def test_comp_with_statsmodels(self):
""" Comparing with confidence intervals and standard errors of statsmodels in the un-weighted case """
np.random.seed(123)
# Single dimensional output y
n = 1000
d = 3
X = np.random.binomial(1, .8, size=(n, d))
T = np.random.binomial(1, .5 * X[:, 0] + .25, size=(n,))
def true_effect(x):
return x[:, 0] + .5
y = true_effect(X) * T + X[:, 0] + X[:, 2] + np.random.normal(0, 1, size=(n,))
X_test = np.unique(np.random.binomial(1, .5, size=(n, d)), axis=0)
for fit_intercept in [True, False]:
for cov_type in ['nonrobust', 'HC0', 'HC1']:
est = OLS(fit_intercept=fit_intercept, cov_type=cov_type).fit(X, y)
lr = StatsModelsOLS(fit_intercept=fit_intercept, fit_args={
'cov_type': cov_type, 'use_t': False}).fit(X, y)
_compare_classes(est, lr, X_test)
n = 1000
d = 3
X = np.random.normal(0, 1, size=(n, d))
y = X[:, 0] + X[:, 2] + np.random.normal(0, 1, size=(n,))
X_test = np.unique(np.random.binomial(1, .5, size=(n, d)), axis=0)
for fit_intercept in [True, False]:
for cov_type in ['nonrobust', 'HC0', 'HC1']:
est = OLS(fit_intercept=fit_intercept, cov_type=cov_type).fit(X, y)
lr = StatsModelsOLS(fit_intercept=fit_intercept, fit_args={
'cov_type': cov_type, 'use_t': False}).fit(X, y)
_compare_classes(est, lr, X_test)
d = 3
X = np.vstack([np.eye(d)])
y = np.concatenate((X[:, 0] - 1, X[:, 0] + 1))
X = np.vstack([X, X])
X_test = np.unique(np.random.binomial(1, .5, size=(n, d)), axis=0)
for cov_type in ['nonrobust', 'HC0', 'HC1']:
for alpha in [.01, .05, .1]:
_compare_classes(OLS(fit_intercept=False, cov_type=cov_type).fit(X, y),
StatsModelsOLS(fit_intercept=False, fit_args={
'cov_type': cov_type, 'use_t': False}).fit(X, y),
X_test, alpha=alpha)
d = 3
X = np.vstack([np.eye(d), np.ones((1, d)), np.zeros((1, d))])
y = np.concatenate((X[:, 0] - 1, X[:, 0] + 1))
X = np.vstack([X, X])
X_test = np.unique(np.random.binomial(1, .5, size=(n, d)), axis=0)
for cov_type in ['nonrobust', 'HC0', 'HC1']:
_compare_classes(OLS(fit_intercept=True, cov_type=cov_type).fit(X, y),
StatsModelsOLS(fit_intercept=True,
fit_args={'cov_type': cov_type, 'use_t': False}).fit(X, y), X_test)
# Multi-dimensional output y
n = 1000
d = 3
for p in np.arange(1, 4):
X = np.random.binomial(1, .8, size=(n, d))
T = np.random.binomial(1, .5 * X[:, 0] + .25, size=(n,))
def true_effect(x):
return np.hstack([x[:, [0]] + .5 + t for t in range(p)])
y = np.zeros((n, p))
y = true_effect(X) * T.reshape(-1, 1) + X[:, [0] * p] + \
(0 * X[:, [0] * p] + 1) * np.random.normal(0, 1, size=(n, p))
for cov_type in ['nonrobust', 'HC0', 'HC1']:
for fit_intercept in [True, False]:
for alpha in [.01, .05, .2]:
est = OLS(fit_intercept=fit_intercept, cov_type=cov_type).fit(X, y)
lr = [StatsModelsOLS(fit_intercept=fit_intercept, fit_args={
'cov_type': cov_type, 'use_t': False}).fit(X, y[:, t]) for t in range(p)]
for t in range(p):
assert np.all(np.abs(est.coef_[t] - lr[t].coef_) < 1e-12),\
"{}, {}, {}: {}, {}".format(cov_type, fit_intercept, t, est.coef_[t], lr[t].coef_)
assert np.all(np.abs(np.array(est.coef__interval(alpha=alpha))[:, t] -
lr[t].coef__interval(alpha=alpha)) < 1e-12),\
"{}, {}, {}: {} vs {}".format(cov_type, fit_intercept, t,
np.array(est.coef__interval(alpha=alpha))[:, t],
lr[t].coef__interval(alpha=alpha))
assert np.all(np.abs(est.intercept_[t] - lr[t].intercept_) < 1e-12),\
"{}, {}, {}: {} vs {}".format(cov_type, fit_intercept, t,
est.intercept_[t], lr[t].intercept_)
assert np.all(np.abs(np.array(est.intercept__interval(alpha=alpha))[:, t] -
lr[t].intercept__interval(alpha=alpha)) < 1e-12),\
"{}, {}, {}: {} vs {}".format(cov_type, fit_intercept, t,
np.array(est.intercept__interval(alpha=alpha))[:, t],
lr[t].intercept__interval(alpha=alpha))
assert np.all(np.abs(est.predict(X_test)[:, t] - lr[t].predict(X_test)) < 1e-12),\
"{}, {}, {}: {} vs {}".format(cov_type, fit_intercept, t, est.predict(X_test)[
:, t], lr[t].predict(X_test))
assert np.all(np.abs(np.array(est.predict_interval(X_test, alpha=alpha))[:, :, t] -
lr[t].predict_interval(X_test, alpha=alpha)) < 1e-12),\
"{}, {}, {}: {} vs {}".format(cov_type, fit_intercept, t,
np.array(est.predict_interval(X_test,
alpha=alpha))[:, :, t],
lr[t].predict_interval(X_test, alpha=alpha))
def test_inference(self):
""" Testing that we recover the expected standard errors and confidence intervals in a known example """
# 1-d output
d = 3
X = np.vstack([np.eye(d)])
y = X[:, 0]
est = OLS(fit_intercept=False).fit(X, y)
assert np.all(np.abs(est.coef_ - [1, 0, 0]) <= 1e-12), "{}, {}".format(est.coef_, [1, 0, 0])
assert np.all(np.abs(est.coef__interval() - np.array([[1, 0, 0], [1, 0, 0]])) <= 1e-12),\
"{}, {}".format(est.coef__interval(), np.array([[1, 0, 0], [1, 0, 0]]))
assert np.all(est.coef_stderr_ <= 1e-12)
assert np.all(est._param_var <= 1e-12)
d = 3
X = np.vstack([np.eye(d), np.ones((1, d)), np.zeros((1, d))])
y = X[:, 0]
est = OLS(fit_intercept=True).fit(X, y)
assert np.all(np.abs(est.coef_ - np.array([1] + [0] * (d - 1))) <=
1e-12), "{}, {}".format(est.coef_, [1] + [0] * (d - 1))
assert np.all(np.abs(est.coef__interval() - np.array([[1] + [0] * (d - 1), [1] + [0] * (d - 1)])) <= 1e-12),\
"{}, {}".format(est.coef__interval(), np.array([[1] + [0] * (d - 1), [1] + [0] * (d - 1)]))
assert np.all(est.coef_stderr_ <= 1e-12)
assert np.all(est._param_var <= 1e-12)
assert np.abs(est.intercept_) <= 1e-12
assert np.all(np.abs(est.intercept__interval()) <= 1e-12)
d = 3
X = np.vstack([np.eye(d)])
y = np.concatenate((X[:, 0] - 1, X[:, 0] + 1))
X = np.vstack([X, X])
est = OLS(fit_intercept=False).fit(X, y)
assert np.all(np.abs(est.coef_ - ([1] + [0] * (d - 1))) <=
1e-12), "{}, {}".format(est.coef_, [1] + [0] * (d - 1))
assert np.all(np.abs(est.coef_stderr_ - np.array([1] * d)) <= 1e-12)
assert np.all(np.abs(est.coef__interval()[0] -
np.array([scipy.stats.norm.ppf(.025, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.025, loc=0, scale=1)] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[0], np.array([scipy.stats.norm.ppf(.025, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.025, loc=0, scale=1)] * (d - 1)))
assert np.all(np.abs(est.coef__interval()[1] -
np.array([scipy.stats.norm.ppf(.975, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.975, loc=0, scale=1)] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[1], np.array([scipy.stats.norm.ppf(.975, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.975, loc=0, scale=1)] * (d - 1)))
# 2-d output
d = 3
p = 4
X = np.vstack([np.eye(d)])
y = np.vstack((X[:, [0] * p] - 1, X[:, [0] * p] + 1))
X = np.vstack([X, X])
est = OLS(fit_intercept=False).fit(X, y)
for t in range(p):
assert np.all(np.abs(est.coef_[t] - ([1] + [0] * (d - 1))) <=
1e-12), "{}, {}".format(est.coef_[t], [1] + [0] * (d - 1))
assert np.all(np.abs(est.coef_stderr_[t] - np.array([1] * d)) <= 1e-12), "{}".format(est.coef_stderr_[t])
assert np.all(np.abs(est.coef__interval()[0][t] -
np.array([scipy.stats.norm.ppf(.025, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.025, loc=0, scale=1)] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[0][t],
np.array([scipy.stats.norm.ppf(.025, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.025, loc=0, scale=1)] * (d - 1)))
assert np.all(np.abs(est.coef__interval()[1][t] -
np.array([scipy.stats.norm.ppf(.975, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.975, loc=0, scale=1)] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[1][t],
np.array([scipy.stats.norm.ppf(.975, loc=1, scale=1)] +
[scipy.stats.norm.ppf(.975, loc=0, scale=1)] * (d - 1)))
assert np.all(np.abs(est.intercept_[t]) <= 1e-12), "{}, {}".format(est.intercept_[t])
assert np.all(np.abs(est.intercept_stderr_[t]) <= 1e-12), "{}".format(est.intercept_stderr_[t])
assert np.all(np.abs(est.intercept__interval()[0][t]) <=
1e-12), "{}".format(est.intercept__interval()[0][t])
d = 3
p = 4
X = np.vstack([np.eye(d), np.zeros((1, d))])
y = np.vstack((X[:, [0] * p] - 1, X[:, [0] * p] + 1))
X = np.vstack([X, X])
est = OLS(fit_intercept=True).fit(X, y)
for t in range(p):
assert np.all(np.abs(est.coef_[t] - ([1] + [0] * (d - 1))) <=
1e-12), "{}, {}".format(est.coef_[t], [1] + [0] * (d - 1))
assert np.all(np.abs(est.coef_stderr_[t] - np.array([np.sqrt(2)] * d)) <=
1e-12), "{}".format(est.coef_stderr_[t])
assert np.all(np.abs(est.coef__interval()[0][t] -
np.array([scipy.stats.norm.ppf(.025, loc=1, scale=np.sqrt(2))] +
[scipy.stats.norm.ppf(.025, loc=0, scale=np.sqrt(2))] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[0][t],
np.array([scipy.stats.norm.ppf(.025, loc=1, scale=np.sqrt(2))] +
[scipy.stats.norm.ppf(.025, loc=0, scale=np.sqrt(2))] * (d - 1)))
assert np.all(np.abs(est.coef__interval()[1][t] -
np.array([scipy.stats.norm.ppf(.975, loc=1, scale=np.sqrt(2))] +
[scipy.stats.norm.ppf(.975, loc=0, scale=np.sqrt(2))] * (d - 1))) <= 1e-12),\
"{}, {}".format(est.coef__interval()[1][t],
np.array([scipy.stats.norm.ppf(.975, loc=1, scale=np.sqrt(2))] +
[scipy.stats.norm.ppf(.975, loc=0, scale=np.sqrt(2))] * (d - 1)))
assert np.all(np.abs(est.intercept_[t]) <= 1e-12), "{}, {}".format(est.intercept_[t])
assert np.all(np.abs(est.intercept_stderr_[t] - 1) <= 1e-12), "{}".format(est.intercept_stderr_[t])
assert np.all(np.abs(est.intercept__interval()[0][t] -
scipy.stats.norm.ppf(.025, loc=0, scale=1)) <= 1e-12),\
"{}, {}".format(est.intercept__interval()[0][t], scipy.stats.norm.ppf(.025, loc=0, scale=1))