Catalog for alternative specific coefficientsΒΆ

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).

Michel Bierlaire, EPFL Sun Apr 27 2025, 15:49:05

from IPython.core.display_functions import display

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.catalog import generic_alt_specific_catalogs
from biogeme.data.swissmetro import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    read_data,
)
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import compile_estimation_results, pareto_optimal

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', 'swissmetro', 'car'),
)

Catalog for travel cost coefficient.

(b_cost_catalog_dict,) = generic_alt_specific_catalogs(
    generic_name='b_cost',
    beta_parameters=[b_cost],
    alternatives=('train', 'swissmetro', 'car'),
)

Definition of the utility functions.

v_train = (
    asc_train
    + b_time_catalog_dict['train'] * TRAIN_TT_SCALED
    + b_cost_catalog_dict['train'] * TRAIN_COST_SCALED
)
v_swissmetro = (
    b_time_catalog_dict['swissmetro'] * SM_TT_SCALED
    + b_cost_catalog_dict['swissmetro'] * SM_COST_SCALED
)
v_car = (
    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: v_train, 2: v_swissmetro, 3: v_car}

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.

log_probability = loglogit(v, av, CHOICE)

Read the data

database = read_data()

Create the Biogeme object.

the_biogeme = BIOGEME(
    database, log_probability, generate_html=False, generate_yaml=False
)
the_biogeme.model_name = 'b01alt_spec'
Biogeme parameters read from biogeme.toml.

Estimate the parameters.

dict_of_results = the_biogeme.estimate_catalog()
Estimating 4 models.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b01alt_spec_000000.iter
Parameter values restored from __b01alt_spec_000000.iter
Starting values for the algorithm: {'asc_train': -0.019677954254812977, 'b_time_train': -1.4035204568960171, 'b_cost_train': -1.8538931895561404, 'b_time_swissmetro': -1.4600247945313696, 'b_cost_swissmetro': -0.7866329830682577, 'asc_car': -0.5950658046556297, 'b_time_car': -1.0574354441678266, 'b_cost_car': -0.6588841886011664}
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train    b_time_train          b_cost b_time_swissmet         asc_car      b_time_car     Function    Relgrad   Radius      Rho
    0           -0.22            -1.6              -1            -1.5           -0.23           -0.73        9e+03       0.11        1      0.5    +
    1           -0.22            -1.6              -1            -1.5           -0.23           -0.73        9e+03       0.11     0.43    0.086    -
    2           -0.26            -1.7            -1.4            -1.5           -0.08           -0.55      8.9e+03       0.12     0.43     0.32    +
    3           -0.24            -1.7            -1.9            -1.6          -0.012           -0.45      8.9e+03       0.15     0.43     0.11    +
    4           -0.24            -1.7            -1.9            -1.6          -0.012           -0.45      8.9e+03       0.15     0.21   -0.041    -
    5           -0.24            -1.7            -1.9            -1.6          -0.012           -0.45      8.9e+03       0.15     0.11   -0.066    -
    6           -0.24            -1.7            -1.9            -1.6          -0.012           -0.45      8.9e+03       0.15    0.054    0.019    -
    7           -0.24            -1.7            -1.9            -1.6          -0.012           -0.45      8.9e+03       0.15    0.027    0.069    -
    8           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15    0.027      0.1    +
    9           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15    0.013    0.059    -
   10           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15   0.0067    0.052    -
   11           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15   0.0034    0.068    -
   12           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15   0.0017    0.075    -
   13           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  0.00084    0.076    -
   14           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  0.00042    0.077    -
   15           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  0.00021    0.077    -
   16           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15   0.0001    0.077    -
   17           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  5.2e-05    0.077    -
   18           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  2.6e-05    0.078    -
   19           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  1.3e-05    0.078    -
   20           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  6.5e-06    0.078    -
   21           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  3.3e-06    0.078    -
   22           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  1.6e-06    0.078    -
   23           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  8.2e-07    0.078    -
   24           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  4.1e-07    0.078    -
   25           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15    2e-07    0.078    -
   26           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15    1e-07    0.078    -
   27           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  5.1e-08    0.078    -
   28           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  2.6e-08    0.078    -
   29           -0.24            -1.7            -1.9            -1.6          0.0039           -0.42      8.9e+03       0.15  1.3e-08    0.078    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.278217874817229e-08
Number of iterations: 30
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:00.383772
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b01alt_spec_000001.iter
Parameter values restored from __b01alt_spec_000001.iter
Starting values for the algorithm: {'asc_train': -0.652238664271019, 'b_time': -1.2789413398819158, 'b_cost': -0.7897904566401142, 'asc_car': 0.01622793815045202}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time    b_cost_train b_cost_swissmet         asc_car      b_cost_car     Function    Relgrad   Radius      Rho
    0           -0.65            -1.3               0               0           0.016               0        9e+03      0.086      0.5    -0.58    -
    1           -0.65            -1.3               0               0           0.016               0        9e+03      0.086     0.25    -0.61    -
    2           -0.65            -1.3               0               0           0.016               0        9e+03      0.086     0.12    -0.86    -
    3           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    0.062     -1.8    -
    4           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    0.031     -1.1    -
    5           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    0.016    -0.78    -
    6           -0.65            -1.3               0               0           0.016               0        9e+03      0.086   0.0078    -0.66    -
    7           -0.65            -1.3               0               0           0.016               0        9e+03      0.086   0.0039    -0.61    -
    8           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    0.002    -0.59    -
    9           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  0.00098    -0.58    -
   10           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  0.00049    -0.57    -
   11           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  0.00024    -0.57    -
   12           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  0.00012    -0.57    -
   13           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  6.1e-05    -0.56    -
   14           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  3.1e-05    -0.56    -
   15           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  1.5e-05    -0.56    -
   16           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  7.6e-06    -0.56    -
   17           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  3.8e-06    -0.56    -
   18           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  1.9e-06    -0.56    -
   19           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  9.5e-07    -0.56    -
   20           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  4.8e-07    -0.56    -
   21           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  2.4e-07    -0.56    -
   22           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  1.2e-07    -0.56    -
   23           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    6e-08    -0.56    -
   24           -0.65            -1.3               0               0           0.016               0        9e+03      0.086    3e-08    -0.56    -
   25           -0.65            -1.3               0               0           0.016               0        9e+03      0.086  1.5e-08    -0.56    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 26
Proportion of Hessian calculation: 1/1 = 100.0%
Optimization time: 0:00:00.316094
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b01alt_spec_000002.iter
Parameter values restored from __b01alt_spec_000002.iter
Starting values for the algorithm: {'asc_train': -0.04600967948106339, 'b_time': -1.2700621694169116, 'b_cost_train': -1.919425253291788, 'b_cost_swissmetro': -0.8231956949362126, 'asc_car': -0.41549753284358953, 'b_cost_car': -0.38347919498386734}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train    b_time_train    b_cost_train b_time_swissmet b_cost_swissmet         asc_car      b_time_car      b_cost_car     Function    Relgrad   Radius      Rho
    0           -0.33           -0.84            -1.9           -0.69            -1.6           -0.13           -0.65           -0.82      9.1e+03       0.19        1     0.47    +
    1           -0.33           -0.84            -1.9           -0.69            -1.6           -0.13           -0.65           -0.82      9.1e+03       0.19     0.46     -9.8    -
    2           -0.33           -0.84            -1.9           -0.69            -1.6           -0.13           -0.65           -0.82      9.1e+03       0.19     0.23     -2.7    -
    3           -0.33           -0.84            -1.9           -0.69            -1.6           -0.13           -0.65           -0.82      9.1e+03       0.19     0.11     -0.7    -
    4           -0.33           -0.84            -1.9           -0.69            -1.6           -0.13           -0.65           -0.82      9.1e+03       0.19    0.057    0.027    -
    5           -0.39            -0.9            -1.9           -0.63            -1.5           -0.18            -0.7           -0.88        9e+03       0.19    0.057     0.23    +
    6           -0.33           -0.95            -1.9           -0.58            -1.4           -0.24           -0.76           -0.93        9e+03       0.19    0.057     0.19    +
    7           -0.28              -1            -1.8           -0.52            -1.4            -0.3           -0.82           -0.99      8.9e+03       0.18    0.057     0.17    +
    8           -0.29            -1.1            -1.8           -0.46            -1.3           -0.35           -0.87              -1      8.9e+03       0.18    0.057     0.14    +
    9           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17    0.057     0.11    +
   10           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17    0.028    0.027    -
   11           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17    0.014    0.073    -
   12           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17   0.0071    0.068    -
   13           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17   0.0036    0.066    -
   14           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17   0.0018    0.064    -
   15           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  0.00089    0.064    -
   16           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  0.00044    0.064    -
   17           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  0.00022    0.064    -
   18           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  0.00011    0.064    -
   19           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  5.6e-05    0.064    -
   20           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  2.8e-05    0.064    -
   21           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  1.4e-05    0.064    -
   22           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17    7e-06    0.064    -
   23           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  3.5e-06    0.064    -
   24           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  1.7e-06    0.064    -
   25           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  8.7e-07    0.064    -
   26           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  4.3e-07    0.064    -
   27           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  2.2e-07    0.064    -
   28           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  1.1e-07    0.064    -
   29           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  5.4e-08    0.064    -
   30           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  2.7e-08    0.064    -
   31           -0.26              -1            -1.7            -0.4            -1.3           -0.41           -0.93            -1.1      8.9e+03       0.17  1.4e-08    0.064    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.3577787116831426e-08
Number of iterations: 32
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:00.441780
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b01alt_spec_000003.iter
Parameter values restored from __b01alt_spec_000003.iter
Starting values for the algorithm: {'asc_train': -0.14412205501933395, 'b_time_train': -1.758918388044104, 'b_cost': -0.7893801438971159, 'b_time_swissmetro': -1.4667704942116189, 'asc_car': -0.5438801230042781, 'b_time_car': -0.9979945188921027}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.59           -0.85           -0.67           -0.18        1e+04       0.19        1     0.52    +
    1           -0.74            -1.7            -0.7            0.19      9.7e+03       0.28        1     0.21    +
    2           -0.74            -1.7            -0.7            0.19      9.7e+03       0.28      0.4    0.075    -
    3            -1.1            -2.1           -0.66            0.29      9.3e+03       0.26      0.4     0.53    +
    4            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24      0.4     0.38    +
    5            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24      0.2   0.0035    -
    6            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24      0.1    0.005    -
    7            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24    0.051   0.0085    -
    8            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24    0.025    0.018    -
    9            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24    0.013    0.036    -
   10            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24   0.0063    0.047    -
   11            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24   0.0032    0.052    -
   12            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24   0.0016    0.055    -
   13            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  0.00079    0.056    -
   14            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  0.00039    0.057    -
   15            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24   0.0002    0.057    -
   16            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  9.9e-05    0.057    -
   17            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  4.9e-05    0.057    -
   18            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  2.5e-05    0.057    -
   19            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  1.2e-05    0.057    -
   20            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  6.2e-06    0.057    -
   21            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  3.1e-06    0.057    -
   22            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  1.5e-06    0.057    -
   23            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  7.7e-07    0.057    -
   24            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  3.9e-07    0.057    -
   25            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  1.9e-07    0.057    -
   26            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  9.6e-08    0.057    -
   27            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  4.8e-08    0.057    -
   28            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  2.4e-08    0.057    -
   29            -1.5            -2.5           -0.69            0.24      9.2e+03       0.24  1.2e-08    0.057    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.2043595453523925e-08
Number of iterations: 30
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:00.426791
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.

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
)
display('All estimated models')
display(compiled_results)
All estimated models
                                     Model_000000  ...    Model_000003
Number of estimated parameters                  6  ...               4
Sample size                                 10719  ...           10719
Final log likelihood                    -11373.86  ...       -10108.68
Akaike Information Criterion             22759.72  ...        20225.36
Bayesian Information Criterion            22803.4  ...        20254.48
asc_train (t-test)                  -0.24  (-2.1)  ...  -1.53  (-11.8)
b_time_train (t-test)              -1.68  (-16.4)  ...
b_cost (t-test)                    -1.88  (-13.2)  ...   -0.688  (-12)
b_time_swissmetro (t-test)         -1.57  (-9.39)  ...
asc_car (t-test)                0.00392  (0.0362)  ...   0.237  (4.44)
b_time_car (t-test)               -0.425  (-6.05)  ...
b_time (t-test)                                    ...  -2.47  (-16.6)
b_cost_train (t-test)                              ...
b_cost_swissmetro (t-test)                         ...
b_cost_car (t-test)                                ...

[15 rows x 4 columns]

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:generic
Model_000002    b_cost_gen_altspec:altspec;b_time_gen_altspec:altspec
Model_000003    b_cost_gen_altspec:generic;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
display('Non dominated models')
display(compiled_pareto_results)
Non dominated models
                                   Model_000000  ...     Model_000002
Number of estimated parameters                8  ...                6
Sample size                               10719  ...            10719
Final log likelihood                  -8936.217  ...        -8976.551
Akaike Information Criterion           17888.43  ...          17965.1
Bayesian Information Criterion         17946.67  ...         18008.78
asc_train (t-test)              -0.264  (-3.26)  ...  -0.652  (-9.77)
b_time_train (t-test)            -1.05  (-14.2)  ...
b_cost_train (t-test)               -1.7  (-14)  ...           0  (0)
b_time_swissmetro (t-test)      -0.404  (-6.14)  ...
b_cost_swissmetro (t-test)       -1.27  (-16.3)  ...           0  (0)
asc_car (t-test)                -0.412  (-5.09)  ...  0.0162  (0.293)
b_time_car (t-test)              -0.931  (-7.8)  ...
b_cost_car (t-test)                -1.1  (-7.8)  ...           0  (0)
b_time (t-test)                                  ...   -1.28  (-17.4)
b_cost (t-test)                                  ...

[15 rows x 3 columns]

Glossary.

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

Total running time of the script: (0 minutes 4.156 seconds)

Gallery generated by Sphinx-Gallery