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):
import statsmodels.tools.numdiff as nd
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 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_grp * grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
exog_re[:, 0] = 1
slopes = np.random.normal(size=(n_grp, k_re))
slopes = np.kron(slopes, np.ones((grpsize, 1)))
re_values = (slopes * exog_re).sum(1)
err = np.random.normal(size=n_grp * grpsize)
endog = exog_fe.sum(1) + re_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
if jl == 0:
md = MixedLM(endog, exog_fe, groups, exog_re)
score = lambda x: -md.score_sqrt(x)
hessian = lambda x: -md.hessian_sqrt(x)
else:
md = MixedLM(endog,
exog_fe,
groups,
exog_re,
use_sqrt=False)
score = lambda x: -md.score_full(x)
hessian = lambda x: -md.hessian_full(x)
md.reml = reml
md.cov_pen = cov_pen
loglike = lambda x: -md.loglike(x)
rslt = md.fit()
# 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)
params = MixedLMParams.from_components(
fe_params, cov_re)
if jl == 0:
params_vec = params.get_packed()
else:
params_vec = params.get_packed(use_sqrt=False)
# Check scores
gr = score(params)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-2)
# Hessian matrices don't agree well away from
# the MLE.
#if cov_pen_wt == 0:
# hess = hessian(params)
# nhess = nd.approx_hess(params_vec, loglike)
# assert_allclose(hess, nhess, rtol=1e-2)
# Check Hessian matrices at the MLE.
if cov_pen_wt == 0:
hess = hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed()
nhess = nd.approx_hess(params_vec, loglike)
assert_allclose(hess, nhess, rtol=1e-2)
def test_compare_numdiff(self):
import statsmodels.tools.numdiff as nd
n_grp = 200
grpsize = 5
k_fe = 3
k_re = 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_grp*grpsize, k_fe))
exog_re = np.random.normal(size=(n_grp*grpsize, k_re))
exog_re[:, 0] = 1
slopes = np.random.normal(size=(n_grp, k_re))
slopes = np.kron(slopes, np.ones((grpsize,1)))
re_values = (slopes * exog_re).sum(1)
err = np.random.normal(size=n_grp*grpsize)
endog = exog_fe.sum(1) + re_values + err
groups = np.kron(range(n_grp), np.ones(grpsize))
if jl == 0:
md = MixedLM(endog, exog_fe, groups, exog_re)
score = lambda x: -md.score_sqrt(x)
hessian = lambda x : -md.hessian_sqrt(x)
else:
md = MixedLM(endog, exog_fe, groups, exog_re, use_sqrt=False)
score = lambda x: -md.score_full(x)
hessian = lambda x: -md.hessian_full(x)
md.reml = reml
md.cov_pen = cov_pen
loglike = lambda x: -md.loglike(x)
rslt = md.fit()
# 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)
params = MixedLMParams.from_components(fe_params, cov_re)
if jl == 0:
params_vec = params.get_packed()
else:
params_vec = params.get_packed(use_sqrt=False)
# Check scores
gr = score(params)
ngr = nd.approx_fprime(params_vec, loglike)
assert_allclose(gr, ngr, rtol=1e-2)
# Hessian matrices don't agree well away from
# the MLE.
#if cov_pen_wt == 0:
# hess = hessian(params)
# nhess = nd.approx_hess(params_vec, loglike)
# assert_allclose(hess, nhess, rtol=1e-2)
# Check Hessian matrices at the MLE.
if cov_pen_wt == 0:
hess = hessian(rslt.params_object)
params_vec = rslt.params_object.get_packed()
nhess = nd.approx_hess(params_vec, loglike)
assert_allclose(hess, nhess, rtol=1e-2)