def test_fast_scanner_statsmodel_gls():
import statsmodels.api as sm
from numpy.linalg import lstsq
def _lstsq(A, B):
return lstsq(A, B, rcond=None)[0]
data = sm.datasets.longley.load()
data.exog = sm.add_constant(data.exog)
ols_resid = sm.OLS(data.endog, data.exog).fit().resid
resid_fit = sm.OLS(ols_resid[1:], sm.add_constant(ols_resid[:-1])).fit()
rho = resid_fit.params[1]
order = toeplitz(range(len(ols_resid)))
sigma = rho ** order
QS = economic_qs(sigma)
lmm = LMM(data.endog, data.exog, QS)
lmm.fit(verbose=False)
sigma = lmm.covariance()
scanner = lmm.get_fast_scanner()
best_beta_se = _lstsq(data.exog.T @ _lstsq(lmm.covariance(), data.exog), eye(7))
best_beta_se = sqrt(best_beta_se.diagonal())
assert_allclose(scanner.null_beta_se, best_beta_se, atol=1e-5)
endog = data.endog.copy()
endog -= endog.mean(0)
endog /= endog.std(0)
exog = data.exog.copy()
exog -= exog.mean(0)
with errstate(invalid="ignore", divide="ignore"):
exog /= exog.std(0)
exog[:, 0] = 1
lmm = LMM(endog, exog, QS)
lmm.fit(verbose=False)
sigma = lmm.covariance()
scanner = lmm.get_fast_scanner()
gls_model = sm.GLS(endog, exog, sigma=sigma)
gls_results = gls_model.fit()
beta_se = gls_results.bse
our_beta_se = sqrt(scanner.null_beta_covariance.diagonal())
# statsmodels scales the covariance matrix we pass, that is why
# we need to account for it here.
assert_allclose(our_beta_se, beta_se / sqrt(gls_results.scale))
assert_allclose(scanner.null_beta_se, beta_se / sqrt(gls_results.scale))
def test_lmm_interface():
random = RandomState(1)
n = 3
G = random.randn(n, n + 1)
X = random.randn(n, 2)
y = X @ random.randn(2) + G @ random.randn(G.shape[1]) + random.randn(n)
y -= y.mean(0)
y /= y.std(0)
QS = economic_qs_linear(G)
lmm = LMM(y, X, QS, restricted=False)
lmm.name = "lmm"
lmm.fit(verbose=False)
assert_allclose(
lmm.covariance(),
[
[0.436311031439718, 2.6243891396439837e-16, 2.0432156171727483e-16],
[2.6243891396439837e-16, 0.4363110314397185, 4.814313140426306e-16],
[2.0432156171727483e-16, 4.814313140426305e-16, 0.43631103143971817],
],
atol=1e-7,
)
assert_allclose(
lmm.mean(),
[0.6398184791042468, -0.8738254794097052, 0.7198112606871158],
atol=1e-7,
)
assert_allclose(lmm.lml(), -3.012715726960625, atol=1e-7)
assert_allclose(lmm.value(), lmm.lml(), atol=1e-7)
assert_allclose(lmm.lml(), -3.012715726960625, atol=1e-7)
assert_allclose(
lmm.X,
[
[-0.3224172040135075, -0.38405435466841564],
[1.1337694423354374, -1.0998912673140309],
[-0.17242820755043575, -0.8778584179213718],
],
atol=1e-7,
)
assert_allclose(lmm.beta, [-1.3155159120000266, -0.5615702941530938], atol=1e-7)
assert_allclose(
lmm.beta_covariance,
[
[0.44737305797088345, 0.20431961864892412],
[0.20431961864892412, 0.29835835133251526],
],
atol=1e-7,
)
assert_allclose(lmm.delta, 0.9999999999999998, atol=1e-7)
assert_equal(lmm.ncovariates, 2)
assert_equal(lmm.nsamples, 3)
assert_allclose(lmm.scale, 0.43631103143971767, atol=1e-7)
assert_allclose(lmm.v0, 9.688051060046502e-17, atol=1e-7)
assert_allclose(lmm.v1, 0.43631103143971756, atol=1e-7)
assert_equal(lmm.name, "lmm")
with pytest.raises(NotImplementedError):
lmm.gradient()
def test_lmm_scan():
random = RandomState(9458)
n = 30
X = _covariates_sample(random, n, n + 1)
offset = 1.0
y = _outcome_sample(random, offset, X)
QS = economic_qs_linear(X)
M0 = random.randn(n, 2)
M1 = random.randn(n, 2)
lmm = LMM(y, M0, QS)
lmm.fit(verbose=False)
v0 = lmm.v0
v1 = lmm.v1
K = v0 * X @ X.T + v1 * eye(n)
M = concatenate((M0, M1), axis=1)
def fun(x):
beta = x[:4]
scale = exp(x[4])
return -st.multivariate_normal(M @ beta, scale * K).logpdf(y)
res = minimize(fun, [0, 0, 0, 0, 0])
scanner = lmm.get_fast_scanner()
r = scanner.scan(M1)
assert_allclose(r["lml"], -res.fun)
assert_allclose(r["effsizes0"], res.x[:2], rtol=1e-5)
assert_allclose(r["effsizes1"], res.x[2:4], rtol=1e-5)
assert_allclose(r["scale"], exp(res.x[4]), rtol=1e-5)
K = r["scale"] * lmm.covariance()
M = concatenate((M0, M1), axis=1)
effsizes_se = sqrt(inv(M.T @ solve(K, M)).diagonal())
assert_allclose(effsizes_se,
concatenate((r["effsizes0_se"], r["effsizes1_se"])))
assert_allclose(scanner.null_lml(), -53.805721275578456, rtol=1e-5)
assert_allclose(scanner.null_beta,
[0.26521964226797085, 0.4334778669761928],
rtol=1e-5)
assert_allclose(
scanner.null_beta_covariance,
[
[0.06302553593799207, 0.00429640179038484],
[0.004296401790384839, 0.05591392416235412],
],
rtol=1e-5,
)
assert_allclose(scanner.null_scale, 1.0)
assert_allclose(scanner.null_beta, lmm.beta, rtol=1e-5)
assert_allclose(scanner.null_beta_covariance,
lmm.beta_covariance,
rtol=1e-5)
def test_lmm_predict():
random = RandomState(9458)
n = 30
X = random.randn(n, n + 1)
X -= X.mean(0)
X /= X.std(0)
X /= sqrt(X.shape[1])
offset = 1.0
mean = OffsetMean(n)
mean.offset = offset
cov_left = LinearCov(X)
cov_left.scale = 1.5
cov_right = EyeCov(n)
cov_right.scale = 1.5
cov = SumCov([cov_left, cov_right])
lik = DeltaProdLik()
y = GGPSampler(lik, mean, cov).sample(random)
QS = economic_qs_linear(X)
lmm = LMM(y, ones((n, 1)), QS)
lmm.fit(verbose=False)
plmm = LMMPredict(y, lmm.beta, lmm.v0, lmm.v1, lmm.mean(),
lmm.covariance())
K = dot(X, X.T)
pm = plmm.predictive_mean(ones((n, 1)), K, K.diagonal())
assert_allclose(corrcoef(y, pm)[0, 1], 0.8358820971891354)
def test_fast_scanner_statsmodel_gls():
from numpy.linalg import lstsq
def _lstsq(A, B):
return lstsq(A, B, rcond=None)[0]
# data = sm.datasets.longley.load()
# data.exog = sm.add_constant(data.exog)
# ols_resid = sm.OLS(data.endog, data.exog).fit().resid
# resid_fit = sm.OLS(ols_resid[1:], sm.add_constant(ols_resid[:-1])).fit()
# rho = resid_fit.params[1]
rho = -0.3634294908774683
# order = toeplitz(range(len(ols_resid)))
order = toeplitz(range(16))
sigma = rho**order
QS = economic_qs(sigma)
endog = reshape(
[
60323.0,
61122.0,
60171.0,
61187.0,
63221.0,
63639.0,
64989.0,
63761.0,
66019.0,
67857.0,
68169.0,
66513.0,
68655.0,
69564.0,
69331.0,
70551.0,
],
(16, ),
)
exog = reshape(
[
1.0,
83.0,
234289.0,
2356.0,
1590.0,
107608.0,
1947.0,
1.0,
88.5,
259426.0,
2325.0,
1456.0,
108632.0,
1948.0,
1.0,
88.2,
258054.0,
3682.0,
1616.0,
109773.0,
1949.0,
1.0,
89.5,
284599.0,
3351.0,
1650.0,
110929.0,
1950.0,
1.0,
96.2,
328975.0,
2099.0,
3099.0,
112075.0,
1951.0,
1.0,
98.1,
346999.0,
1932.0,
3594.0,
113270.0,
1952.0,
1.0,
99.0,
365385.0,
1870.0,
3547.0,
115094.0,
1953.0,
1.0,
100.0,
363112.0,
3578.0,
3350.0,
116219.0,
1954.0,
1.0,
101.2,
397469.0,
2904.0,
3048.0,
117388.0,
1955.0,
1.0,
104.6,
419180.0,
2822.0,
2857.0,
118734.0,
1956.0,
1.0,
108.4,
442769.0,
2936.0,
2798.0,
120445.0,
1957.0,
1.0,
110.8,
444546.0,
4681.0,
2637.0,
121950.0,
1958.0,
1.0,
112.6,
482704.0,
3813.0,
2552.0,
123366.0,
1959.0,
1.0,
114.2,
502601.0,
3931.0,
2514.0,
125368.0,
1960.0,
1.0,
115.7,
518173.0,
4806.0,
2572.0,
127852.0,
1961.0,
1.0,
116.9,
554894.0,
4007.0,
2827.0,
130081.0,
1962.0,
],
(16, 7),
)
lmm = LMM(endog, exog, QS)
lmm.fit(verbose=False)
sigma = lmm.covariance()
scanner = lmm.get_fast_scanner()
best_beta_se = _lstsq(exog.T @ _lstsq(lmm.covariance(), exog), eye(7))
best_beta_se = sqrt(best_beta_se.diagonal())
assert_allclose(scanner.null_beta_se, best_beta_se, atol=1e-4)
endog = endog.copy()
endog -= endog.mean(0)
endog /= endog.std(0)
exog = exog.copy()
exog -= exog.mean(0)
with errstate(invalid="ignore", divide="ignore"):
exog /= exog.std(0)
exog[:, 0] = 1
lmm = LMM(endog, exog, QS)
lmm.fit(verbose=False)
sigma = lmm.covariance()
scanner = lmm.get_fast_scanner()
# gls_model = sm.GLS(endog, exog, sigma=sigma)
# gls_results = gls_model.fit()
# scale = gls_results.scale
scale = 1.7777777777782937
# beta_se = gls_results.bse
beta_se = array([
0.014636888951505144,
0.21334653097414055,
0.7428559936739378,
0.10174713767252333,
0.032745906589939845,
0.3494488802468581,
0.4644879873404213,
])
our_beta_se = sqrt(scanner.null_beta_covariance.diagonal())
# statsmodels scales the covariance matrix we pass, that is why
# we need to account for it here.
assert_allclose(our_beta_se, beta_se / sqrt(scale), rtol=1e-6)
assert_allclose(scanner.null_beta_se, beta_se / sqrt(scale), rtol=1e-6)
