"""

3. Moneymetric and heteroscedastic specification
================================================

Although normalizing the scale to 1 is a common practice in random utility models, it is sometimes preferable to
normalize another parameter. For instance, normalizing the cost coefficient to -1 sets the units of the utility function
as currency units (CHF here), and the estimated coefficients are easily interpreted as willingness to pay. In that
case, the scale must be estimated.

 We also illustrate here a heteroscedastic specification, where a different scale is
 associated with different segments of the sample.

Michel Bierlaire, EPFL
Wed Jun 18 2025, 11:25:26

"""

from IPython.core.display_functions import display

from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

# %%
# See the data processing script: :ref:`swissmetro_data`.
from swissmetro_data import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    GROUP,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    database,
)

# %%
# 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', -1, None, None, 1)
scale_not_group3 = Beta('scale_not_group3', 1, 0.001, None, 0)
scale_group3 = Beta('scale_group3', 1, 0.001, None, 0)

# %%
# Definition of the utility functions.
v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED

# %%
# The scale is defined based on the group membership of each individual.
scale = (GROUP != 3) * scale_not_group3 + (GROUP == 3) * scale_group3

# %%
# Scale the utility functions, and associate them with the numbering
# of alternatives.
v = {1: scale * v_train, 2: scale * v_swissmetro, 3: scale * v_car}

# %%
# 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 = loglogit(v, av, CHOICE)

# %%
# These notes will be included as such in the report file.
USER_NOTES = (
    'Illustrates a moneymetric and heteroscedastic specification. A different scale is'
    ' associated with different segments of the sample. The utility function is expressed in CHF.'
)

# %%
# Create the Biogeme object.
the_biogeme = BIOGEME(database, logprob, user_notes=USER_NOTES)
the_biogeme.model_name = 'b03_scale'

# %%
# Estimate the parameters.
try:
    results = EstimationResults.from_yaml_file(
        filename=f'saved_results/{the_biogeme.model_name}.yaml'
    )
except FileNotFoundError:
    results = the_biogeme.estimate()

# %%
print(results.short_summary())

# %%
# Get the results in a pandas table
pandas_results = get_pandas_estimated_parameters(estimation_results=results)
display(pandas_results)