statsmodels.regression.linear_model.OLSResults.el_test#

OLSResults.el_test(b0_vals, param_nums, return_weights=0, ret_params=0, method='nm', stochastic_exog=1, *, result_object=None)[source]#

Test single or joint hypotheses using Empirical Likelihood.

Parameters:

b0_vals1darray: The hypothesized value of the parameter to be tested.
param_nums1darray: The parameter number to be tested.
return_weightsbool: If true, returns the weights that optimize the likelihood ratio at b0_vals. The default is False.
ret_paramsbool: If true, returns the parameter vector that maximizes the likelihood ratio at b0_vals. Also returns the weights. The default is False. Has no effect when len(param_nums) == len(params), since there are then no nuisance parameters to report.
methodstr: Can either be ‘nm’ for Nelder-Mead or ‘powell’ for Powell. The optimization method that optimizes over nuisance parameters. The default is ‘nm’.
stochastic_exogbool: When True, the exogenous variables are assumed to be stochastic. When the regressors are nonstochastic, moment conditions are placed on the exogenous variables. Confidence intervals for stochastic regressors are at least as large as non-stochastic regressors. The default is True.
result_objectbool, optional: Flag indicating whether to return the results as an ELTestResult NamedTuple instead of a plain tuple. When the nuisance parameters are produced – ret_params is True and len(param_nums) < len(params) – the NamedTuple holds the same four elements as the legacy tuple, so it unpacks identically and is always returned, with no warning. Every other combination returns the shorter legacy tuple by default and issues a FutureWarning.

Deprecated since version 0.15.0: In release 0.16.0 or after July 2027, whichever is later, the default will change to returning an ELTestResult. Set result_object=True to opt in now, or result_object=False to silence the warning and keep the current return type. ELTestResult will become mandatory in release 0.17.0 or after July 2028, whichever is later.

Returns:

ELTestResult

A NamedTuple with fields statistic, pvalue, weights and nuisance_params (weights is None unless return_weights or ret_params is True; nuisance_params is None unless ret_params is True and len(param_nums) < len(params)). See ELTestResult.

This is returned whenever result_object=True. It is also returned by default when the nuisance parameters were produced – that is, when ret_params is True and len(param_nums) < len(params) – because the NamedTuple then has exactly the same four elements as the legacy tuple and so unpacks identically; that case is adopted silently.

Otherwise (the deprecated default), a plain tuple whose length

depends on return_weights and ret_params, made up of a subset

of:

llrfloat

-2 times the log-likelihood ratio for the hypothesized values.

pvalfloat

The p-value of the test.

weightsndarray, optional

The weights that optimize the likelihood ratio at b0_vals.

nuisance_paramsndarray, optional

The parameter vector that maximizes the likelihood ratio at b0_vals.

Examples

>>> import statsmodels.api as sm
>>> data = sm.datasets.stackloss.load()
>>> endog = data.endog
>>> exog = sm.add_constant(data.exog)
>>> model = sm.OLS(endog, exog)
>>> fitted = model.fit()
>>> fitted.params
>>> array([-39.91967442,   0.7156402 ,   1.29528612,  -0.15212252])
>>> fitted.rsquared
>>> 0.91357690446068196
>>> # Test that the slope on the first variable is 0
>>> fitted.el_test([0], [1])
>>> (27.248146353888796, 1.7894660442330235e-07)