statsmodels.base.model.LikelihoodModelResults.t_test

method

LikelihoodModelResults.t_test(r_matrix, cov_p=None, scale=None, use_t=None)

Compute a t-test for a each linear hypothesis of the form Rb = q

Parameters

r_matrixarray-like, str, tuple

• array : If an array is given, a p x k 2d array or length k 1d array specifying the linear restrictions. It is assumed that the linear combination is equal to zero.

• str : The full hypotheses to test can be given as a string. See the examples.

• tuple : A tuple of arrays in the form (R, q). If q is given, can be either a scalar or a length p row vector.

cov_parray-like, optional

An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used.

scalefloat, optional

Deprecated since version 0.10.0.

An optional scale to use. Default is the scale specified by the model fit.

use_tbool, optional

If use_t is None, then the default of the model is used. If use_t is True, then the p-values are based on the t distribution. If use_t is False, then the p-values are based on the normal distribution.

Returns

resContrastResults instance

The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in summary().

See also

tvalues

individual t statistics

f_test

for F tests

patsy.DesignInfo.linear_constraint

Examples

>>> import numpy as np
>>> import statsmodels.api as sm
>>> data = sm.datasets.longley.load(as_pandas=False)
>>> data.exog = sm.add_constant(data.exog)
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> r = np.zeros_like(results.params)
>>> r[5:] = [1,-1]
>>> print(r)
[ 0.  0.  0.  0.  0.  1. -1.]

r tests that the coefficients on the 5th and 6th independent variable are the same.

>>> T_test = results.t_test(r)
>>> print(T_test)
                             Test for Constraints
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
c0         -1829.2026    455.391     -4.017      0.003   -2859.368    -799.037
==============================================================================
>>> T_test.effect
-1829.2025687192481
>>> T_test.sd
455.39079425193762
>>> T_test.tvalue
-4.0167754636411717
>>> T_test.pvalue
0.0015163772380899498

Alternatively, you can specify the hypothesis tests using a string

>>> from statsmodels.formula.api import ols
>>> dta = sm.datasets.longley.load_pandas().data
>>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
>>> results = ols(formula, dta).fit()
>>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1'
>>> t_test = results.t_test(hypotheses)
>>> print(t_test)
                             Test for Constraints
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
c0            15.0977     84.937      0.178      0.863    -177.042     207.238
c1            -2.0202      0.488     -8.231      0.000      -3.125      -0.915
c2             1.0001      0.249      0.000      1.000       0.437       1.563
==============================================================================