28. Explicit parameter overrides in a simple model

This example illustrates the preprocessing API used to control parameters in an expression. The override is applied before the expression is passed to BIOGEME; estimation itself is unchanged.

Two types of control are shown:

• b_cost is replaced by a fixed Beta with a user-supplied initial value and bounds;

• asc_train is replaced by Numeric(0), so it is no longer an estimated parameter.

The same mechanism can later be used with parameters generated by catalogs, assisted specification, or latent-variable builders.

Michel Bierlaire, EPFL

from swissmetro_data import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    database,
)

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import (
    Beta,
    Numeric,
    ParameterOverrides,
    apply_parameter_overrides,
)
from biogeme.models import loglogit

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example plot_b28_parameter_overrides.py')

Example plot_b28_parameter_overrides.py

Define the ordinary multinomial-logit specification.

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)

v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED

utilities = {1: v_train, 2: v_swissmetro, 3: v_car}
availability = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}
log_probability = loglogit(utilities, availability, CHOICE)

Explicitly control parameters before creating the BIOGEME object. The key is the original Beta name. A replacement can be a full Beta definition or any other valid Biogeme expression.

overrides = ParameterOverrides()
overrides.set('b_cost', Beta('b_cost', -1.0, -10.0, 0.0, 1))
overrides.set('asc_train', Numeric(0))

log_probability = apply_parameter_overrides(log_probability, overrides)

Estimate the resulting model.

biogeme = BIOGEME(database, log_probability)
biogeme.model_name = 'b28_parameter_overrides'
results = biogeme.estimate()

print(results.short_summary())
print(results.get_beta_values())

Biogeme parameters read from biogeme.toml.
*** Initial values of the parameters are obtained from the file __b28_parameter_overrides.iter
Cannot read file __b28_parameter_overrides.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.          b_time         asc_car     Function    Relgrad   Radius      Rho
    0              -1           -0.22      5.7e+03      0.095       10      1.1   ++
    1            -1.7            0.13      5.4e+03      0.026    1e+02      1.1   ++
    2            -1.8            0.19      5.4e+03     0.0013    1e+03        1   ++
    3            -1.8            0.19      5.4e+03    2.9e-06    1e+03        1   ++
Optimization algorithm has converged.
Relative gradient: 2.9461076069227843e-06
Cause of termination: Relative gradient = 2.9e-06 <= 6.1e-06
Number of function evaluations: 13
Number of gradient evaluations: 9
Number of hessian evaluations: 4
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 4
Proportion of Hessian calculation: 4/4 = 100.0%
Optimization time: 0:00:01.913543
Optimization is complete. Save recoverable results in b28_parameter_overrides.yaml.
File b28_parameter_overrides.yaml has been generated.
Calculate final gradient and BHHH
File b28_parameter_overrides.yaml has been generated.
Calculate second derivatives
File b28_parameter_overrides.yaml has been generated.
File b28_parameter_overrides.html has been generated.
File b28_parameter_overrides.yaml has been generated.
Results for model b28_parameter_overrides
Nbr of parameters:              2
Sample size:                    6768
Excluded data:                  3960
Final log likelihood:           -5415.079
Akaike Information Criterion:   10834.16
Bayesian Information Criterion: 10847.8

{'b_time': -1.8213472801478152, 'asc_car': 0.19347324604661698}