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20. Estimation of several modelsΒΆ
Example of the estimation of several specifications of the model.
Michel Bierlaire, EPFL Thu Jun 26 2025, 16:04:27
from biogeme.biogeme import BIOGEME
from biogeme.catalog import (
Catalog,
segmentation_catalogs,
)
from biogeme.expressions import Beta, log
from biogeme.models import loglogit
from biogeme.results_processing import (
compare_parameters,
compile_estimation_results,
pareto_optimal,
)
See the data processing script: Data preparation for Swissmetro.
from swissmetro_data import (
CAR_AV_SP,
CAR_CO_SCALED,
CAR_TT_SCALED,
CHOICE,
MALE,
SM_AV,
SM_COST_SCALED,
SM_TT_SCALED,
TRAIN_AV_SP,
TRAIN_COST_SCALED,
TRAIN_TT_SCALED,
database,
)
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)
segmentation_gender = database.generate_segmentation(
variable=MALE, mapping={0: 'female', 1: 'male'}
)
We define catalogs with two different specifications for the ASC_CAR: non segmented, and segmented.
asc_train_catalog, asc_car_catalog = segmentation_catalogs(
generic_name='asc',
beta_parameters=[asc_train, asc_car],
potential_segmentations=(segmentation_gender,),
maximum_number=1,
)
We now define a catalog with the log travel time as well as the travel time.
First for train
train_tt_catalog = Catalog.from_dict(
catalog_name='train_tt_catalog',
dict_of_expressions={
'linear': TRAIN_TT_SCALED,
'log': log(TRAIN_TT_SCALED),
},
)
Then for SM. But we require that the specification is the same as train by defining the same controller.
sm_tt_catalog = Catalog.from_dict(
catalog_name='sm_tt_catalog',
dict_of_expressions={
'linear': SM_TT_SCALED,
'log': log(SM_TT_SCALED),
},
controlled_by=train_tt_catalog.controlled_by,
)
Definition of the utility functions with linear cost.
v_train = asc_train_catalog + b_time * train_tt_catalog + b_cost * TRAIN_COST_SCALED
v_swissmetro = b_time * sm_tt_catalog + b_cost * SM_COST_SCALED
v_car = asc_car_catalog + b_time * CAR_TT_SCALED + b_cost * 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)
the_biogeme: BIOGEME = BIOGEME(database=database, formulas=log_probability)
the_biogeme.model_name = 'b20multiple_models'
dict_of_results = the_biogeme.estimate_catalog()
print(f'A total of {len(dict_of_results)} models have been estimated:')
for config, res in dict_of_results.items():
print(f'{config}: LL={res.final_log_likelihood:.2f} K={res.number_of_parameters}')
A total of 4 models have been estimated:
asc:no_seg;train_tt_catalog:linear: LL=-5331.25 K=4
asc:MALE;train_tt_catalog:linear: LL=-5187.98 K=6
asc:no_seg;train_tt_catalog:log: LL=-5350.59 K=4
asc:MALE;train_tt_catalog:log: LL=-5184.07 K=6
summary, description = compile_estimation_results(dict_of_results, use_short_names=True)
print(summary)
Model_000000 ... Model_000003
Number of estimated parameters 4 ... 6
Sample size 6768 ... 6768
Final log likelihood -5331.252 ... -5184.073
Akaike Information Criterion 10670.5 ... 10380.15
Bayesian Information Criterion 10697.78 ... 10421.07
asc_train (t-test) -0.701 (-8.49) ...
b_time (t-test) -1.28 (-12.3) ... -1.38 (-14.1)
b_cost (t-test) -1.08 (-15.9) ... -1.07 (-16.1)
asc_car (t-test) -0.155 (-2.66) ...
asc_train_ref (t-test) ... 0.183 (2.05)
asc_train_diff_male (t-test) ... -1.35 (-17.1)
asc_car_ref (t-test) ... 1.19 (7.3)
asc_car_diff_male (t-test) ... 0.261 (2.56)
[13 rows x 4 columns]
Explanation of the names of the models.
for k, v in description.items():
if k != v:
print(f'{k}: {v}')
Model_000000: asc:no_seg;train_tt_catalog:linear
Model_000001: asc:MALE;train_tt_catalog:linear
Model_000002: asc:no_seg;train_tt_catalog:log
Model_000003: asc:MALE;train_tt_catalog:log
non_dominated_models = pareto_optimal(dict_of_results)
print(f'Out of them, {len(non_dominated_models)} are non dominated.')
for config, res in non_dominated_models.items():
print(f'{config}')
Out of them, 2 are non dominated.
asc:no_seg;train_tt_catalog:linear
asc:MALE;train_tt_catalog:log
summary, description = compile_estimation_results(
non_dominated_models, use_short_names=False
)
print(summary)
asc:no_seg;train_tt_catalog:linear asc:MALE;train_tt_catalog:log
Number of estimated parameters 4 6
Sample size 6768 6768
Final log likelihood -5331.252 -5184.073
Akaike Information Criterion 10670.5 10380.15
Bayesian Information Criterion 10697.78 10421.07
asc_train (t-test) -0.701 (-8.49)
b_time (t-test) -1.28 (-12.3) -1.38 (-14.1)
b_cost (t-test) -1.08 (-15.9) -1.07 (-16.1)
asc_car (t-test) -0.155 (-2.66)
asc_train_ref (t-test) 0.183 (2.05)
asc_train_diff_male (t-test) -1.35 (-17.1)
asc_car_ref (t-test) 1.19 (7.3)
asc_car_diff_male (t-test) 0.261 (2.56)
It is possible to generate a LaTeX table comparing the results
latex_code = compare_parameters(estimation_results=dict_of_results)
print(latex_code)
\usepackage{longtable}
\usepackage{siunitx}
\sisetup{
parse-numbers=false, % Prevents automatic parsing (needed for parentheses & superscripts)
detect-inline-weight=math,% Ensures proper formatting in tables
tight-spacing=true % Keeps spacing consistent
}
\begin{longtable}{rlSSSS}
& & \multicolumn{1}{c}{asc:no_seg;train_tt_catalog:linear} & \multicolumn{1}{c}{asc:MALE;train_tt_catalog:linear} & \multicolumn{1}{c}{asc:no_seg;train_tt_catalog:log} & \multicolumn{1}{c}{asc:MALE;train_tt_catalog:log} \\
& Parameter name & \multicolumn{1}{c}{Coef./(SE)} & \multicolumn{1}{c}{Coef./(SE)} & \multicolumn{1}{c}{Coef./(SE)} & \multicolumn{1}{c}{Coef./(SE)} \\
\hline
0 &asc\_car& -0.155\textsuperscript{***} & & 1.43\textsuperscript{***} & \\
& &(0.0582) & &(0.153) & \\
1 &asc\_car\_diff\_male & & 0.309\textsuperscript{***} & & 0.261\textsuperscript{**} \\
& & &(0.102) & &(0.102) \\
2 &asc\_car\_ref & & -0.461\textsuperscript{***} & & 1.19\textsuperscript{***} \\
& & &(0.0973) & &(0.163) \\
3 &asc\_train& -0.701\textsuperscript{***} & & -0.727\textsuperscript{***} & \\
& &(0.0826) & &(0.0741) & \\
4 &asc\_train\_diff\_male & & -1.23\textsuperscript{***} & & -1.35\textsuperscript{***} \\
& & &(0.0792) & &(0.0789) \\
5 &asc\_train\_ref & & 0.0906 & & 0.183\textsuperscript{**} \\
& & &(0.0913) & &(0.089) \\
6 &b\_cost& -1.08\textsuperscript{***} & -1.08\textsuperscript{***} & -1.06\textsuperscript{***} & -1.07\textsuperscript{***} \\
& &(0.0682)&(0.067)&(0.067)&(0.0668) \\
7 &b\_time& -1.28\textsuperscript{***} & -1.25\textsuperscript{***} & -1.37\textsuperscript{***} & -1.38\textsuperscript{***} \\
& &(0.104)&(0.105)&(0.097)&(0.0981) \\
\hline
\multicolumn{2}{l}{Number of observations} &6768 & 6768 & 6768 & 6768 \\
\multicolumn{2}{l}{Number of parameters} &4 & 6 & 4 & 6 \\
\multicolumn{2}{l}{Akaike Information Criterion} &10670.5 & 10388.0 & 10709.2 & 10380.1 \\
\multicolumn{2}{l}{Bayesian Information Criterion} &10697.8 & 10428.9 & 10736.5 & 10421.1 \\
\hline
\multicolumn{4}{l}{\footnotesize Standard errors: \textsuperscript{***}: $p < 0.01$, \textsuperscript{**}: $p < 0.05$, \textsuperscript{*}: $p < 0.1$}
\end{longtable}
Total running time of the script: (0 minutes 3.516 seconds)