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Logit model
Estimation of a logit model with several algorithms.
- author:
Michel Bierlaire, EPFL
- date:
Tue Nov 7 17:00:09 2023
import itertools
import pandas as pd
from biogeme.tools import format_timedelta
import biogeme.biogeme as bio
from biogeme import models
import biogeme.exceptions as excep
from biogeme.expressions import Beta
See the data processing script: Data preparation for Swissmetro.
from swissmetro_data import (
database,
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,
)
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.
V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * 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)
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 = pd.DataFrame(
columns=[
'LogLikelihood',
'GradientNorm',
'Optimization time',
'TerminationCause',
'Status',
]
)
for infeasible_cg, initial_radius, second_derivatives in itertools.product(
infeasible_cg_values, initial_radius_values, second_derivatives_values
):
# Create the Biogeme object
the_biogeme = bio.BIOGEME(database, logprob, parameter_file='few_draws.toml')
# We set the parameters of the optimization algorithm
the_biogeme.infeasible_cg = infeasible_cg
the_biogeme.initial_radius = initial_radius
the_biogeme.second_derivatives = second_derivatives
# We cancel the generation of the outputfiles
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False
name = (
f'cg_{infeasible_cg}_radius_{initial_radius}_second_deriv_{second_derivatives}'
)
the_biogeme.modelName = 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()
opt_time = format_timedelta(
results[name].data.optimizationMessages["Optimization time"]
)
result_data.update(
{
'LogLikelihood': results[name].data.logLike,
'GradientNorm': results[name].data.gradientNorm,
'Optimization time': opt_time,
'TerminationCause': results[name].data.optimizationMessages[
"Cause of termination"
],
}
)
except excep.BiogemeError as e:
print(e)
result_data.update(
{
'Status': 'Failed',
'LogLikelihood': None,
'GradientNorm': None,
'Optimization time': None,
'TerminationCause': str(e),
}
)
results[name] = None
summary = pd.concat([summary, pd.DataFrame([result_data])], ignore_index=True)
/Users/bierlair/OnlineFiles/FilesOnGoogleDrive/github/biogeme/docs/examples/swissmetro/plot_b01logit_all_algos.py:146: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.
summary = pd.concat([summary, pd.DataFrame([result_data])], ignore_index=True)
summary
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 2.593 seconds)