Re-estimate the Pareto optimal models

The assisted specification algorithm generates a file containg the pareto optimal specification. This script is designed to re-estimate the Pareto optimal models. The catalog of specifications is defined in Specification of a catalog of models .

author:

Michel Bierlaire, EPFL

date:

Wed Apr 12 17:25:41 2023

try:
    import matplotlib.pyplot as plt

    can_plot = True
except ModuleNotFoundError:
    can_plot = False
from biogeme.assisted import ParetoPostProcessing
from biogeme.results import compile_estimation_results
from plot_b22multiple_models_spec import the_biogeme

PARETO_FILE_NAME = 'saved_results/b22multiple_models.pareto'

CSV_FILE = 'b22process_pareto.csv'
SEP_CSV = ','

The constructor of the Pareto post processing object takes two arguments:

• the biogeme object,

• the name of the file where the algorithm has stored the estimated models.

the_pareto_post = ParetoPostProcessing(
    biogeme_object=the_biogeme,
    pareto_file_name=PARETO_FILE_NAME,
)

the_pareto_post.log_statistics()

all_results = the_pareto_post.reestimate(recycle=True)

summary, description = compile_estimation_results(all_results, use_short_names=True)
print(summary)

                                   Model_000000  ...     Model_000005
Number of estimated parameters                8  ...                6
Sample size                                6768  ...             6768
Final log likelihood               -4834.225553  ...     -4958.518685
Akaike Information Criterion        9684.451106  ...      9929.037369
Bayesian Information Criterion      9739.010793  ...      9969.957135
ASC_CAR (t-test)                -0.619  (-5.91)  ...  -0.153  (-2.64)
ASC_CAR_male (t-test)              0.49  (4.55)  ...
ASC_CAR_with_ga (t-test)         -2.01  (-9.67)  ...     1.16  (5.03)
ASC_TRAIN (t-test)               -0.475  (-4.9)  ...     -1.14  (-14)
ASC_TRAIN_male (t-test)          -1.11  (-13.2)  ...
ASC_TRAIN_with_ga (t-test)         2.03  (22.4)  ...     2.07  (23.7)
B_COST (t-test)                    -1.47  (-18)  ...   -2.79  (-17.2)
B_TIME (t-test)                    -2.95  (-16)  ...     -3.11  (-17)
lambda_TT (t-test)                               ...
lambda_COST (t-test)                             ...
B_HEADWAY (t-test)                               ...

[16 rows x 6 columns]

print(f'Summary table available in {CSV_FILE}')
summary.to_csv(CSV_FILE, sep=SEP_CSV)

Summary table available in b22process_pareto.csv

Explanation of the short names of the models.

with open(CSV_FILE, 'a', encoding='utf-8') as f:
    print('\n\n', file=f)
    for k, v in description.items():
        if k != v:
            print(f'{k}: {v}')
            print(f'{k}{SEP_CSV}{v}', file=f)

Model_000000: ASC:no_seg;TRAIN_COST_catalog:sqrt;TRAIN_HEADWAY_catalog:without_headway;TRAIN_TT_catalog:sqrt
Model_000001: ASC:MALE-GA;TRAIN_COST_catalog:log;TRAIN_HEADWAY_catalog:with_headway;TRAIN_TT_catalog:log
Model_000002: ASC:GA;TRAIN_COST_catalog:log;TRAIN_HEADWAY_catalog:with_headway;TRAIN_TT_catalog:log
Model_000003: ASC:GA;TRAIN_COST_catalog:sqrt;TRAIN_HEADWAY_catalog:without_headway;TRAIN_TT_catalog:sqrt
Model_000004: ASC:MALE-GA;TRAIN_COST_catalog:log;TRAIN_HEADWAY_catalog:with_headway;TRAIN_TT_catalog:boxcox
Model_000005: ASC:MALE-GA;TRAIN_COST_catalog:sqrt;TRAIN_HEADWAY_catalog:without_headway;TRAIN_TT_catalog:sqrt

The following plot illustrates all models that have been estimated. Each dot corresponds to a model. The x-coordinate corresponds to the Akaike Information Criterion (AIC). The y-coordinate corresponds to the Bayesian Information Criterion (BIC). Note that there is a third objective that does not appear on this picture: the number of parameters. If the shape of the dot is a circle, it means that it corresponds to a Pareto optimal model. If the shape is a cross, it means that the model has been Pareto optimal at some point during the algorithm and later removed as a new model dominating it has been found. If the shape is a start, it means that the model has been deemed invalid.

if can_plot:
    _ = the_pareto_post.plot(label_x='AIC', label_y='BIC')
    plt.show()

It is possible to plot two different objectives: AIC and number of parameters.

if can_plot:
    _ = the_pareto_post.plot(
        objective_x=0, objective_y=2, label_x='AIC', label_y='Number of parameters'
    )
    plt.show()

It is possible to plot two different objectives: BIC and number of parameters.

if can_plot:
    _ = the_pareto_post.plot(
        objective_x=1, objective_y=2, label_x='BIC', label_y='Number of parameters'
    )
    plt.show()