biogeme.results_processing

Examples of use of several functions.

This is designed for programmers who need examples of use of the functions of the module. The examples are designed to illustrate the syntax. They do not correspond to any meaningful model.

Michel Bierlaire Mon Oct 7 18:46:39 2024

import pandas as pd
from IPython.core.display_functions import display

from biogeme.biogeme import BIOGEME
from biogeme.database import Database
from biogeme.expressions import Beta, Variable, exp
from biogeme.results_processing import (
    EstimateVarianceCovariance,
    EstimationResults,
    calc_p_value,
    compile_estimation_results,
    get_f12,
    get_html_estimated_parameters,
    get_latex_estimated_parameters,
    get_pandas_correlation_results,
    get_pandas_estimated_parameters,
)
from biogeme.version import get_text

Version of Biogeme.

print(get_text())

Definition of a database

df = pd.DataFrame(
    {
        'Person': [1, 1, 1, 2, 2],
        'Exclude': [0, 0, 1, 0, 1],
        'Variable1': [1, 2, 3, 4, 5],
        'Variable2': [10, 20, 30, 40, 50],
        'Choice': [1, 2, 3, 1, 2],
        'Av1': [0, 1, 1, 1, 1],
        'Av2': [1, 1, 1, 1, 1],
        'Av3': [0, 1, 1, 1, 1],
    }
)
display(df)

my_data = Database('test', df)

Definition of various expressions

Variable1 = Variable('Variable1')
Variable2 = Variable('Variable2')
beta1 = Beta('beta1', -1.0, -3, 3, 0)
beta2 = Beta('beta2', 2.0, -3, 10, 0)
likelihood = -(beta1**2) * Variable1 - exp(beta2 * beta1) * Variable2 - beta2**4
simul = beta1 / Variable1 + beta2 / Variable2
dict_of_expressions = {'log_like': likelihood, 'beta1': beta1, 'simul': simul}

Creation of the BIOGEME object

my_biogeme = BIOGEME(my_data, dict_of_expressions, bootstrap_samples=100)
my_biogeme.model_name = 'simple_example'
results = my_biogeme.estimate(run_bootstrap=True)
print(results)

Dump results on a file

the_yaml_file = my_biogeme.yaml_filename
results.dump_yaml_file(filename=the_yaml_file)
print(the_yaml_file)

Results can be imported from a file previously generated

read_results = EstimationResults.from_yaml_file(filename=the_yaml_file)
print(read_results)

Results can be formatted in LaTeX

print(get_latex_estimated_parameters(estimation_results=read_results))

Results can be formatted in HTML

print(get_html_estimated_parameters(estimation_results=read_results))

General statistics, including a suggested format.

statistics = read_results.get_general_statistics()
display(statistics)

Estimated parameters as pandas dataframe

pandas_parameters = get_pandas_estimated_parameters(estimation_results=read_results)
display(pandas_parameters)

Correlation results

pandas_correlation = get_pandas_correlation_results(estimation_results=read_results)
display(pandas_correlation)

Obtain the values of the parameters

beta_values = read_results.get_beta_values()
display(beta_values)

Obtain the value of one or several specific parameters

some_beta_values = read_results.get_beta_values(my_betas=['beta2'])
display(some_beta_values)

Variance-covariance matrix (Rao-Cramer)

rao_cramer = read_results.get_variance_covariance_matrix(
    variance_covariance_type=EstimateVarianceCovariance.RAO_CRAMER
)
display(rao_cramer)

Variance-covariance matrix (robust)

robust = read_results.get_variance_covariance_matrix(
    variance_covariance_type=EstimateVarianceCovariance.ROBUST
)
display(robust)

Variance-covariance matrix (bootstrap)

bootstrap = read_results.get_variance_covariance_matrix(
    variance_covariance_type=EstimateVarianceCovariance.BOOTSTRAP
)
display(bootstrap)

Draws for sensitivity analysis are generated using bootstrapping. Any indicator can be generated by the model for each draw, and its empirical distribution can be investigated.

read_results.get_betas_for_sensitivity_analysis(['beta1', 'beta2'], size=10)

Results can be produced in the ALOGIT F12 format

print(get_f12(estimation_results=read_results))

Miscellaneous functions

Likelihood ratio test. Let’s first estimate a constrained model

beta2_constrained = Beta('beta2_constrained', 2.0, -3, 10, 1)
likelihood_constrained = (
    -(beta1**2) * Variable1
    - exp(beta2_constrained * beta1) * Variable2
    - beta2_constrained**4
)
my_biogeme_constrained = BIOGEME(my_data, likelihood_constrained)
my_biogeme_constrained.model_name = 'simple_example_constrained'
results_constrained = my_biogeme_constrained.estimate()
print(results_constrained.short_summary())

We can now perform a likelihood ratio test.

test_results = results.likelihood_ratio_test(results_constrained, 0.95)
print(test_results.message)
print(f'Statistic: {test_results.statistic}')
print(f'Threshold: {test_results.threshold}')

Calculation of the \(p\)-value

calc_p_value(1.96)

Compilation of results

dict_of_results = {'Model A': read_results, 'Model B': the_yaml_file}

df = compile_estimation_results(dict_of_results)
display(df)