Note
Go to the end to download the full example code.
Logit model¶
Estimation of a logit model with several algorithms.
Michel Bierlaire, EPFL Wed Jun 18 2025, 10:03:04
import itertools
import pandas as pd
from IPython.core.display_functions import display
from biogeme.biogeme import BIOGEME
from biogeme.exceptions import BiogemeError
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.tools import format_timedelta
from tqdm import tqdm
See the data processing script: Data preparation for Swissmetro.
from swissmetro_data 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,
database,
)
Parameters to be estimated.
asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)
asc_sm = Beta('asc_sm', 0, None, None, 1)
b_time = Beta('b_time', 0, None, None, 0)
b_cost = Beta('b_cost', 0, None, None, 0)
Definition of the utility functions.
v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_sm = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED
Associate utility functions with the numbering of alternatives.
V = {1: v_train, 2: v_sm, 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.
logprob = loglogit(V, av, CHOICE)
Options for the optimization algorithm¶
The conjugate gradient iteration can be constrained to stay feasible, or not.
infeasible_cg_values = [True, False]
The radius of the first trust region is tested with three different values.
initial_radius_values = [0.1, 1.0, 10.0]
The percentage of iterations such that the analytical second derivatives is evaluated.
second_derivatives_values = [0.0, 0.5, 1.0]
We run the optimization algorithm with all possible combinations of the parameters.
The results are stored in a Pandas DataFrame called summary.
results = {}
summary_data = []
The first estimation is performed twice, to warm up the python code, so that the execution times are comparable
first = True
for infeasible_cg, initial_radius, second_derivatives in tqdm(
itertools.product(
infeasible_cg_values, initial_radius_values, second_derivatives_values
)
):
# Create the Biogeme object
the_biogeme = BIOGEME(
database,
logprob,
infeasible_cg=infeasible_cg,
initial_radius=initial_radius,
second_derivatives=second_derivatives,
generate_html=False,
generate_yaml=False,
)
name = (
f'cg_{infeasible_cg}_radius_{initial_radius}_second_deriv_{second_derivatives}'
)
the_biogeme.model_name = f'b05normal_mixture_algo_{name}'.strip()
result_data = {
'InfeasibleCG': infeasible_cg,
'InitialRadius': initial_radius,
'SecondDerivatives': second_derivatives,
'Status': 'Success', # Assume success unless an exception is caught
}
try:
results[name] = the_biogeme.estimate()
if first:
results[name] = the_biogeme.estimate()
first = False
opt_time = format_timedelta(
results[name].optimization_messages["Optimization time"]
)
result_data.update(
{
'LogLikelihood': results[name].final_log_likelihood,
'GradientNorm': results[name].gradient_norm,
'Number of draws': results[name].number_of_draws,
'Optimization time': opt_time,
'TerminationCause': results[name].optimization_messages[
"Cause of termination"
],
}
)
except BiogemeError as e:
print(e)
result_data.update(
{
'Status': 'Failed',
'LogLikelihood': None,
'GradientNorm': None,
'Number of draws': None,
'Optimization time': None,
'TerminationCause': str(e),
}
)
results[name] = None
summary_data.append(result_data)
summary = pd.DataFrame(summary_data)
0it [00:00, ?it/s]
1it [00:01, 1.39s/it]
2it [00:02, 1.03s/it]
3it [00:02, 1.08it/s]
4it [00:04, 1.03s/it]
5it [00:04, 1.10it/s]
6it [00:05, 1.19it/s]
7it [00:06, 1.20it/s]
8it [00:07, 1.25it/s]
9it [00:07, 1.29it/s]
10it [00:08, 1.33it/s]
11it [00:09, 1.34it/s]
12it [00:10, 1.29it/s]
13it [00:10, 1.33it/s]
14it [00:11, 1.35it/s]
15it [00:12, 1.37it/s]
16it [00:13, 1.31it/s]
17it [00:13, 1.25it/s]
18it [00:14, 1.29it/s]
18it [00:14, 1.23it/s]
display(summary)
InfeasibleCG ... TerminationCause
0 True ... Relative gradient = 8e-07 <= 6.1e-06
1 True ... Trust region is too small: 1.1920928955078126e-08
2 True ... Trust region is too small: 1.1920928955078126e-08
3 True ... Trust region is too small: 1.4901161193847656e-08
4 True ... Trust region is too small: 1.4901161193847656e-08
5 True ... Trust region is too small: 1.4901161193847656e-08
6 True ... Trust region is too small: 9.263433906788452e-09
7 True ... Trust region is too small: 9.263433906788452e-09
8 True ... Trust region is too small: 9.263433906788452e-09
9 False ... Trust region is too small: 1.1920928954904653e-08
10 False ... Trust region is too small: 1.1920928955077447e-08
11 False ... Trust region is too small: 1.1920928955077447e-08
12 False ... Trust region is too small: 1.4901161193847656e-08
13 False ... Trust region is too small: 1.4901161193847656e-08
14 False ... Trust region is too small: 1.4901161193847656e-08
15 False ... Trust region is too small: 9.263433906788452e-09
16 False ... Trust region is too small: 9.263433906788452e-09
17 False ... Trust region is too small: 9.263433906788452e-09
[18 rows x 9 columns]
SUMMARY_FILE = '01logit_all_algos.csv'
summary.to_csv(SUMMARY_FILE, index=False)
print(f'Summary reported in file {SUMMARY_FILE}')
Summary reported in file 01logit_all_algos.csv
Total running time of the script: (0 minutes 14.936 seconds)