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Nested logit¶
Estimation of a nested logit model using sampling of alternatives.
Michel Bierlaire Sat Jul 26 2025, 13:01:22
import pandas as pd
from alternatives import ID_COLUMN, all_alternatives, alternatives, asian, partitions
from compare import compare
from IPython.core.display_functions import display
from specification_sampling import V, combined_variables
import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta
from biogeme.nests import NestsForNestedLogit, OneNestForNestedLogit
from biogeme.results_processing import (
EstimationResults,
get_pandas_estimated_parameters,
)
from biogeme.sampling_of_alternatives import (
ChoiceSetsGeneration,
GenerateModel,
SamplingContext,
generate_segment_size,
)
from biogeme.tools import timeit
logger = blog.get_screen_logger(level=blog.INFO)
SAMPLE_SIZE = 20 # out of 100
SAMPLE_SIZE_MEV = 33 # out of 33
CHOICE_COLUMN = 'nested_0'
PARTITION = 'downtown'
MEV_PARTITION = 'uniform_asian'
MODEL_NAME = f'nested_{PARTITION}_{SAMPLE_SIZE}'
FILE_NAME = f'{MODEL_NAME}.dat'
the_partition = partitions.get(PARTITION)
if the_partition is None:
raise ValueError(f'Unknown partition: {PARTITION}')
segment_sizes = generate_segment_size(SAMPLE_SIZE, the_partition.number_of_segments())
We use all alternatives in the nest.
mev_partition = partitions.get(MEV_PARTITION)
if mev_partition is None:
raise ValueError(f'Unknown partition: {MEV_PARTITION}')
mev_segment_sizes = [SAMPLE_SIZE_MEV]
observations = pd.read_csv('obs_choice.dat')
context = SamplingContext(
the_partition=the_partition,
sample_sizes=segment_sizes,
individuals=observations,
choice_column=CHOICE_COLUMN,
alternatives=alternatives,
id_column=ID_COLUMN,
biogeme_file_name=FILE_NAME,
utility_function=V,
combined_variables=combined_variables,
mev_partition=mev_partition,
mev_sample_sizes=mev_segment_sizes,
)
logger.info(context.reporting())
Size of the choice set: 100
Main partition: 2 segment(s) of size 46, 54
Main sample: 20: 10/46, 10/54
Nbr of MEV alternatives: 33
MEV partition: 1 segment(s) of size 33
MEV sample: 33: 33/33
the_data_generation = ChoiceSetsGeneration(context=context)
the_model_generation = GenerateModel(context=context)
biogeme_database = the_data_generation.sample_and_merge(recycle=False)
Generating 20 + 33 alternatives for 10000 observations
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File nested_downtown_20.dat has been created.
Definition of the nest.
mu_asian = Beta('mu_asian', 1.0, 1.0, None, 0)
nest_asian = OneNestForNestedLogit(
nest_param=mu_asian, list_of_alternatives=asian, name='asian'
)
nests = NestsForNestedLogit(
choice_set=all_alternatives,
tuple_of_nests=(nest_asian,),
)
The following elements do not appear in any nest and are assumed each to be alone in a separate nest: {2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 39, 41, 42, 43, 44, 46, 48, 49, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 73, 74, 75, 77, 82, 83, 84, 85, 86, 88, 90, 93, 95, 96, 97, 99}. If it is not the intention, check the assignment of alternatives to nests.
log_probability = the_model_generation.get_nested_logit(nests)
the_biogeme = BIOGEME(biogeme_database, log_probability)
the_biogeme.model_name = MODEL_NAME
Biogeme parameters read from biogeme.toml.
Calculate the null log likelihood for reporting.
the_biogeme.calculate_null_loglikelihood(
{i: 1 for i in range(context.total_sample_size)}
)
-29957.32273553991
Estimate the parameters.
try:
results = EstimationResults.from_yaml_file(
filename=f'saved_results/{the_biogeme.model_name}.yaml'
)
except FileNotFoundError:
with timeit(f'Estimate of model {the_biogeme.model_name}'):
results = the_biogeme.estimate()
print(results.short_summary())
Results for model nested_downtown_20
Nbr of parameters: 12
Sample size: 10000
Excluded data: 0
Null log likelihood: -29957.32
Final log likelihood: -22988.55
Likelihood ratio test (null): 13937.55
Rho square (null): 0.233
Rho bar square (null): 0.232
Akaike Information Criterion: 46001.09
Bayesian Information Criterion: 46087.62
parameters_tables = get_pandas_estimated_parameters(estimation_results=results)
estimated_parameters = parameters_tables['Estimated parameters']
display(estimated_parameters)
Name Value Robust std err. Robust t-stat. Robust p-value
0 beta_rating 0.767500 0.015274 50.248559 0.0
1 beta_price -0.402806 0.012340 -32.641652 0.0
2 beta_chinese 0.649011 0.070900 9.153916 0.0
3 beta_japanese 1.213496 0.053821 22.546799 0.0
4 beta_korean 0.662360 0.061760 10.724798 0.0
5 beta_indian 0.938903 0.063494 14.787377 0.0
6 beta_french 0.729052 0.049069 14.857732 0.0
7 beta_mexican 1.193994 0.029053 41.096749 0.0
8 beta_lebanese 0.738656 0.049844 14.819238 0.0
9 beta_ethiopian 0.493428 0.040229 12.265577 0.0
10 beta_log_dist -0.600718 0.012805 -46.913354 0.0
11 mu_asian 2.008861 0.058474 34.355009 0.0
df, msg = compare(estimated_parameters)
print(df)
Name True Value Estimated Value T-Test
0 beta_rating 0.75 0.767500 -1.145712
1 beta_price -0.40 -0.402806 0.227386
2 beta_chinese 0.75 0.649011 1.424398
3 beta_japanese 1.25 1.213496 0.678244
4 beta_korean 0.75 0.662360 1.419052
5 beta_indian 1.00 0.938903 0.962250
6 beta_french 0.75 0.729052 0.426912
7 beta_mexican 1.25 1.193994 1.927709
8 beta_lebanese 0.75 0.738656 0.227592
9 beta_ethiopian 0.50 0.493428 0.163373
10 beta_log_dist -0.60 -0.600718 0.056103
11 mu_asian 2.00 2.008861 -0.151546
print(msg)
Parameters not estimated: ['mu_downtown']
Total running time of the script: (0 minutes 46.944 seconds)