Calculation of market shares

We use an estimated model to calculate market shares.

author:

Michel Bierlaire, EPFL

date:

Wed Apr 12 21:03:52 2023

import sys
from biogeme import models
import biogeme.biogeme as bio
from biogeme.exceptions import BiogemeError
import biogeme.results as res
from biogeme.data.optima import read_data, normalized_weight
from scenarios import scenario

Obtain the specification for the default scenario

V, nests, _, _ = scenario()

Obtain the expression for the choice probability of each alternative.

prob_PT = models.nested(V, None, nests, 0)
prob_CAR = models.nested(V, None, nests, 1)
prob_SM = models.nested(V, None, nests, 2)

Read the estimation results from the file

try:
    results = res.bioResults(pickle_file='saved_results/b02estimation.pickle')
except BiogemeError:
    sys.exit(
        'Run first the script b02simulation.py '
        'in order to generate the '
        'file b02estimation.pickle.'
    )

Read the database

database = read_data()

We now simulate the choice probabilities and the weight

simulate = {
    'weight': normalized_weight,
    'Prob. PT': prob_PT,
    'Prob. car': prob_CAR,
    'Prob. SM': prob_SM,
}

the_biogeme = bio.BIOGEME(database, simulate)
simulated_values = the_biogeme.simulate(results.get_beta_values())

We also calculate confidence intervals for the calculated quantities,

betas = the_biogeme.free_beta_names
b = results.get_betas_for_sensitivity_analysis(betas)
left, right = the_biogeme.confidence_intervals(b, 0.9)

Market shares are calculated using the weighted mean of the individual probabilities.

Alternative car

simulated_values['Weighted prob. car'] = (
    simulated_values['weight'] * simulated_values['Prob. car']
)
left['Weighted prob. car'] = left['weight'] * left['Prob. car']
right['Weighted prob. car'] = right['weight'] * right['Prob. car']

marketShare_car = simulated_values['Weighted prob. car'].mean()
marketShare_car_left = left['Weighted prob. car'].mean()
marketShare_car_right = right['Weighted prob. car'].mean()

Alternative public transportation

simulated_values['Weighted prob. PT'] = (
    simulated_values['weight'] * simulated_values['Prob. PT']
)
left['Weighted prob. PT'] = left['weight'] * left['Prob. PT']
right['Weighted prob. PT'] = right['weight'] * right['Prob. PT']

marketShare_PT = simulated_values['Weighted prob. PT'].mean()
marketShare_PT_left = left['Weighted prob. PT'].mean()
marketShare_PT_right = right['Weighted prob. PT'].mean()

Alternative slow modes

simulated_values['Weighted prob. SM'] = (
    simulated_values['weight'] * simulated_values['Prob. SM']
)
left['Weighted prob. SM'] = left['weight'] * left['Prob. SM']
right['Weighted prob. SM'] = right['weight'] * right['Prob. SM']

marketShare_SM = simulated_values['Weighted prob. SM'].mean()
marketShare_SM_left = left['Weighted prob. SM'].mean()
marketShare_SM_right = right['Weighted prob. SM'].mean()

Reporting.

Car.

print(
    f'Market share for car: {100*marketShare_car:.1f}% '
    f'[{100*marketShare_car_left:.1f}%, '
    f'{100*marketShare_car_right:.1f}%]'
)

Market share for car: 65.4% [62.2%, 69.1%]

Public transportation.

print(
    f'Market share for PT:  {100*marketShare_PT:.1f}% '
    f'[{100*marketShare_PT_left:.1f}%, '
    f'{100*marketShare_PT_right:.1f}%]'
)

Market share for PT:  27.6% [24.0%, 31.4%]

Slow modes.

print(
    f'Market share for SM:   {100*marketShare_SM:.1f}% '
    f'[{100*marketShare_SM_left:.1f}%, '
    f'{100*marketShare_SM_right:.1f}%]'
)

Market share for SM:   7.0% [4.3%, 9.3%]