def test_glmmexpfam_layout():
y = asarray([1.0, 0.5])
X = asarray([[0.5, 1.0]])
K = asarray([[1.0, 0.0], [0.0, 1.0]])
QS = economic_qs(K)
with pytest.raises(ValueError):
GLMMExpFam(y, "poisson", X, QS=QS)
y = asarray([1.0])
with pytest.raises(ValueError):
GLMMExpFam(y, "poisson", X, QS=QS)
def _fit_glmm_simple_model(self, verbose):
from numpy_sugar.linalg import economic_qs
from glimix_core.glmm import GLMMExpFam
from numpy import asarray
K = self._get_matrix_simple_model()
y = asarray(self._y, float).ravel()
QS = None
if K is not None:
QS = economic_qs(K)
glmm = GLMMExpFam(y, self._lik, self._M, QS)
glmm.fit(verbose=verbose)
self._set_simple_model_variances(glmm.v0, glmm.v1)
self._glmm = glmm
def estimate(y, lik, K, M=None, verbose=True):
from numpy_sugar.linalg import economic_qs
from numpy import pi, var, diag
from glimix_core.glmm import GLMMExpFam
from glimix_core.lmm import LMM
from limix._data._assert import assert_likelihood
from limix._data import normalize_likelihood, conform_dataset
from limix.qtl._assert import assert_finite
from limix._display import session_block, session_line
lik = normalize_likelihood(lik)
lik_name = lik[0]
with session_block("Heritability analysis", disable=not verbose):
with session_line("Normalising input...", disable=not verbose):
data = conform_dataset(y, M=M, K=K)
y = data["y"]
M = data["M"]
K = data["K"]
assert_finite(y, M, K)
if K is not None:
# K = K / diag(K).mean()
QS = economic_qs(K)
else:
QS = None
if lik_name == "normal":
method = LMM(y.values, M.values, QS, restricted=True)
method.fit(verbose=verbose)
else:
method = GLMMExpFam(y, lik, M.values, QS, n_int=500)
method.fit(verbose=verbose, factr=1e6, pgtol=1e-3)
g = method.scale * (1 - method.delta)
e = method.scale * method.delta
if lik_name == "bernoulli":
e += pi * pi / 3
v = var(method.mean())
return g, v, e
def estimate(y_phe, lik, kin, marker_mat=None, verbose=True):
''' estimate variance components '''
lik = normalize_likelihood(lik)
lik_name = lik[0]
with session_block("Heritability analysis", disable=not verbose):
with session_line("Normalising input...", disable=not verbose):
data = conform_dataset(y_phe, M=marker_mat, K=kin)
y_phe = data["y"]
marker_mat = data["M"]
kin = data["K"]
assert_finite(y_phe, marker_mat, kin)
if kin is not None:
# K = K / diag(K).mean()
q_s = economic_qs(kin)
else:
q_s = None
if lik_name == "normal":
method = LMM(y_phe.values, marker_mat.values, q_s, restricted=True)
method.fit(verbose=verbose)
else:
method = GLMMExpFam(y_phe, lik, marker_mat.values, q_s, n_int=500)
method.fit(verbose=verbose, factr=1e6, pgtol=1e-3)
v_g = method.scale * (1 - method.delta)
v_e = method.scale * method.delta
if lik_name == "bernoulli":
v_e += pi * pi / 3
v_v = var(method.mean())
return v_g, v_v, v_e
def _glmm(y, lik, M, QS, verbose):
from glimix_core.glmm import GLMMExpFam, GLMMNormal
glmm = GLMMExpFam(y.ravel(), lik, M, QS)
glmm.fit(verbose=verbose)
v0 = glmm.v0
v1 = glmm.v1
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M, QS)
gnormal.fit(verbose=verbose)
scanner = ScannerWrapper(gnormal.get_fast_scanner())
return scanner, v0, v1
def test_glmmexpfam_wrong_qs():
random = RandomState(0)
X = random.randn(10, 15)
linear_eye_cov().value()
QS = [0, 1]
ntri = random.randint(1, 30, 10)
nsuc = [random.randint(0, i) for i in ntri]
with pytest.raises(ValueError):
GLMMExpFam((nsuc, ntri), "binomial", X, QS)
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 _perform_glmm(y, lik, M, K, QS, G, verbose):
from glimix_core.glmm import GLMMExpFam, GLMMNormal
from pandas import Series
from xarray import DataArray
glmm = GLMMExpFam(y.ravel(), lik, M.values, QS)
glmm.fit(verbose=verbose)
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M.values, QS)
gnormal.fit(verbose=verbose)
beta = gnormal.beta
covariates = list(M.coords["covariate"].values)
ncov_effsizes = Series(beta, covariates)
flmm = gnormal.get_fast_scanner()
flmm.set_scale(1.0)
null_lml = flmm.null_lml()
if hasattr(G, "data"):
values = G.data
else:
values = G.values
alt_lmls, effsizes = flmm.fast_scan(values, verbose=verbose)
coords = {
k: ("candidate", G.coords[k].values)
for k in G.coords.keys()
if G.coords[k].dims[0] == "candidate"
}
alt_lmls = DataArray(alt_lmls, dims=["candidate"], coords=coords)
effsizes = DataArray(effsizes, dims=["candidate"], coords=coords)
return QTLModel(null_lml, alt_lmls, effsizes, ncov_effsizes)
def _st_glmm(y, lik, M, QS, verbose):
from numpy import nan
from glimix_core.glmm import GLMMExpFam, GLMMNormal
glmm = GLMMExpFam(y, lik, M, QS)
glmm.fit(verbose=verbose)
if QS is None:
v0 = nan
else:
v0 = glmm.v0
v1 = glmm.v1
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M, QS)
gnormal.fit(verbose=verbose)
return gnormal.get_fast_scanner(), v0, v1
def test_glmmexpfam_predict():
random = RandomState(4)
n = 100
p = n + 1
X = ones((n, 2))
X[:, 1] = random.randn(n)
G = random.randn(n, p)
G /= G.std(0)
G -= G.mean(0)
G /= sqrt(p)
K = dot(G, G.T)
i = asarray(arange(0, n), int)
si = random.choice(i, n, replace=False)
ntest = int(n // 5)
itrain = si[:-ntest]
itest = si[-ntest:]
Xtrain = X[itrain, :]
Ktrain = K[itrain, :][:, itrain]
Xtest = X[itest, :]
beta = random.randn(2)
z = random.multivariate_normal(dot(X, beta), 0.9 * K + 0.1 * eye(n))
ntri = random.randint(1, 100, n)
nsuc = zeros(n, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
QStrain = economic_qs(Ktrain)
nsuc_train = ascontiguousarray(nsuc[itrain])
ntri_train = ascontiguousarray(ntri[itrain])
nsuc_test = ascontiguousarray(nsuc[itest])
ntri_test = ascontiguousarray(ntri[itest])
glmm = GLMMExpFam(nsuc_train, ("binomial", ntri_train), Xtrain, QStrain)
glmm.fit(verbose=False)
ks = K[itest, :][:, itrain]
kss = asarray([K[i, i] for i in itest])
pm = glmm.predictive_mean(Xtest, ks, kss)
pk = glmm.predictive_covariance(Xtest, ks, kss)
r = nsuc_test / ntri_test
assert_(corrcoef([pm, r])[0, 1] > 0.8)
assert_allclose(pk[0], 54.263705682514846)
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)
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_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_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_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_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_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_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_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_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 estimate(pheno, lik, K, covs=None, verbose=True):
r"""Estimate the so-called narrow-sense heritability.
It supports Normal, Bernoulli, Binomial, and Poisson phenotypes.
Let :math:`N` be the sample size and :math:`S` the number of covariates.
Parameters
----------
pheno : tuple, array_like
Phenotype. Dimensions :math:`N\\times 0`.
lik : {'normal', 'bernoulli', 'binomial', 'poisson'}
Likelihood name.
K : array_like
Kinship matrix. Dimensions :math:`N\\times N`.
covs : array_like
Covariates. Default is an offset. Dimensions :math:`N\\times S`.
Returns
-------
float
Estimated heritability.
Examples
--------
.. doctest::
>>> from numpy import dot, exp, sqrt
>>> from numpy.random import RandomState
>>> from limix.heritability import estimate
>>>
>>> random = RandomState(0)
>>>
>>> G = random.randn(50, 100)
>>> K = dot(G, G.T)
>>> z = dot(G, random.randn(100)) / sqrt(100)
>>> y = random.poisson(exp(z))
>>>
>>> print('%.2f' % estimate(y, 'poisson', K, verbose=False))
0.70
"""
K = _background_standardize(K)
QS = economic_qs(K)
lik = lik.lower()
if lik == "binomial":
p = len(pheno[0])
else:
p = len(pheno)
if covs is None:
covs = ones((p, 1))
glmm = GLMMExpFam(pheno, lik, covs, QS)
glmm.feed().maximize(verbose=verbose)
g = glmm.scale * (1 - glmm.delta)
e = glmm.scale * glmm.delta
h2 = g / (var(glmm.mean()) + g + e)
return h2
import numpy as np
import numpy_sugar as ns
from glimix_core.glmm import GLMMExpFam
from time import time
G = np.load('null_G.npy')
ntri = np.load('null_ntri.npy')
nsuc = np.load('null_nsuc.npy')
N, P = G.shape
QS = ns.linalg.economic_qs(G.dot(G.T))
X = np.ones((N, 1))
ntri = np.asarray(ntri, float)
nsuc = np.asarray(nsuc, float)
start = time()
glmm = GLMMExpFam((nsuc, ntri), "binomial", X, QS)
glmm.fit(verbose=True)
stop = time()
elapsed = stop - start
print("Elapsed: {}".format(elapsed))
np.save("out/fastglmm_N{}".format(N), elapsed)
def estimate(y, lik, K, M=None, verbose=True):
r"""Estimate the so-called narrow-sense heritability.
It supports Normal, Bernoulli, Probit, Binomial, and Poisson phenotypes.
Let :math:`N` be the sample size and :math:`S` the number of covariates.
Parameters
----------
y : array_like
Either a tuple of two arrays of `N` individuals each (Binomial
phenotypes) or an array of `N` individuals (Normal, Poisson, or
Bernoulli phenotypes). If a continuous phenotype is provided (i.e., a Normal
one), make sure they have been normalised in such a way that its values are
not extremely large; it might cause numerical errors otherwise. For example,
by using :func:`limix.qc.mean_standardize` or
:func:`limix.qc.quantile_gaussianize`.
lik : "normal", "bernoulli", "probit", binomial", "poisson"
Sample likelihood describing the residual distribution.
K : array_like
:math:`N`-by-:math:`N` covariance matrix. It might be, for example, the
estimated kinship relationship between the individuals. The provided matrix will
be normalised via the function :func:`limix.qc.normalise_covariance`.
M : array_like, optional
:math:`N` individuals by :math:`S` covariates.
It will create a :math:`N`-by-:math:`1` matrix ``M`` of ones representing the offset
covariate if ``None`` is passed. If an array is passed, it will used as is.
Defaults to ``None``.
verbose : bool, optional
``True`` to display progress and summary; ``False`` otherwise.
Returns
-------
float
Estimated heritability.
Examples
--------
.. doctest::
>>> from numpy import dot, exp, sqrt
>>> from numpy.random import RandomState
>>> from limix.her import estimate
>>>
>>> random = RandomState(0)
>>>
>>> G = random.randn(150, 200) / sqrt(200)
>>> K = dot(G, G.T)
>>> z = dot(G, random.randn(200)) + random.randn(150)
>>> y = random.poisson(exp(z))
>>>
>>> print('%.3f' % estimate(y, 'poisson', K, verbose=False)) # doctest: +FLOAT_CMP
0.183
Notes
-----
It will raise a ``ValueError`` exception if non-finite values are passed. Please,
refer to the :func:`limix.qc.mean_impute` function for missing value imputation.
"""
from numpy_sugar import is_all_finite
from numpy_sugar.linalg import economic_qs
from numpy import ones, pi, var
from glimix_core.glmm import GLMMExpFam
from glimix_core.lmm import LMM
if not isinstance(lik, (tuple, list)):
lik = (lik,)
lik_name = lik[0].lower()
check_likelihood_name(lik_name)
with session_block("heritability analysis", disable=not verbose):
if M is None:
M = ones((len(y), 1))
with session_line("Normalising input...", disable=not verbose):
data = conform_dataset(y, M=M, K=K)
y = data["y"]
M = data["M"]
K = data["K"]
if not is_all_finite(y):
raise ValueError("Outcome must have finite values only.")
if not is_all_finite(M):
raise ValueError("Covariates must have finite values only.")
if K is not None:
if not is_all_finite(K):
raise ValueError("Covariate matrix must have finite values only.")
K = normalise_covariance(K)
y = normalise_extreme_values(y, lik)
if K is not None:
QS = economic_qs(K)
else:
QS = None
if lik_name == "normal":
method = LMM(y.values, M.values, QS)
method.fit(verbose=verbose)
else:
method = GLMMExpFam(y, lik, M.values, QS, n_int=500)
method.fit(verbose=verbose, factr=1e6, pgtol=1e-3)
g = method.scale * (1 - method.delta)
e = method.scale * method.delta
if lik_name == "bernoulli":
e += pi * pi / 3
if lik_name == "normal":
v = method.fixed_effects_variance
else:
v = var(method.mean())
return g / (v + g + e)
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_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_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 qtl_test_glmm(
snps,
pheno,
lik,
K,
covs=None,
test="lrt",
NumIntervalsDeltaAlt=100,
searchDelta=False,
verbose=True,
):
"""
Wrapper function for univariate single-variant association testing
using a generalised linear mixed model.
Args:
snps (array_like):
`N` individuals by `S` SNPs.
pheno (tuple, array_like):
Either a tuple of two arrays of `N` individuals each (Binomial
phenotypes) or an array of `N` individuals (Poisson or Bernoulli
phenotypes). It does not support missing values yet.
lik ({'bernoulli', 'binomial', 'poisson'}):
Sample likelihood describing the residual distribution.
K (array_like):
`N` by `N` covariance matrix (e.g., kinship coefficients).
covs (array_like, optional):
`N` individuals by `D` covariates.
By default, ``covs`` is a (`N`, `1`) array of ones.
test ({'lrt'}, optional):
Likelihood ratio test (default).
NumIntervalsDeltaAlt (int, optional):
number of steps for delta optimization on the alternative model.
Requires ``searchDelta=True`` to have an effect.
searchDelta (bool, optional):
if ``True``, delta optimization on the alternative model is
carried out. By default ``searchDelta`` is ``False``.
verbose (bool, optional):
if ``True``, details such as runtime are displayed.
Returns:
:class:`limix.qtl.LMM`: LIMIX LMM object
Examples
--------
.. doctest::
>>> from numpy import dot, exp, sqrt
>>> from numpy.random import RandomState
>>> from limix.qtl import qtl_test_glmm
>>>
>>> random = RandomState(0)
>>>
>>> G = random.randn(250, 500) / sqrt(500)
>>> beta = 0.01 * random.randn(500)
>>>
>>> z = dot(G, beta) + 0.1 * random.randn(250)
>>> z += dot(G[:, 0], 1) # causal SNP
>>>
>>> y = random.poisson(exp(z))
>>>
>>> candidates = G[:, :5]
>>> K = dot(G[:, 5:], G[:, 5:].T)
>>> lm = qtl_test_glmm(candidates, y, 'poisson', K, verbose=False)
>>>
>>> print(lm.getPv())
[[0.0694 0.3336 0.5899 0.7388 0.7796]]
"""
snps = _asarray(snps)
if covs is None:
covs = ones((snps.shape[0], 1))
else:
covs = _asarray(covs)
K = _asarray(K)
if isinstance(pheno, (tuple, list)):
y = tuple([asarray(p, float) for p in pheno])
else:
y = asarray(pheno, float)
start = time()
QS = economic_qs(K)
glmm = GLMMExpFam(y, lik, covs, QS)
glmm.feed().maximize(verbose=verbose)
# extract stuff from glmm
eta = glmm.site.eta
tau = glmm.site.tau
scale = float(glmm.scale)
delta = float(glmm.delta)
# define useful quantities
mu = eta / tau
var = 1. / tau
s2_g = scale * (1 - delta)
tR = s2_g * K + diag(var - var.min() + 1e-4)
start = time()
lmm = LMM(snps=snps, pheno=mu, K=tR, covs=covs, verbose=verbose)
# if verbose:
# print("Elapsed time for LMM part: %.3f" % (time() - start))
return lmm