DiscreteResults.f_test()

statsmodels.discrete.discrete_model.DiscreteResults.f_test

DiscreteResults.f_test(r_matrix, cov_p=None, scale=1.0, invcov=None)

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, or tuple 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_p : array-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. invcov : array-like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix.

Returns:

res : ContrastResults instance The results for the test are attributes of this results instance.

See also

statsmodels.stats.contrast.ContrastResults, wald_test, t_test, patsy.DesignInfo.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

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>>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load() >>> 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.

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>>> print(results.f_test(A)) <F contrast: F=330.28533923463488, p=4.98403052872e-10,  df_denom=9, df_num=6>

Compare this to

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>>> results.fvalue 330.2853392346658 >>> results.f_pvalue 4.98403096572e-10

1	>>> 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.

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>>> print(results.f_test(B)) <F contrast: F=9.740461873303655, p=0.00560528853174, df_denom=9,  df_num=2>

Alternatively, you can specify the hypothesis tests using a string

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>>> 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)