def inverse_deriv2(self, z):
"""
Second derivative of the inverse link function g^(-1)(z).
Parameters
----------
z : array_like
`z` is usually the linear predictor for a GLM or GEE model.
Returns
-------
g^(-1)''(z) : ndarray
The value of the second derivative of the inverse of the link
function
Notes
-----
This method should be overwritten by subclasses.
The inherited method is implemented through numerical differentiation.
"""
from statsmodels.tools.numdiff import _approx_fprime_scalar
z = np.atleast_1d(z)
# Note: special function for norm.ppf does not support complex
return _approx_fprime_scalar(z, self.inverse_deriv, centered=True)
def _deriv_score_obs_dendog(self, params):
"""derivative of score_obs w.r.t. endog
Parameters
----------
params : ndarray
parameter at which score is evaluated
Returns
-------
derivative : ndarray_2d
The derivative of the score_obs with respect to endog.
"""
raise NotImplementedError
# The below currently does not work, discontinuity at zero
# see https://github.com/statsmodels/statsmodels/pull/7951#issuecomment-996355875 # noqa
from statsmodels.tools.numdiff import _approx_fprime_scalar
endog_original = self.endog
def f(y):
if y.ndim == 2 and y.shape[1] == 1:
y = y[:, 0]
self.endog = y
self.model_main.endog = y
sf = self.score_obs(params)
self.endog = endog_original
self.model_main.endog = endog_original
return sf
ds = _approx_fprime_scalar(self.endog[:, None], f, epsilon=1e-2)
return ds
def deriv2_numdiff(self, p):
"""
Second derivative of the link function g''(p)
implemented through numerical differentiation
"""
from statsmodels.tools.numdiff import _approx_fprime_scalar
p = np.atleast_1d(p)
# Note: special function for norm.ppf does not support complex
return _approx_fprime_scalar(p, self.deriv, centered=True)
def test_vectorized():
def f(x):
return 2 * x
desired = np.array([2, 2])
# vectorized parameter, column vector
p = np.array([[1, 2]]).T
assert_allclose(_approx_fprime_scalar(p, f), desired[:, None], rtol=1e-8)
assert_allclose(_approx_fprime_scalar(p.squeeze(), f), desired, rtol=1e-8)
assert_allclose(_approx_fprime_cs_scalar(p, f),
desired[:, None],
rtol=1e-8)
assert_allclose(_approx_fprime_cs_scalar(p.squeeze(), f),
desired,
rtol=1e-8)
# check 2-d row, see #7680
# not allowed/implemented for approx_fprime, raises broadcast ValueError
# assert_allclose(approx_fprime(p.T, f), desired, rtol=1e-8)
# similar as used in MarkovSwitching unit test
assert_allclose(approx_fprime_cs(p.T, f).squeeze(), desired, rtol=1e-8)