def test_glmmexpfam_precise():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = [random.randint(0, i) for i in ntri]
glmm = GLMMExpFam(nsuc, ["binomial", ntri], X, QS)
glmm.beta = asarray([1.0, 0, 0.5, 0.1, 0.4])
glmm.scale = 1.0
assert_allclose(glmm.lml(), -44.74191041468836, atol=ATOL, rtol=RTOL)
glmm.scale = 2.0
assert_allclose(glmm.lml(), -36.19907331929086, atol=ATOL, rtol=RTOL)
glmm.scale = 3.0
assert_allclose(glmm.lml(), -33.02139830387104, atol=ATOL, rtol=RTOL)
glmm.scale = 4.0
assert_allclose(glmm.lml(), -31.42553401678996, atol=ATOL, rtol=RTOL)
glmm.scale = 5.0
assert_allclose(glmm.lml(), -30.507029479473243, atol=ATOL, rtol=RTOL)
glmm.scale = 6.0
assert_allclose(glmm.lml(), -29.937569702301232, atol=ATOL, rtol=RTOL)
glmm.delta = 0.1
assert_allclose(glmm.lml(), -30.09977907145003, atol=ATOL, rtol=RTOL)
assert_allclose(glmm._check_grad(), 0, atol=1e-3, rtol=RTOL)
def test_glmmexpfam_scale_very_high():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = [random.randint(0, i) for i in ntri]
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
glmm.beta = asarray([1.0, 0, 0.5, 0.1, 0.4])
glmm.scale = 30.0
assert_allclose(glmm.lml(), -29.632791380478736, atol=ATOL, rtol=RTOL)
assert_allclose(glmm._check_grad(), 0, atol=1e-3)
def test_glmmexpfam_bernoulli_probit_problematic():
random = RandomState(1)
N = 30
G = random.randn(N, N + 50)
y = bernoulli_sample(0.0, G, random_state=random)
G = ascontiguousarray(G, dtype=float)
_stdnorm(G, 0, out=G)
G /= sqrt(G.shape[1])
QS = economic_qs_linear(G)
S0 = QS[1]
S0 /= S0.mean()
X = ones((len(y), 1))
model = GLMMExpFam(y, "probit", X, QS=(QS[0], QS[1]))
model.delta = 0
model.fix("delta")
model.fit(verbose=False)
assert_allclose(model.lml(), -20.725623168378615, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0.0001220703125, atol=1e-3)
assert_allclose(model.scale, 0.33022865011938707, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.002617161564786044], atol=ATOL, rtol=RTOL)
h20 = model.scale * (1 - model.delta) / (model.scale + 1)
model.unfix("delta")
model.delta = 0.5
model.scale = 1.0
model.fit(verbose=False)
assert_allclose(model.lml(), -20.725623168378522, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0.5017852859580029, atol=1e-3)
assert_allclose(model.scale, 0.9928931515372, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.003203427206253548], atol=ATOL, rtol=RTOL)
h21 = model.scale * (1 - model.delta) / (model.scale + 1)
assert_allclose(h20, h21, atol=ATOL, rtol=RTOL)