statsmodels.base.model.LikelihoodModelResults.f_test¶
-
LikelihoodModelResults.
f_test
(r_matrix, cov_p=None, scale=1.0, invcov=None)[source]¶ Compute the F-test for a joint linear hypothesis.
This is a special case of wald_test that always uses the F distribution.
- Parameters
- r_matrix{array_like,
str
,tuple
} One of:
array : An r x k array where r is the number of restrictions to test and k is the number of regressors. 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),
q
can be either a scalar or a length k row vector.
- cov_parray_like,
optional
An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used.
- scale
float
,optional
Default is 1.0 for no scaling.
Deprecated since version 0.10.0.
- invcovarray_like,
optional
A q x q array to specify an inverse covariance matrix based on a restrictions matrix.
- r_matrix{array_like,
- Returns
ContrastResults
The results for the test are attributes of this results instance.
See also
t_test
Perform a single hypothesis test.
wald_test
Perform a Wald-test using a quadratic form.
statsmodels.stats.contrast.ContrastResults
Test results.
patsy.DesignInfo.linear_constraint
Specify a linear constraint.
Notes
The matrix r_matrix is assumed to be non-singular. More precisely,
r_matrix (pX pX.T) r_matrix.T
is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full.
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() >>> A = np.identity(len(results.params)) >>> A = A[1:,:]
This tests that each coefficient is jointly statistically significantly different from zero.
>>> print(results.f_test(A)) <F test: F=array([[ 330.28533923]]), p=4.984030528700946e-10, df_denom=9, df_num=6>
Compare this to
>>> results.fvalue 330.2853392346658 >>> results.f_pvalue 4.98403096572e-10
>>> B = np.array(([0,0,1,-1,0,0,0],[0,0,0,0,0,1,-1]))
This tests that the coefficient on the 2nd and 3rd regressors are equal and jointly that the coefficient on the 5th and 6th regressors are equal.
>>> print(results.f_test(B)) <F test: F=array([[ 9.74046187]]), p=0.005605288531708235, df_denom=9, df_num=2>
Alternatively, you can specify the hypothesis tests using a string
>>> from statsmodels.datasets import longley >>> from statsmodels.formula.api import ols >>> dta = 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)' >>> f_test = results.f_test(hypotheses) >>> print(f_test) <F test: F=array([[ 144.17976065]]), p=6.322026217355609e-08, df_denom=9, df_num=3>