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
from IPython.core.display_functions import display

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


from biogeme.data.swissmetro import (
    read_data,
    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,
)

Read the data

database = read_data()

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
)

display(compiled_results)

                                      Model_000000  ...      Model_000011
Number of estimated parameters                   5  ...                 8
Sample size                                  10719  ...             10719
Final log likelihood                  -8669.931927  ...      -8562.781428
Akaike Information Criterion          17349.863853  ...      17141.562856
Bayesian Information Criterion        17386.262719  ...      17199.801041
ASC_CAR (t-test)                   0.0172  (0.441)  ...     0.0443  (0.9)
ASC_TRAIN (t-test)                    -0.65  (-11)  ...    -1.37  (-16.5)
B_COST (t-test)                    -0.789  (-15.5)  ...   -0.783  (-15.5)
B_TIME (t-test)                     -1.27  (-23.1)  ...    -1.26  (-19.1)
B_TIME_commuters (t-test)        -0.0604  (-0.292)  ...
ASC_CAR_GA (t-test)                                 ...
ASC_CAR_one_lugg (t-test)                           ...  -0.0791  (-1.56)
ASC_CAR_several_lugg (t-test)                       ...   -0.534  (-2.56)
ASC_TRAIN_GA (t-test)                               ...
ASC_TRAIN_one_lugg (t-test)                         ...     0.955  (12.6)
ASC_TRAIN_several_lugg (t-test)                     ...     0.949  (5.42)
B_TIME_1st_class (t-test)                           ...

[17 rows x 12 columns]

Glossary

for short_name, spec in specs.items():
    print(f'{short_name}\t{spec}')

Model_000000    ASC:no_seg;B_TIME:COMMUTERS
Model_000001    ASC:GA-LUGGAGE;B_TIME:FIRST
Model_000002    ASC:GA;B_TIME:COMMUTERS
Model_000003    ASC:LUGGAGE;B_TIME:COMMUTERS
Model_000004    ASC:no_seg;B_TIME:FIRST
Model_000005    ASC:GA;B_TIME:FIRST
Model_000006    ASC:LUGGAGE;B_TIME:FIRST
Model_000007    ASC:GA-LUGGAGE;B_TIME:COMMUTERS
Model_000008    ASC:GA;B_TIME:no_seg
Model_000009    ASC:GA-LUGGAGE;B_TIME:no_seg
Model_000010    ASC:no_seg;B_TIME:no_seg
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
)

display(compiled_pareto_results)

                                    Model_000000  ...     Model_000004
Number of estimated parameters                 5  ...                6
Sample size                                10719  ...            10719
Final log likelihood                -8598.531022  ...     -8313.612897
Akaike Information Criterion        17207.062044  ...     16639.225794
Bayesian Information Criterion       17243.46091  ...     16682.904433
ASC_CAR (t-test)                 0.0091  (0.245)  ...  0.0142  (0.357)
ASC_TRAIN (t-test)               -0.707  (-12.5)  ...   -1.12  (-18.2)
B_COST (t-test)                   -0.87  (-15.6)  ...  -0.704  (-13.3)
B_TIME (t-test)                  -0.916  (-10.9)  ...   -1.19  (-18.3)
B_TIME_1st_class (t-test)        -0.688  (-9.57)  ...
ASC_CAR_GA (t-test)                               ...   -1.26  (-8.18)
ASC_CAR_one_lugg (t-test)                         ...
ASC_CAR_several_lugg (t-test)                     ...
ASC_TRAIN_GA (t-test)                             ...     1.52  (22.1)
ASC_TRAIN_one_lugg (t-test)                       ...
ASC_TRAIN_several_lugg (t-test)                   ...

[16 rows x 5 columns]

Glossary.

for short_name, spec in pareto_specs.items():
    print(f'{short_name}\t{spec}')

Model_000000    ASC:no_seg;B_TIME:FIRST
Model_000001    ASC:no_seg;B_TIME:no_seg
Model_000002    ASC:GA-LUGGAGE;B_TIME:FIRST
Model_000003    ASC:GA;B_TIME:FIRST
Model_000004    ASC:GA;B_TIME:no_seg