Note
Go to the end to download the full example code.
Logit¶
Estimation of a logit model using sampling of alternatives.
Michel Bierlaire Fri Jul 25 2025, 17:36:23
import pandas as pd
from alternatives import ID_COLUMN, alternatives, 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.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
ID rating price ... rest_lon distance downtown
0 0 1 4 ... 42.220972 71.735518 1.0
1 1 2 2 ... 50.549434 106.267205 0.0
2 2 3 3 ... 97.830520 136.298409 0.0
3 3 4 1 ... 69.152206 85.941147 0.0
4 4 4 3 ... 89.145620 96.773021 0.0
.. .. ... ... ... ... ... ...
95 95 4 3 ... 9.511387 84.166441 0.0
96 96 1 1 ... 92.144641 95.601366 0.0
97 97 4 2 ... 27.657518 30.440555 1.0
98 98 4 4 ... 32.303213 45.027143 1.0
99 99 4 1 ... 13.672495 25.703295 1.0
[100 rows x 16 columns]
Number of asian restaurants: 33
logger = blog.get_screen_logger(level=blog.INFO)
The data file contains several columns associated with synthetic choices. Here we arbitrarily select logit_4.
CHOICE_COLUMN = 'logit_4'
SAMPLE_SIZE = 10
PARTITION = 'asian'
MODEL_NAME = f'logit_{PARTITION}_{SAMPLE_SIZE}_alt'
FILE_NAME = f'{MODEL_NAME}.dat'
OBS_FILE = 'obs_choice.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())
observations = pd.read_csv(OBS_FILE)
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,
)
logger.info(context.reporting())
Size of the choice set: 100
Main partition: 2 segment(s) of size 33, 67
Main sample: 10: 5/33, 5/67
the_data_generation = ChoiceSetsGeneration(context=context)
the_model_generation = GenerateModel(context=context)
biogeme_database = the_data_generation.sample_and_merge(recycle=False)
Generating 10 + 0 alternatives for 10000 observations
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Define new variables
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File logit_asian_10_alt.dat has been created.
logprob = the_model_generation.get_logit()
the_biogeme = BIOGEME(biogeme_database, logprob)
the_biogeme.modelName = MODEL_NAME
Default values of the Biogeme parameters are used.
File biogeme.toml has been created
/Users/bierlair/MyFiles/github/biogeme/docs/source/examples/sampling/plot_b01logit.py:88: DeprecationWarning: 'modelName' is deprecated. Please use 'model_name' instead.
the_biogeme.modelName = MODEL_NAME
Calculate the null log likelihood for reporting.
the_biogeme.calculate_null_loglikelihood({i: 1 for i in range(SAMPLE_SIZE)})
-23025.850929940458
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 logit_asian_10_alt
Nbr of parameters: 11
Sample size: 10000
Excluded data: 0
Null log likelihood: -23025.85
Final log likelihood: -18461.47
Likelihood ratio test (null): 9128.762
Rho square (null): 0.198
Rho bar square (null): 0.198
Akaike Information Criterion: 36944.94
Bayesian Information Criterion: 37024.25
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 0.745578 0.015276 48.807683 0.0
1 beta_price -0.397459 0.012809 -31.030521 0.0
2 beta_chinese 0.604055 0.050288 12.011878 0.0
3 beta_japanese 1.193128 0.046261 25.791428 0.0
4 beta_korean 0.704947 0.042994 16.396519 0.0
5 beta_indian 0.895273 0.042947 20.846162 0.0
6 beta_french 0.663347 0.061966 10.704956 0.0
7 beta_mexican 1.190282 0.036481 32.627696 0.0
8 beta_lebanese 0.644906 0.062411 10.333229 0.0
9 beta_ethiopian 0.437794 0.050607 8.650927 0.0
10 beta_log_dist -0.582005 0.015147 -38.423348 0.0
df, msg = compare(estimated_parameters)
print(df)
Name True Value Estimated Value T-Test
0 beta_rating 0.75 0.745578 0.289480
1 beta_price -0.40 -0.397459 -0.198364
2 beta_chinese 0.75 0.604055 2.902167
3 beta_japanese 1.25 1.193128 1.229387
4 beta_korean 0.75 0.704947 1.047895
5 beta_indian 1.00 0.895273 2.438528
6 beta_french 0.75 0.663347 1.398390
7 beta_mexican 1.25 1.190282 1.636973
8 beta_lebanese 0.75 0.644906 1.683908
9 beta_ethiopian 0.50 0.437794 1.229203
10 beta_log_dist -0.60 -0.582005 -1.188012
print(msg)
Parameters not estimated: ['mu_asian', 'mu_downtown']
Total running time of the script: (0 minutes 18.793 seconds)