Catalog for alternative specific coefficients

Investigate alternative specific parameters:

  • two specifications for the travel time coefficient: generic, and alternative specific,

  • two specifications for the travel cost coefficient: generic, and alternative specific,

for a total of 4 specifications. See Bierlaire and Ortelli (2023).

author:

Michel Bierlaire, EPFL

date:

Thu Jul 13 16:18:10 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 generic_alt_specific_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,
)

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)

Catalog for travel time coefficient.

(B_TIME_catalog_dict,) = generic_alt_specific_catalogs(
    generic_name='B_TIME', beta_parameters=[B_TIME], alternatives=('TRAIN', 'SM', 'CAR')
)

Catalog for travel cost coefficient.

(B_COST_catalog_dict,) = generic_alt_specific_catalogs(
    generic_name='B_COST', beta_parameters=[B_COST], alternatives=('TRAIN', 'SM', 'CAR')
)

Definition of the utility functions.

V1 = (
    ASC_TRAIN
    + B_TIME_catalog_dict['TRAIN'] * TRAIN_TT_SCALED
    + B_COST_catalog_dict['TRAIN'] * TRAIN_COST_SCALED
)
V2 = (
    B_TIME_catalog_dict['SM'] * SM_TT_SCALED
    + B_COST_catalog_dict['SM'] * SM_COST_SCALED
)
V3 = (
    ASC_CAR
    + B_TIME_catalog_dict['CAR'] * CAR_TT_SCALED
    + B_COST_catalog_dict['CAR'] * 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)

Read the data

database = read_data()

Create the Biogeme object.

the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b01alt_spec'
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False
Biogeme parameters read from biogeme.toml.

Estimate the parameters.

dict_of_results = the_biogeme.estimate_catalog()
Estimating 4 models.
Biogeme parameters read from biogeme.toml.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b01alt_spec_000000.iter
Cannot read file __b01alt_spec_000000.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
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_CAR       B_TIME_SM    B_TIME_TRAIN     Function    Relgrad   Radius      Rho
    0           -0.42           -0.77           -0.68           -0.78              -1           -0.88      8.8e+03      0.076       10      1.1   ++
    1           -0.53           -0.37           -0.78           -0.98            -1.4            -1.5      8.6e+03      0.025    1e+02      1.1   ++
    2           -0.54           -0.17           -0.79              -1            -1.5            -1.7      8.6e+03     0.0028    1e+03      1.1   ++
    3           -0.54           -0.17           -0.79              -1            -1.5            -1.7      8.6e+03      3e-05    1e+03        1   ++
Biogeme parameters read from biogeme.toml.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b01alt_spec_000001.iter
Cannot read file __b01alt_spec_000001.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
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_CAR       B_COST_SM    B_COST_TRAIN      B_TIME_CAR       B_TIME_SM    B_TIME_TRAIN     Function    Relgrad   Radius      Rho
    0            -0.6          -0.032           -0.33            -0.8              -1            -1.2            -1.4            -1.6      8.6e+03      0.055       10     0.96   ++
    1           -0.59          -0.021           -0.64           -0.77            -1.6              -1            -1.5            -1.5      8.4e+03      0.016    1e+02      1.1   ++
    2           -0.59          -0.019           -0.66           -0.79            -1.8            -1.1            -1.5            -1.4      8.4e+03      0.002    1e+03      1.1   ++
    3           -0.59          -0.019           -0.66           -0.79            -1.8            -1.1            -1.5            -1.4      8.4e+03      3e-05    1e+03        1   ++
Biogeme parameters read from biogeme.toml.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b01alt_spec_000002.iter
Cannot read file __b01alt_spec_000002.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
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           -0.16           -0.53           -0.66           -0.87      8.8e+03      0.048       10      1.1   ++
    1          -0.003           -0.63           -0.77            -1.2      8.7e+03     0.0073    1e+02      1.1   ++
    2           0.016           -0.65           -0.79            -1.3      8.7e+03    0.00016    1e+03        1   ++
    3           0.016           -0.65           -0.79            -1.3      8.7e+03    7.3e-08    1e+03        1   ++
Biogeme parameters read from biogeme.toml.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b01alt_spec_000003.iter
Cannot read file __b01alt_spec_000003.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
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_CAR       B_COST_SM    B_COST_TRAIN          B_TIME     Function    Relgrad   Radius      Rho
    0           -0.39           0.098           -0.39           -0.81            -1.8            -1.3      8.5e+03      0.026        1      0.8    +
    1           -0.42          -0.044           -0.38           -0.82            -1.9            -1.3      8.4e+03     0.0019       10        1   ++
    2           -0.42          -0.044           -0.38           -0.82            -1.9            -1.3      8.4e+03    1.5e-05       10        1   ++

Number of estimated models.

print(f'A total of {len(dict_of_results)} models have been estimated')
A total of 4 models have been estimated

All estimation results

compiled_results, specs = compile_estimation_results(
    dict_of_results, use_short_names=True
)
compiled_results
Model_000000 Model_000001 Model_000002 Model_000003
Number of estimated parameters 6 8 4 6
Sample size 10719 10719 10719 10719
Final log likelihood -8579.524042 -8430.710721 -8670.163119 -8448.605446
Akaike Information Criterion 17171.048085 16877.421442 17348.326237 16909.210893
Bayesian Information Criterion 17214.726724 16935.659627 17377.44533 16952.889531
ASC_CAR (t-test) -0.544 (-7.24) -0.595 (-8.17) 0.0162 (0.438) -0.415 (-7.36)
ASC_TRAIN (t-test) -0.144 (-1.73) -0.0197 (-0.234) -0.652 (-12) -0.046 (-0.733)
B_COST (t-test) -0.789 (-17) -0.79 (-15.5)
B_TIME_CAR (t-test) -0.998 (-14.9) -1.06 (-11.1)
B_TIME_SM (t-test) -1.47 (-14.3) -1.46 (-14.4)
B_TIME_TRAIN (t-test) -1.76 (-23.4) -1.4 (-15.8)
B_COST_CAR (t-test) -0.659 (-6.68) -0.383 (-5)
B_COST_SM (t-test) -0.787 (-14.8) -0.823 (-15.5)
B_COST_TRAIN (t-test) -1.85 (-14.2) -1.92 (-16.8)
B_TIME (t-test) -1.28 (-19.5) -1.27 (-16.9)


Glossary

for short_name, spec in specs.items():
    print(f'{short_name}\t{spec}')
Model_000000    B_COST_gen_altspec:generic;B_TIME_gen_altspec:altspec
Model_000001    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:altspec
Model_000002    B_COST_gen_altspec:generic;B_TIME_gen_altspec:generic
Model_000003    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:generic

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
Model_000000 Model_000001 Model_000002
Number of estimated parameters 4 8 6
Sample size 10719 10719 10719
Final log likelihood -8670.163119 -8430.710721 -8448.605446
Akaike Information Criterion 17348.326237 16877.421442 16909.210893
Bayesian Information Criterion 17377.44533 16935.659627 16952.889531
ASC_CAR (t-test) 0.0162 (0.438) -0.595 (-8.17) -0.415 (-7.36)
ASC_TRAIN (t-test) -0.652 (-12) -0.0197 (-0.234) -0.046 (-0.733)
B_COST (t-test) -0.79 (-15.5)
B_TIME (t-test) -1.28 (-19.5) -1.27 (-16.9)
B_COST_CAR (t-test) -0.659 (-6.68) -0.383 (-5)
B_COST_SM (t-test) -0.787 (-14.8) -0.823 (-15.5)
B_COST_TRAIN (t-test) -1.85 (-14.2) -1.92 (-16.8)
B_TIME_CAR (t-test) -1.06 (-11.1)
B_TIME_SM (t-test) -1.46 (-14.4)
B_TIME_TRAIN (t-test) -1.4 (-15.8)


Glossary.

for short_name, spec in pareto_specs.items():
    print(f'{short_name}\t{spec}')
Model_000000    B_COST_gen_altspec:generic;B_TIME_gen_altspec:generic
Model_000001    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:altspec
Model_000002    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:generic

Total running time of the script: (0 minutes 1.286 seconds)

Gallery generated by Sphinx-Gallery