Base model

Logit model.

author:

Michel Bierlaire, EPFL

date:

Thu Jul 13 16:18:10 2023

import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta
from IPython.core.display_functions import display

from biogeme.data.swissmetro import (
    read_data,
    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)
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 = 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)

Read the data

database = read_data()

Create the Biogeme object.

the_biogeme = bio.BIOGEME(database, logprob)
the_biogeme.modelName = 'b00logit'
the_biogeme.generate_html = False
the_biogeme.generate_pickle = False

File biogeme.toml has been created

Calculate the null log likelihood for reporting.

the_biogeme.calculate_null_loglikelihood(av)

np.float64(-11093.62734528626)

Estimate the parameters

results = the_biogeme.estimate()

print(results.short_summary())

Results for model b00logit
Nbr of parameters:              4
Sample size:                    10719
Excluded data:                  9
Null log likelihood:            -11093.63
Final log likelihood:           -8670.164
Likelihood ratio test (null):           4846.927
Rho square (null):                      0.218
Rho bar square (null):                  0.218
Akaike Information Criterion:   17348.33
Bayesian Information Criterion: 17377.45

Get the results in a pandas table

pandas_results = results.get_estimated_parameters()
display(pandas_results)

              Value  Rob. Std err  Rob. t-test  Rob. p-value
ASC_CAR    0.015903      0.037081     0.428887      0.668006
ASC_TRAIN -0.652484      0.054375   -11.999761      0.000000
B_COST    -0.789434      0.050943   -15.496572      0.000000
B_TIME    -1.277788      0.065558   -19.490834      0.000000