Calculation of individual level parameters

Calculation of the individual level parameters for the model defined in Mixture of logit models.

author:

Michel Bierlaire, EPFL

date:

Mon Apr 10 12:17:12 2023

import os
import pickle
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import Beta, bioDraws, MonteCarlo

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. The initial value is irrelevant.

ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
B_COST = Beta('B_COST', 0, None, None, 0)

Define a random parameter, normally distributed, designed to be used for Monte-Carlo simulation.

B_TIME = Beta('B_TIME', 0, None, None, 0)
B_TIME_S = Beta('B_TIME_S', 1, None, None, 0)
B_TIME_RND = B_TIME + B_TIME_S * bioDraws('b_time_rnd', 'NORMAL')

Define values for these parameters

beta_values = {
    'ASC_CAR': 0.137,
    'ASC_TRAIN': -0.402,
    'B_COST': -1.28,
    'B_TIME': -2.26,
    'B_TIME_S': 1.65,
}

Definition of the utility functions.

V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
V2 = B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
V3 = ASC_CAR + B_TIME_RND * 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}

Conditional on b_time_rnd, we have a logit model (called the kernel).

prob_chosen = models.logit(V, av, CHOICE)

Numerator and denominator of the formula for individual parameters.

numerator = MonteCarlo(B_TIME_RND * prob_chosen)
denominator = MonteCarlo(prob_chosen)
simulate = {
    'Numerator': numerator,
    'Denominator': denominator,
    'Choice': CHOICE,
}

The results are saved in a picke file. The next time the script is run, if the file exists, the results are simply loaded instead of being re-calcuated.

PICKLE_FILE = 'b19individual_level_parameters.pickle'
if os.path.isfile(PICKLE_FILE):
    with open(PICKLE_FILE, 'rb') as f:
        sim = pickle.load(f)
else:
    biosim = bio.BIOGEME(database, simulate)
    sim = biosim.simulate(beta_values)
    sim['Individual-level parameters'] = sim['Numerator'] / sim['Denominator']
    with open(PICKLE_FILE, 'wb') as f:
        pickle.dump(sim, f)

sim
Numerator Denominator Choice Individual-level parameters
0 -1.806244 0.636585 2.0 -2.837398
1 -1.683576 0.653032 2.0 -2.578092
2 -1.758933 0.614881 2.0 -2.860606
3 -1.118352 0.440239 2.0 -2.540333
4 -1.586545 0.624901 2.0 -2.538874
... ... ... ... ...
8446 -0.207631 0.165505 1.0 -1.254530
8447 -0.211674 0.152122 1.0 -1.391477
8448 -0.157355 0.150780 1.0 -1.043610
8449 -0.096541 0.146320 1.0 -0.659791
8450 -0.227840 0.175656 1.0 -1.297079

6768 rows × 4 columns



Total running time of the script: (0 minutes 1.258 seconds)

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