def test_glmmexpfam_qs_none():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
z = random.multivariate_normal(0.2 * ones(nsamples), K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, None)
assert_allclose(glmm.lml(), -38.30173374439622, atol=ATOL, rtol=RTOL)
glmm.fix("beta")
glmm.fix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -32.03927471370041, atol=ATOL, rtol=RTOL)
glmm.unfix("beta")
glmm.unfix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -19.575736561760586, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_optimize():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
z = random.multivariate_normal(0.2 * ones(nsamples), K)
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm.lml(), -29.102168129099287, atol=ATOL, rtol=RTOL)
glmm.fix("beta")
glmm.fix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -27.635788105778012, atol=ATOL, rtol=RTOL)
glmm.unfix("beta")
glmm.unfix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -19.68486269551159, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_delta_one_zero():
random = RandomState(1)
n = 30
X = random.randn(n, 6)
K = dot(X, X.T)
K /= K.diagonal().mean()
QS = economic_qs(K)
ntri = random.randint(1, 30, n)
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, -0.2])
glmm.delta = 0
assert_allclose(glmm.lml(), -113.24570457063275)
assert_allclose(glmm._check_grad(step=1e-4), 0, atol=1e-2)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -98.21144899310399, atol=ATOL, rtol=RTOL)
assert_allclose(glmm.delta, 0, atol=ATOL, rtol=RTOL)
glmm.delta = 1
assert_allclose(glmm.lml(), -98.00058169240869, atol=ATOL, rtol=RTOL)
assert_allclose(glmm._check_grad(step=1e-4), 0, atol=1e-1)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -72.82680948264196, atol=ATOL, rtol=RTOL)
assert_allclose(glmm.delta, 0.9999999850988439, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_poisson():
from numpy import ones, stack, exp, zeros
from numpy.random import RandomState
from numpy_sugar.linalg import economic_qs
from pandas import DataFrame
random = RandomState(1)
# sample size
n = 30
# covariates
offset = ones(n) * random.randn()
age = random.randint(16, 75, n)
M = stack((offset, age), axis=1)
M = DataFrame(stack([offset, age], axis=1), columns=["offset", "age"])
M["sample"] = [f"sample{i}" for i in range(n)]
M = M.set_index("sample")
# genetic variants
G = random.randn(n, 4)
# sampling the phenotype
alpha = random.randn(2)
beta = random.randn(4)
eps = random.randn(n)
y = M @ alpha + G @ beta + eps
# Whole genotype of each sample.
X = random.randn(n, 50)
# Estimate a kinship relationship between samples.
X_ = (X - X.mean(0)) / X.std(0) / sqrt(X.shape[1])
K = X_ @ X_.T + eye(n) * 0.1
# Update the phenotype
y += random.multivariate_normal(zeros(n), K)
y = (y - y.mean()) / y.std()
z = y.copy()
y = random.poisson(exp(z))
M = M - M.mean(0)
QS = economic_qs(K)
glmm = GLMMExpFam(y, "poisson", M, QS)
assert_allclose(glmm.lml(), -52.479557279193585)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -34.09720756737648)
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_optimize_low_rank():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = dot(X, X.T)
z = dot(X, 0.2 * random.randn(5))
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm.lml(), -18.60476792256323, atol=ATOL, rtol=RTOL)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -7.800621320491801, atol=ATOL, rtol=RTOL)
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)
def test_glmmexpfam_poisson():
random = RandomState(1)
# sample size
n = 30
# covariates
offset = ones(n) * random.randn()
age = random.randint(16, 75, n)
M = stack((offset, age), axis=1)
# genetic variants
G = random.randn(n, 4)
# sampling the phenotype
alpha = random.randn(2)
beta = random.randn(4)
eps = random.randn(n)
y = M @ alpha + G @ beta + eps
# Whole genotype of each sample.
X = random.randn(n, 50)
# Estimate a kinship relationship between samples.
X_ = (X - X.mean(0)) / X.std(0) / sqrt(X.shape[1])
K = X_ @ X_.T + eye(n) * 0.1
# Update the phenotype
y += random.multivariate_normal(zeros(n), K)
y = (y - y.mean()) / y.std()
z = y.copy()
y = random.poisson(exp(z))
M = M - M.mean(0)
QS = economic_qs(K)
glmm = GLMMExpFam(y, "poisson", M, QS)
assert_allclose(glmm.lml(), -52.479557279193585)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -34.09720756737648)
def test_glmmexpfam_copy():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
z = random.multivariate_normal(0.2 * ones(nsamples), K)
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm0 = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm0.lml(), -29.10216812909928, atol=ATOL, rtol=RTOL)
glmm0.fit(verbose=False)
v = -19.575736562427252
assert_allclose(glmm0.lml(), v)
glmm1 = glmm0.copy()
assert_allclose(glmm1.lml(), v)
glmm1.scale = 0.92
assert_allclose(glmm0.lml(), v, atol=ATOL, rtol=RTOL)
assert_allclose(glmm1.lml(), -30.832831740038056, atol=ATOL, rtol=RTOL)
glmm0.fit(verbose=False)
glmm1.fit(verbose=False)
v = -19.575736562378573
assert_allclose(glmm0.lml(), v)
assert_allclose(glmm1.lml(), v)
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_delta1():
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.delta = 1
assert_allclose(glmm.lml(), -47.09677870648636, atol=ATOL, rtol=RTOL)
assert_allclose(glmm._check_grad(), 0, atol=1e-4)
def test_glmmexpfam_binomial_large_ntrials():
random = RandomState(0)
n = 10
X = random.randn(n, 2)
G = random.randn(n, 100)
K = dot(G, G.T)
ntrials = random.randint(1, 100000, n)
z = dot(G, random.randn(100)) / sqrt(100)
successes = zeros(len(ntrials), int)
for i in range(len(ntrials)):
for _ in range(ntrials[i]):
successes[i] += int(z[i] + 0.1 * random.randn() > 0)
QS = economic_qs(K)
glmm = GLMMExpFam(successes, ("binomial", ntrials), X, QS)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -43.067433588125446)
def test_glmmexpfam_bernoulli_probit_assure_delta_fixed():
random = RandomState(1)
N = 10
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.fit(verbose=False)
assert_allclose(model.lml(), -6.108751595773174, rtol=RTOL)
assert_allclose(model.delta, 1.4901161193847673e-08, atol=1e-5)
assert_(model._isfixed("logitdelta"))
def test_glmmexpfam_bernoulli_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, "bernoulli", X, QS=(QS[0], QS[1]))
model.delta = 0
model.fix("delta")
model.fit(verbose=False)
assert_allclose(model.lml(), -20.727007958026853, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0, atol=1e-3)
assert_allclose(model.scale, 0.879915823030081, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.00247856564728], atol=ATOL, rtol=RTOL)