Note
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Catalog for segmented parameters
Investigate the segmentations of parameters.
We consider 4 specifications for the constants:
Not segmented
Segmented by GA (yearly subscription to public transport)
Segmented by luggage
Segmented both by GA and luggage
We consider 3 specifications for the time coefficients:
Not Segmented
Segmented with first class
Segmented with trip purpose
We obtain a total of 12 specifications. See Bierlaire and Ortelli (2023).
- author:
Michel Bierlaire, EPFL
- date:
Thu Jul 13 16:18:10 2023
import numpy as np
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta
from biogeme.catalog import segmentation_catalogs
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,
)
Definition of the segmentations.
segmentation_ga = database.generate_segmentation(
variable='GA', mapping={0: 'noGA', 1: 'GA'}
)
segmentation_luggage = database.generate_segmentation(
variable='LUGGAGE', mapping={0: 'no_lugg', 1: 'one_lugg', 3: 'several_lugg'}
)
segmentation_first = database.generate_segmentation(
variable='FIRST', mapping={0: '2nd_class', 1: '1st_class'}
)
We consider two trip purposes: ‘commuters’ and anything else. We need to define a binary variable first.
database.data['COMMUTERS'] = np.where(database.data['PURPOSE'] == 1, 1, 0)
segmentation_purpose = database.generate_segmentation(
variable='COMMUTERS', mapping={0: 'non_commuters', 1: 'commuters'}
)
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)
Catalogs for the alternative specific constants.
ASC_TRAIN_catalog, ASC_CAR_catalog = segmentation_catalogs(
generic_name='ASC',
beta_parameters=[ASC_TRAIN, ASC_CAR],
potential_segmentations=(
segmentation_ga,
segmentation_luggage,
),
maximum_number=2,
)
Catalog for the travel time coefficient. Note that the function returns a list of catalogs. Here, the list contains only one of them. This is why there is a comma after “B_TIME_catalog”.
(B_TIME_catalog,) = segmentation_catalogs(
generic_name='B_TIME',
beta_parameters=[B_TIME],
potential_segmentations=(
segmentation_first,
segmentation_purpose,
),
maximum_number=1,
)
Definition of the utility functions.
V1 = ASC_TRAIN_catalog + B_TIME_catalog * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = B_TIME_catalog * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR_catalog + B_TIME_catalog * 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 model. This is the contribution of each observation to the log likelihood function.
logprob = models.loglogit(V, av, CHOICE)
Create the Biogeme object.
the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b04segmentation'
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False
Estimate the parameters
dict_of_results = the_biogeme.estimate_catalog()
Number of estimated models.
print(f'A total of {len(dict_of_results)} models have been estimated')
A total of 12 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 ASC:GA;B_TIME:FIRST
Model_000001 ASC:GA;B_TIME:COMMUTERS
Model_000002 ASC:no_seg;B_TIME:COMMUTERS
Model_000003 ASC:GA-LUGGAGE;B_TIME:no_seg
Model_000004 ASC:no_seg;B_TIME:no_seg
Model_000005 ASC:no_seg;B_TIME:FIRST
Model_000006 ASC:GA;B_TIME:no_seg
Model_000007 ASC:GA-LUGGAGE;B_TIME:COMMUTERS
Model_000008 ASC:LUGGAGE;B_TIME:FIRST
Model_000009 ASC:GA-LUGGAGE;B_TIME:FIRST
Model_000010 ASC:LUGGAGE;B_TIME:COMMUTERS
Model_000011 ASC:LUGGAGE;B_TIME:no_seg
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
)
compiled_pareto_results
Glossary.
for short_name, spec in pareto_specs.items():
print(f'{short_name}\t{spec}')
Model_000000 ASC:GA-LUGGAGE;B_TIME:FIRST
Model_000001 ASC:no_seg;B_TIME:no_seg
Model_000002 ASC:no_seg;B_TIME:FIRST
Model_000003 ASC:GA;B_TIME:no_seg
Model_000004 ASC:GA;B_TIME:FIRST
Total running time of the script: (0 minutes 2.647 seconds)