WESML

Example of a logit model with Weighted Exogenous Sample Maximum Likelihood (WESML).

author:

Michel Bierlaire, EPFL

date:

Sun Apr 9 17:02:59 2023

import biogeme.biogeme as bio
from biogeme import models
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,
    GROUP,
)

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)

Definition of the weight.

weight = 8.890991e-01 * (1.0 * (GROUP == 2) + 1.2 * (GROUP == 3))

These notes will be included as such in the report file.

USER_NOTES = (
    'Example of a logit model with three alternatives: '
    'Train, Car and Swissmetro.'
    ' Weighted Exogenous Sample Maximum Likelihood estimator (WESML)'
)

Create the Biogeme object

formulas = {'log_like': logprob, 'weight': weight}
the_biogeme = bio.BIOGEME(database, formulas, user_notes=USER_NOTES)
the_biogeme.modelName = 'b02weight'

It is possible to control the generation of the HTML and the pickle .py. Note that these parameters can also be modified in the .TOML configuration file.

the_biogeme.generate_html = True
the_biogeme.generate_pickle = False

Estimate the parameters.

results = the_biogeme.estimate()
print(results.short_summary())

Results for model b02weight
Nbr of parameters:              4
Sample size:                    6768
Excluded data:                  3960
Final log likelihood:           -5273.743
Akaike Information Criterion:   10555.49
Bayesian Information Criterion: 10582.77

Get the results in a pandas table

pandas_results = results.get_estimated_parameters()
pandas_results

	Value	Rob. Std err	Rob. t-test	Rob. p-value
ASC_CAR	-0.114315	0.058312	-1.960402	0.049949
ASC_TRAIN	-0.756521	0.083257	-9.086524	0.000000
B_COST	-1.119658	0.067679	-16.543708	0.000000
B_TIME	-1.321529	0.103658	-12.748875	0.000000