def test_hess(self):
#NOTE: I had to overwrite this to lessen the tolerance
for test_params in self.params:
he = self.mod.hessian(test_params)
hefd = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hefd, decimal=DEC8)
#NOTE: notice the accuracy below and the epsilon changes
# this doesn't work well for score -> hessian with non-cs step
# it's a little better around the optimum
assert_almost_equal(he, hefd, decimal=7)
hefd = numdiff.approx_fprime(test_params, self.mod.score,
centered=True)
assert_almost_equal(he, hefd, decimal=4)
hefd = numdiff.approx_fprime(test_params, self.mod.score, 1e-9,
centered=False)
assert_almost_equal(he, hefd, decimal=2)
hescs = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hescs, decimal=DEC8)
hecs = numdiff.approx_hess_cs(test_params, self.mod.loglike)
assert_almost_equal(he, hecs, decimal=5)
#NOTE: these just don't work well
#hecs = numdiff.approx_hess1(test_params, self.mod.loglike, 1e-3)
#assert_almost_equal(he, hecs, decimal=1)
#hecs = numdiff.approx_hess2(test_params, self.mod.loglike, 1e-4)
#assert_almost_equal(he, hecs, decimal=0)
hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-4)
assert_almost_equal(he, hecs, decimal=0)
def test_hess_fun1_fd(self):
for test_params in self.params:
#hetrue = 0
hetrue = self.hesstrue(test_params)
if hetrue is not None: #Hessian does not work for 2d return of fun
fun = self.fun()
#default works, epsilon 1e-6 or 1e-8 is not precise enough
hefd = numdiff.approx_hess1(
test_params,
fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
#TODO: I reduced precision to DEC3 from DEC4 because of
# TestDerivativeFun
hefd = numdiff.approx_hess2(
test_params,
fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
hefd = numdiff.approx_hess3(
test_params,
fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
def test_hess(self):
#NOTE: I had to overwrite this to lessen the tolerance
for test_params in self.params:
he = self.mod.hessian(test_params)
hefd = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hefd, decimal=DEC8)
#NOTE: notice the accuracy below and the epsilon changes
# this does not work well for score -> hessian with non-cs step
# it's a little better around the optimum
assert_almost_equal(he, hefd, decimal=7)
hefd = numdiff.approx_fprime(test_params,
self.mod.score,
centered=True)
assert_almost_equal(he, hefd, decimal=4)
hefd = numdiff.approx_fprime(test_params,
self.mod.score,
1e-9,
centered=False)
assert_almost_equal(he, hefd, decimal=2)
hescs = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hescs, decimal=DEC8)
hecs = numdiff.approx_hess_cs(test_params, self.mod.loglike)
assert_almost_equal(he, hecs, decimal=5)
#NOTE: these just do not work well
#hecs = numdiff.approx_hess1(test_params, self.mod.loglike, 1e-3)
#assert_almost_equal(he, hecs, decimal=1)
#hecs = numdiff.approx_hess2(test_params, self.mod.loglike, 1e-4)
#assert_almost_equal(he, hecs, decimal=0)
hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-4)
assert_almost_equal(he, hecs, decimal=0)
def test_hess(self):
for test_params in self.params:
he = self.mod.hessian(test_params)
hefd = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hefd, decimal=DEC8)
#NOTE: notice the accuracy below
assert_almost_equal(he, hefd, decimal=7)
hefd = numdiff.approx_fprime(test_params,
self.mod.score,
centered=True)
assert_allclose(he, hefd, rtol=1e-9)
hefd = numdiff.approx_fprime(test_params,
self.mod.score,
centered=False)
assert_almost_equal(he, hefd, decimal=4)
hescs = numdiff.approx_fprime_cs(test_params.ravel(),
self.mod.score)
assert_allclose(he, hescs, rtol=1e-13)
hecs = numdiff.approx_hess_cs(test_params.ravel(),
self.mod.loglike)
assert_allclose(he, hecs, rtol=1e-9)
#NOTE: Look at the lack of precision - default epsilon not always
#best
grad = self.mod.score(test_params)
hecs, gradcs = numdiff.approx_hess1(test_params,
self.mod.loglike,
1e-6,
return_grad=True)
assert_almost_equal(he, hecs, decimal=1)
assert_almost_equal(grad, gradcs, decimal=1)
hecs, gradcs = numdiff.approx_hess2(test_params,
self.mod.loglike,
1e-4,
return_grad=True)
assert_almost_equal(he, hecs, decimal=3)
assert_almost_equal(grad, gradcs, decimal=1)
hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-5)
assert_almost_equal(he, hecs, decimal=4)
def test_hess_fun1_fd(self):
for test_params in self.params:
#hetrue = 0
hetrue = self.hesstrue(test_params)
if not hetrue is None: #Hessian doesn't work for 2d return of fun
fun = self.fun()
#default works, epsilon 1e-6 or 1e-8 is not precise enough
hefd = numdiff.approx_hess1(test_params, fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
#TODO: I reduced precision to DEC3 from DEC4 because of
# TestDerivativeFun
hefd = numdiff.approx_hess2(test_params, fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
hefd = numdiff.approx_hess3(test_params, fun, #epsilon=1e-8,
# TODO: should be kwds
args=self.args)
assert_almost_equal(hetrue, hefd, decimal=DEC3)
def test_hess(self):
for test_params in self.params:
he = self.mod.hessian(test_params)
hefd = numdiff.approx_fprime_cs(test_params, self.mod.score)
assert_almost_equal(he, hefd, decimal=DEC8)
#NOTE: notice the accuracy below
assert_almost_equal(he, hefd, decimal=7)
hefd = numdiff.approx_fprime(test_params, self.mod.score,
centered=True)
assert_allclose(he, hefd, rtol=1e-9)
hefd = numdiff.approx_fprime(test_params, self.mod.score,
centered=False)
assert_almost_equal(he, hefd, decimal=4)
hescs = numdiff.approx_fprime_cs(test_params.ravel(),
self.mod.score)
assert_allclose(he, hescs, rtol=1e-13)
hecs = numdiff.approx_hess_cs(test_params.ravel(),
self.mod.loglike)
assert_allclose(he, hecs, rtol=1e-9)
#NOTE: Look at the lack of precision - default epsilon not always
#best
grad = self.mod.score(test_params)
hecs, gradcs = numdiff.approx_hess1(test_params, self.mod.loglike,
1e-6, return_grad=True)
assert_almost_equal(he, hecs, decimal=1)
assert_almost_equal(grad, gradcs, decimal=1)
hecs, gradcs = numdiff.approx_hess2(test_params, self.mod.loglike,
1e-4, return_grad=True)
assert_almost_equal(he, hecs, decimal=3)
assert_almost_equal(grad, gradcs, decimal=1)
hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-5)
assert_almost_equal(he, hecs, decimal=4)
((y==1) * (norm.cdf(c1 - xb))) +
((y==2) * (norm.cdf(c2 - xb) - norm.cdf(c1 - xb))) +
((y==3) * (norm.cdf(c3 - xb) - norm.cdf(c2 - xb))) +
((y==4) * (norm.cdf(c4 - xb) - norm.cdf(c3- xb))) +
((y==5) * (1-norm.cdf(c4- xb)))
))
return -llf
probit_est = minimize(OrderProbit5, bhats, method='nelder-mead', options={'maxiter':500000, 'maxfev':500000})
log_likelihood = -probit_est['fun'] #log likelihood
#Find CRLB
b_estimates = probit_est['x']
Hessian = smt.approx_hess3(b_estimates, OrderProbit5)
invHessian = np.linalg.inv(Hessian)
#Standard Errors from CRLB
SE = np.array([])
for i in range(0, len(invHessian)):
SE = np.append(SE, np.sqrt(invHessian[i,i]))
#t and p values(b_estimates/SE)
t_statistics = (b_estimates/SE)
pval = (sc.stats.t.sf(np.abs(t_statistics), 999)*2)
def intercept(betas):
return np.sum((y-betas)**2)
inter = np.array([0.5])
inter_est = minimize(intercept, inter)
