def test_pat():
x = np.asarray([[1, np.nan, 3], [np.nan, 2, np.nan], [3, np.nan, 0],
[np.nan, 1, np.nan], [3, 2, 1]])
bm = BayesGaussMI(x)
assert_allclose(bm.patterns[0], np.r_[0, 2])
assert_allclose(bm.patterns[1], np.r_[1, 3])
def test_MI():
np.random.seed(414)
x = np.random.normal(size=(200, 4))
x[[1, 3, 9], 0] = np.nan
x[[1, 4, 3], 1] = np.nan
x[[2, 11, 21], 2] = np.nan
x[[11, 22, 99], 3] = np.nan
def model_args_fn(x):
# Return endog, exog
# Regress x0 on x1 and x2
if type(x) is np.ndarray:
return (x[:, 0], x[:, 1:])
else:
return (x.iloc[:, 0].values, x.iloc[:, 1:].values)
for j in (0, 1):
np.random.seed(2342)
imp = BayesGaussMI(x.copy())
mi = MI(imp, sm.OLS, model_args_fn, burn=0)
r = mi.fit()
r.summary() # smoke test
# TODO: why does the test tolerance need to be so slack?
# There is unexpected variation across versions on travis.
assert_allclose(r.params, np.r_[-0.05347919, -0.02479701, 0.10075517],
0.25, 0)
c = np.asarray([[0.00418232, 0.00029746, -0.00035057],
[0.00029746, 0.00407264, 0.00019496],
[-0.00035057, 0.00019496, 0.00509413]])
assert_allclose(r.cov_params(), c, 0.3, 0)
# Test with ndarray and pandas input
x = pd.DataFrame(x)
def test_mi_formula():
np.random.seed(414)
x = np.random.normal(size=(200, 4))
x[[1, 3, 9], 0] = np.nan
x[[1, 4, 3], 1] = np.nan
x[[2, 11, 21], 2] = np.nan
x[[11, 22, 99], 3] = np.nan
df = pd.DataFrame({
"y": x[:, 0],
"x1": x[:, 1],
"x2": x[:, 2],
"x3": x[:, 3]
})
fml = "y ~ 0 + x1 + x2 + x3"
np.random.seed(2342)
imp = BayesGaussMI(df.copy())
mi = MI(imp, sm.OLS, formula=fml, burn=0)
r = mi.fit()
r.summary() # smoke test
# TODO: why does the test tolerance need to be so slack?
# There is unexpected variation across versions on travis.
assert_allclose(r.params, np.r_[-0.05347919, -0.02479701, 0.10075517],
0.25, 0)
c = np.asarray([[0.00418232, 0.00029746, -0.00035057],
[0.00029746, 0.00407264, 0.00019496],
[-0.00035057, 0.00019496, 0.00509413]])
assert_allclose(r.cov_params(), c, 0.3, 0)
def test_2x2():
# Generate correlated data with mean and variance
np.random.seed(3434)
x = np.random.normal(size=(1000, 2))
r = 0.5
x[:, 1] = r*x[:, 0] + np.sqrt(1-r**2)*x[:, 1]
x[:, 0] *= 2
x[:, 1] *= 3
x[:, 0] += 1
x[:, 1] -= 2
# Introduce some missing values
u = np.random.normal(size=x.shape[0])
x[u > 1, 0] = np.nan
u = np.random.normal(size=x.shape[0])
x[u > 1, 1] = np.nan
bm = BayesGaussMI(x)
# Burn-in
for k in range(500):
bm.update()
# Estimate the posterior mean
mean = 0
cov = 0
dmean = 0
dcov = 0
for k in range(500):
bm.update()
mean += bm.mean
cov += bm.cov
dmean += bm.data.mean(0)
dcov += np.cov(bm.data.T)
mean /= 500
cov /= 500
dmean /= 500
dcov /= 500
assert_allclose(mean, np.r_[1, -2], 0.1)
assert_allclose(dmean, np.r_[1, -2], 0.1)
assert_allclose(cov, np.asarray([[4, 6*r], [6*r, 9]]), 0.1)
assert_allclose(dcov, np.asarray([[4, 6*r], [6*r, 9]]), 0.1)
def test_MI_stat():
# Test for MI where we know statistically what should happen. The
# analysis model is x0 ~ x1 with standard error 1/sqrt(n) for the
# slope parameter. The nominal n is 1000, but half of the cases
# have missing x1. Then we introduce x2 that is either
# independent of x1, or almost perfectly correlated with x1. In
# the first case the SE is 1/sqrt(500), in the second case the SE
# is 1/sqrt(1000).
np.random.seed(414)
z = np.random.normal(size=(1000, 3))
z[:, 0] += 0.5 * z[:, 1]
# Control the degree to which x2 proxies for x1
exp = [1 / np.sqrt(500), 1 / np.sqrt(1000)]
fmi = [0.5, 0]
for j, r in enumerate((0, 0.9999)):
x = z.copy()
x[:, 2] = r * x[:, 1] + np.sqrt(1 - r**2) * x[:, 2]
x[0:500, 1] = np.nan
def model_args(x):
# Return endog, exog
# Regress x1 on x2
return (x[:, 0], x[:, 1])
np.random.seed(2342)
imp = BayesGaussMI(x.copy())
mi = MI(imp, sm.OLS, model_args, nrep=100, skip=10)
r = mi.fit()
# Check the SE
d = np.abs(r.bse[0] - exp[j]) / exp[j]
assert (d < 0.03)
# Check the FMI
d = np.abs(r.fmi[0] - fmi[j])
assert (d < 0.05)
def test_2x2():
# Generate correlated data with mean and variance
np.random.seed(3434)
x = np.random.normal(size=(1000, 2))
r = 0.5
x[:, 1] = r * x[:, 0] + np.sqrt(1 - r**2) * x[:, 1]
x[:, 0] *= 2
x[:, 1] *= 3
x[:, 0] += 1
x[:, 1] -= 2
# Introduce some missing values
u = np.random.normal(size=x.shape[0])
x[u > 1, 0] = np.nan
u = np.random.normal(size=x.shape[0])
x[u > 1, 1] = np.nan
bm = BayesGaussMI(x)
# Burn-in
for k in range(500):
bm.update()
# Estimate the posterior mean
mean = 0
cov = 0
dmean = 0
dcov = 0
for k in range(500):
bm.update()
mean += bm.mean
cov += bm.cov
dmean += bm.data.mean(0)
dcov += np.cov(bm.data.T)
mean /= 500
cov /= 500
dmean /= 500
dcov /= 500
assert_allclose(mean, np.r_[1, -2], 0.1)
assert_allclose(dmean, np.r_[1, -2], 0.1)
assert_allclose(cov, np.asarray([[4, 6 * r], [6 * r, 9]]), 0.1)
assert_allclose(dcov, np.asarray([[4, 6 * r], [6 * r, 9]]), 0.1)
