def get_results_mice_imputation_includingy(X_incomplete, y):
# Impute incomplete data using the IterativeImputer as a MICEImputer
# Now using the output variable in the imputation loop
m = 5
multiple_imputations = []
for i in range(m):
Xy = np.column_stack((X_incomplete, y))
imputer = ChainedImputer(n_burn_in=99, n_imputations=1, random_state=i)
imputer.fit(Xy)
data_imputed = imputer.transform(Xy)
# We save only the X imputed data because we do not want to use y to
# predict y later on.
X_imputed = data_imputed[:, :-1]
multiple_imputations.append(X_imputed)
# Perform linear regression on mice multiple imputed data
# Estimate beta estimates and their variances
m_coefs = []
m_vars = []
for i in range(m):
estimator = LinearRegression()
estimator.fit(multiple_imputations[i], y)
y_predict = estimator.predict(multiple_imputations[i])
m_coefs.append(estimator.coef_)
m_vars.append(
calculate_variance_of_beta_estimates(y, y_predict,
multiple_imputations[i]))
# Calculate the end estimates by applying Rubin's rules.
Qbar = calculate_Qbar(m_coefs)
T = calculate_T(m_coefs, m_vars, Qbar)
mice_errorbar = 1.96 * np.sqrt(T)
return Qbar, T, mice_errorbar
def get_results_mice_imputation(X_incomplete, y):
# Impute incomplete data using the IterativeImputer to perform multiple
# imputation. We set n_burn_in at 99 and use only last imputation and
# loop this procedure m times.
m = 5
multiple_imputations = []
for i in range(m):
imputer = ChainedImputer(n_burn_in=99, n_imputations=1, random_state=i)
imputer.fit(X_incomplete)
X_imputed = imputer.transform(X_incomplete)
multiple_imputations.append(X_imputed)
# Perform a model on each of the m imputed datasets
# Estimate the estimates for each model/dataset
m_coefs = []
m_vars = []
for i in range(m):
estimator = LinearRegression()
estimator.fit(multiple_imputations[i], y)
y_predict = estimator.predict(multiple_imputations[i])
m_coefs.append(estimator.coef_)
m_vars.append(
calculate_variance_of_beta_estimates(y, y_predict,
multiple_imputations[i]))
# Calculate the end estimates by applying Rubin's rules.
Qbar = calculate_Qbar(m_coefs)
T = calculate_T(m_coefs, m_vars, Qbar)
mice_errorbar = 1.96 * np.sqrt(T)
return Qbar, T, mice_errorbar
def test_chained_imputer_transform_stochasticity():
rng = np.random.RandomState(0)
n = 100
d = 10
X = sparse_random_matrix(n, d, density=0.10, random_state=rng).toarray()
imputer = ChainedImputer(missing_values=0,
n_imputations=1,
n_burn_in=1,
random_state=rng)
imputer.fit(X)
X_fitted_1 = imputer.transform(X)
X_fitted_2 = imputer.transform(X)
# sufficient to assert that the means are not the same
assert np.mean(X_fitted_1) != pytest.approx(np.mean(X_fitted_2))
def test_chained_imputer_transform_stochasticity():
rng = np.random.RandomState(0)
n = 100
d = 10
X = sparse_random_matrix(n, d, density=0.10,
random_state=rng).toarray()
imputer = ChainedImputer(missing_values=0,
n_imputations=1,
n_burn_in=1,
random_state=rng)
imputer.fit(X)
X_fitted_1 = imputer.transform(X)
X_fitted_2 = imputer.transform(X)
# sufficient to assert that the means are not the same
assert np.mean(X_fitted_1) != pytest.approx(np.mean(X_fitted_2))
def test_chained_imputer_no_missing():
rng = np.random.RandomState(0)
X = rng.rand(100, 100)
X[:, 0] = np.nan
m1 = ChainedImputer(n_imputations=10, random_state=rng)
m2 = ChainedImputer(n_imputations=10, random_state=rng)
pred1 = m1.fit(X).transform(X)
pred2 = m2.fit_transform(X)
# should exclude the first column entirely
assert_allclose(X[:, 1:], pred1)
# fit and fit_transform should both be identical
assert_allclose(pred1, pred2)
def test_chained_imputer_no_missing():
rng = np.random.RandomState(0)
X = rng.rand(100, 100)
X[:, 0] = np.nan
m1 = ChainedImputer(n_imputations=10, random_state=rng)
m2 = ChainedImputer(n_imputations=10, random_state=rng)
pred1 = m1.fit(X).transform(X)
pred2 = m2.fit_transform(X)
# should exclude the first column entirely
assert_allclose(X[:, 1:], pred1)
# fit and fit_transform should both be identical
assert_allclose(pred1, pred2)
def get_results_chained_imputation(X_incomplete, y):
# Impute incomplete data with IterativeImputer using single imputation
# We set n_burn_in at 99 and use only the last imputation
imputer = ChainedImputer(n_burn_in=99, n_imputations=1)
imputer.fit(X_incomplete)
X_imputed = imputer.transform(X_incomplete)
# Perform linear regression on chained single imputed data
# Estimate beta estimates and their variances
estimator = LinearRegression()
estimator.fit(X_imputed, y)
y_predict = estimator.predict(X_imputed)
# Save the beta estimates, the variance of these estimates and 1.96 *
# standard error of the estimates
chained_coefs = estimator.coef_
chained_vars = calculate_variance_of_beta_estimates(
y, y_predict, X_imputed)
chained_errorbar = 1.96 * np.sqrt(chained_vars)
return chained_coefs, chained_vars, chained_errorbar