit with two nests existing and future modes
for a total of 3 specifications. See Bierlaire and Ortelli (2023).
- author:
Michel Bierlaire, EPFL
- date:
Fri Jul 14 09:47:21 2023
import biogeme.biogeme as bio
import biogeme.biogeme_logging as blog
from biogeme import models
from biogeme.expressions import Beta
from biogeme.catalog import Catalog
from biogeme.nests import OneNestForNestedLogit, NestsForNestedLogit
from biogeme.results import compile_estimation_results, pareto_optimal
See 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)
Parameters to be estimated
ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
B_TIME = Beta('B_TIME', 0, None, None, 0)
B_COST = Beta('B_COST', 0, None, None, 0)
Definition of the utility functions
V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = 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 the logit model. This is the contribution of each observation to the log likelihood function.
logprob_logit = models.loglogit(V, av, CHOICE)
Nested logit model: nest with existing alternatives.
mu_existing = Beta('mu_existing', 1, 1, 10, 0)
existing = OneNestForNestedLogit(
nest_param=mu_existing, list_of_alternatives=[1, 3], name='Existing'
)
nests_existing = NestsForNestedLogit(choice_set=list(V), tuple_of_nests=(existing,))
logprob_nested_existing = models.lognested(V, av, nests_existing, CHOICE)
Nested logit model: nest with public transportation alternatives.
mu_public = Beta('mu_public', 1, 1, 10, 0)
public = OneNestForNestedLogit(
nest_param=mu_public, list_of_alternatives=[1, 2], name='Public'
)
nests_public = NestsForNestedLogit(choice_set=list(V), tuple_of_nests=(public,))
logprob_nested_public = models.lognested(V, av, nests_public, CHOICE)
Catalog.
model_catalog = Catalog.from_dict(
catalog_name='model_catalog',
dict_of_expressions={
'logit': logprob_logit,
'nested existing': logprob_nested_existing,
'nested public': logprob_nested_public,
},
)
Create the Biogeme object.
the_biogeme = bio.BIOGEME(database, model_catalog)
the_biogeme.modelName = 'b01model'
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False
File biogeme.toml has been parsed.
Estimate the parameters.
dict_of_results = the_biogeme.estimate_catalog()
Estimating 3 models.
File biogeme.toml has been parsed.
*** Initial values of the parameters are obtained from the file __b01model_000000.iter
Cannot read file __b01model_000000.iter. Statement is ignored.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST B_TIME Function Relgrad Radius Rho
0 -0.49 -0.92 -0.88 -0.67 5.4e+03 0.041 10 1.1 ++
1 -0.18 -0.73 -1 -1.2 5.3e+03 0.0072 1e+02 1.1 ++
2 -0.16 -0.7 -1.1 -1.3 5.3e+03 0.00018 1e+03 1 ++
3 -0.16 -0.7 -1.1 -1.3 5.3e+03 1.1e-07 1e+03 1 ++
Results saved in file b01model_000000.html
Results saved in file b01model_000000.pickle
File biogeme.toml has been parsed.
*** Initial values of the parameters are obtained from the file __b01model_000001.iter
Cannot read file __b01model_000001.iter. Statement is ignored.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST B_TIME mu_public Function Relgrad Radius Rho
0 -0.49 -0.92 -0.88 -0.67 1 5.4e+03 0.041 10 1.1 ++
1 -0.31 -0.86 -1.1 -1.1 1 5.3e+03 0.011 1e+02 1.1 ++
2 -0.15 -0.7 -1.1 -1.3 1 5.3e+03 0.00021 1e+03 1 ++
3 -0.15 -0.7 -1.1 -1.3 1 5.3e+03 2.1e-07 1e+03 1 ++
Results saved in file b01model_000001.html
Results saved in file b01model_000001.pickle
File biogeme.toml has been parsed.
*** Initial values of the parameters are obtained from the file __b01model_000002.iter
Cannot read file __b01model_000002.iter. Statement is ignored.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST B_TIME mu_existing Function Relgrad Radius Rho
0 0.1 -0.75 -1 -0.8 1.5 5.4e+03 0.082 10 0.92 ++
1 -0.22 -0.28 -0.82 -0.86 2.2 5.3e+03 0.076 10 0.44 +
2 -0.17 -0.52 -0.7 -0.7 2.7 5.3e+03 0.023 10 0.72 +
3 -0.17 -0.52 -0.7 -0.7 2.7 5.3e+03 0.023 0.84 -4.6 -
4 -0.14 -0.52 -0.87 -0.92 1.8 5.2e+03 0.006 0.84 0.63 +
5 -0.16 -0.51 -0.87 -0.91 2 5.2e+03 0.0014 8.4 1.1 ++
6 -0.17 -0.51 -0.86 -0.9 2.1 5.2e+03 8.1e-05 84 1 ++
7 -0.17 -0.51 -0.86 -0.9 2.1 5.2e+03 2.8e-07 84 1 ++
Results saved in file b01model_000002.html
Results saved in file b01model_000002.pickle
Number of estimated models.
print(f'A total of {len(dict_of_results)} models have been estimated')
A total of 3 models have been estimated
All estimation results
compiled_results, specs = compile_estimation_results(
dict_of_results, use_short_names=True
)
compiled_results
Glossary
for short_name, spec in specs.items():
print(f'{short_name}\t{spec}')
Model_000000 model_catalog:logit
Model_000001 model_catalog:nested public
Model_000002 model_catalog:nested existing
Estimation results of the Pareto optimal models.
pareto_results = pareto_optimal(dict_of_results)
compiled_pareto_results, pareto_specs = compile_estimation_results(
pareto_results, use_short_names=True
)
No Pareto file has been provided
compiled_pareto_results
Glossary.
for short_name, spec in pareto_specs.items():
print(f'{short_name}\t{spec}')
Model_000000 model_catalog:logit
Model_000001 model_catalog:nested existing
Total running time of the script: (0 minutes 0.617 seconds)