def test_score(self):
n = 200
m = 5
p = 3
pr = 2
for jl in 0, 1:
for reml in False, True:
for cov_pen_wt in 0, 10:
cov_pen = penalties.PSD(cov_pen_wt)
np.random.seed(3558)
exog_fe = np.random.normal(size=(n * m, p))
exog_re = np.random.normal(size=(n * m, pr))
endog = exog_fe.sum(1) + np.random.normal(size=n * m)
groups = np.kron(range(n), np.ones(m))
md = MixedLM(endog, exog_fe, groups, exog_re)
md.reml = reml
md.cov_pen = cov_pen
if jl == 0:
like = lambda x: -md.loglike_sqrt(x)
score = lambda x: -md.score_sqrt(x)
else:
like = lambda x: -md.loglike(x)
score = lambda x: -md.score(x)
for kr in range(5):
fe_params = np.random.normal(size=p)
cov_re = np.random.normal(size=(pr, pr))
cov_re = np.dot(cov_re.T, cov_re)
params_prof = md._pack(fe_params, cov_re)
gr = score(params_prof)
ngr = np.zeros_like(gr)
for k in range(len(ngr)):
def f(x):
pp = params_prof.copy()
pp[k] = x
return like(pp)
ngr[k] = derivative(f, params_prof[k], dx=1e-6)
assert_almost_equal(gr / ngr,
np.ones(len(gr)),
decimal=3)
def test_score(self):
n = 200
m = 5
p = 3
pr = 2
for jl in 0,1:
for reml in False,True:
for cov_pen_wt in 0,10:
cov_pen = penalties.PSD(cov_pen_wt)
np.random.seed(3558)
exog_fe = np.random.normal(size=(n*m, p))
exog_re = np.random.normal(size=(n*m, pr))
endog = exog_fe.sum(1) + np.random.normal(size=n*m)
groups = np.kron(range(n), np.ones(m))
md = MixedLM(endog, exog_fe, groups, exog_re)
md.reml = reml
md.cov_pen = cov_pen
if jl == 0:
like = lambda x: -md.loglike_sqrt(x)
score = lambda x: -md.score_sqrt(x)
else:
like = lambda x: -md.loglike(x)
score = lambda x: -md.score(x)
for kr in range(5):
fe_params = np.random.normal(size=p)
cov_re = np.random.normal(size=(pr,pr))
cov_re = np.dot(cov_re.T, cov_re)
params_prof = md._pack(fe_params, cov_re)
gr = score(params_prof)
ngr = np.zeros_like(gr)
for k in range(len(ngr)):
def f(x):
pp = params_prof.copy()
pp[k] = x
return like(pp)
ngr[k] = derivative(f, params_prof[k],
dx=1e-6)
assert_almost_equal(gr / ngr, np.ones(len(gr)),
decimal=3)
def test_compare_numdiff(self):
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 2
for use_sqrt in False, True:
for reml in False, True:
for profile_fe in False, True:
np.random.seed(3558)
exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
exog_re[:, 0] = 1
exog_vc = np.random.normal(size=(n_grp * grpsize, 3))
slopes = np.random.normal(size=(n_grp, k_re))
slopes[:, -1] *= 2
slopes = np.kron(slopes, np.ones((grpsize, 1)))
slopes_vc = np.random.normal(size=(n_grp, 3))
slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1)))
slopes_vc[:, -1] *= 2
re_values = (slopes * exog_re).sum(1)
vc_values = (slopes_vc * exog_vc).sum(1)
err = np.random.normal(size=n_grp * grpsize)
endog = exog_fe.sum(1) + re_values + vc_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
vc = {"a": {}, "b": {}}
for i in range(n_grp):
ix = np.flatnonzero(groups == i)
vc["a"][i] = exog_vc[ix, 0:2]
vc["b"][i] = exog_vc[ix, 2:3]
model = MixedLM(endog,
exog_fe,
groups,
exog_re,
exog_vc=vc,
use_sqrt=use_sqrt)
rslt = model.fit(reml=reml)
loglike = loglike_function(model,
profile_fe=profile_fe,
has_fe=not profile_fe)
# Test the score at several points.
for kr in range(5):
fe_params = np.random.normal(size=k_fe)
cov_re = np.random.normal(size=(k_re, k_re))
cov_re = np.dot(cov_re.T, cov_re)
vcomp = np.random.normal(size=2)**2
params = MixedLMParams.from_components(fe_params,
cov_re=cov_re,
vcomp=vcomp)
params_vec = params.get_packed(has_fe=not profile_fe,
use_sqrt=use_sqrt)
# Check scores
gr = -model.score(params, profile_fe=profile_fe)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-3)
# Check Hessian matrices at the MLE (we don't have
# the profile Hessian matrix and we don't care
# about the Hessian for the square root
# transformed parameter).
if (profile_fe is False) and (use_sqrt is False):
hess = -model.hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed(
use_sqrt=False, has_fe=True)
loglike_h = loglike_function(model,
profile_fe=False,
has_fe=True)
nhess = nd.approx_hess(params_vec, loglike_h)
assert_allclose(hess, nhess, rtol=1e-3)
def test_compare_numdiff(self):
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 2
for use_sqrt in False, True:
for reml in False, True:
for profile_fe in False, True:
np.random.seed(3558)
exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
exog_re[:, 0] = 1
exog_vc = np.random.normal(size=(n_grp * grpsize, 3))
slopes = np.random.normal(size=(n_grp, k_re))
slopes[:, -1] *= 2
slopes = np.kron(slopes, np.ones((grpsize, 1)))
slopes_vc = np.random.normal(size=(n_grp, 3))
slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1)))
slopes_vc[:, -1] *= 2
re_values = (slopes * exog_re).sum(1)
vc_values = (slopes_vc * exog_vc).sum(1)
err = np.random.normal(size=n_grp * grpsize)
endog = exog_fe.sum(1) + re_values + vc_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
vc = {"a": {}, "b": {}}
for i in range(n_grp):
ix = np.flatnonzero(groups == i)
vc["a"][i] = exog_vc[ix, 0:2]
vc["b"][i] = exog_vc[ix, 2:3]
model = MixedLM(endog, exog_fe, groups, exog_re, exog_vc=vc, use_sqrt=use_sqrt)
rslt = model.fit(reml=reml)
loglike = loglike_function(model, profile_fe=profile_fe, has_fe=not profile_fe)
# Test the score at several points.
for kr in range(5):
fe_params = np.random.normal(size=k_fe)
cov_re = np.random.normal(size=(k_re, k_re))
cov_re = np.dot(cov_re.T, cov_re)
vcomp = np.random.normal(size=2) ** 2
params = MixedLMParams.from_components(fe_params, cov_re=cov_re, vcomp=vcomp)
params_vec = params.get_packed(has_fe=not profile_fe, use_sqrt=use_sqrt)
# Check scores
gr = -model.score(params, profile_fe=profile_fe)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-3)
# Check Hessian matrices at the MLE (we don't have
# the profile Hessian matrix and we don't care
# about the Hessian for the square root
# transformed parameter).
if (profile_fe is False) and (use_sqrt is False):
hess = -model.hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed(use_sqrt=False, has_fe=True)
loglike_h = loglike_function(model, profile_fe=False, has_fe=True)
nhess = nd.approx_hess(params_vec, loglike_h)
assert_allclose(hess, nhess, rtol=1e-3)
def test_compare_numdiff(self, use_sqrt, reml, profile_fe):
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 2
np.random.seed(3558)
exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
exog_re[:, 0] = 1
exog_vc = np.random.normal(size=(n_grp * grpsize, 3))
slopes = np.random.normal(size=(n_grp, k_re))
slopes[:, -1] *= 2
slopes = np.kron(slopes, np.ones((grpsize, 1)))
slopes_vc = np.random.normal(size=(n_grp, 3))
slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1)))
slopes_vc[:, -1] *= 2
re_values = (slopes * exog_re).sum(1)
vc_values = (slopes_vc * exog_vc).sum(1)
err = np.random.normal(size=n_grp * grpsize)
endog = exog_fe.sum(1) + re_values + vc_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
vc = {"a": {}, "b": {}}
for i in range(n_grp):
ix = np.flatnonzero(groups == i)
vc["a"][i] = exog_vc[ix, 0:2]
vc["b"][i] = exog_vc[ix, 2:3]
model = MixedLM(
endog,
exog_fe,
groups,
exog_re,
exog_vc=vc,
use_sqrt=use_sqrt)
rslt = model.fit(reml=reml)
loglike = loglike_function(
model, profile_fe=profile_fe, has_fe=not profile_fe)
try:
# Test the score at several points.
for kr in range(5):
fe_params = np.random.normal(size=k_fe)
cov_re = np.random.normal(size=(k_re, k_re))
cov_re = np.dot(cov_re.T, cov_re)
vcomp = np.random.normal(size=2)**2
params = MixedLMParams.from_components(
fe_params, cov_re=cov_re, vcomp=vcomp)
params_vec = params.get_packed(
has_fe=not profile_fe, use_sqrt=use_sqrt)
# Check scores
gr = -model.score(params, profile_fe=profile_fe)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-3)
# Check Hessian matrices at the MLE (we don't have
# the profile Hessian matrix and we don't care
# about the Hessian for the square root
# transformed parameter).
if (profile_fe is False) and (use_sqrt is False):
hess = -model.hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed(
use_sqrt=False, has_fe=True)
loglike_h = loglike_function(
model, profile_fe=False, has_fe=True)
nhess = nd.approx_hess(params_vec, loglike_h)
assert_allclose(hess, nhess, rtol=1e-3)
except AssertionError:
# See GH#5628; because this test fails unpredictably but only on
# OSX, we only xfail it there.
if PLATFORM_OSX:
pytest.xfail("fails on OSX due to unresolved "
"numerical differences")
else:
raise
def test_compare_numdiff(self, use_sqrt, reml, profile_fe):
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 2
np.random.seed(3558)
exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
exog_re[:, 0] = 1
exog_vc = np.random.normal(size=(n_grp * grpsize, 3))
slopes = np.random.normal(size=(n_grp, k_re))
slopes[:, -1] *= 2
slopes = np.kron(slopes, np.ones((grpsize, 1)))
slopes_vc = np.random.normal(size=(n_grp, 3))
slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1)))
slopes_vc[:, -1] *= 2
re_values = (slopes * exog_re).sum(1)
vc_values = (slopes_vc * exog_vc).sum(1)
err = np.random.normal(size=n_grp * grpsize)
endog = exog_fe.sum(1) + re_values + vc_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
vc = {"a": {}, "b": {}}
for i in range(n_grp):
ix = np.flatnonzero(groups == i)
vc["a"][i] = exog_vc[ix, 0:2]
vc["b"][i] = exog_vc[ix, 2:3]
model = MixedLM(endog,
exog_fe,
groups,
exog_re,
exog_vc=vc,
use_sqrt=use_sqrt)
rslt = model.fit(reml=reml)
loglike = loglike_function(model,
profile_fe=profile_fe,
has_fe=not profile_fe)
try:
# Test the score at several points.
for kr in range(5):
fe_params = np.random.normal(size=k_fe)
cov_re = np.random.normal(size=(k_re, k_re))
cov_re = np.dot(cov_re.T, cov_re)
vcomp = np.random.normal(size=2)**2
params = MixedLMParams.from_components(fe_params,
cov_re=cov_re,
vcomp=vcomp)
params_vec = params.get_packed(has_fe=not profile_fe,
use_sqrt=use_sqrt)
# Check scores
gr = -model.score(params, profile_fe=profile_fe)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-3)
# Check Hessian matrices at the MLE (we do not have
# the profile Hessian matrix and we do not care
# about the Hessian for the square root
# transformed parameter).
if (profile_fe is False) and (use_sqrt is False):
hess = -model.hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed(use_sqrt=False,
has_fe=True)
loglike_h = loglike_function(model,
profile_fe=False,
has_fe=True)
nhess = nd.approx_hess(params_vec, loglike_h)
assert_allclose(hess, nhess, rtol=1e-3)
except AssertionError:
# See GH#5628; because this test fails unpredictably but only on
# OSX, we only xfail it there.
if PLATFORM_OSX:
pytest.xfail("fails on OSX due to unresolved "
"numerical differences")
else:
raise
