def test_influence_dtype():
# see #2148 bug when endog is integer
y = np.ones(20)
np.random.seed(123)
x = np.random.randn(20, 3)
res1 = OLS(y, x).fit()
res2 = OLS(y*1., x).fit()
cr1 = res1.get_influence().cov_ratio
cr2 = res2.get_influence().cov_ratio
assert_allclose(cr1, cr2, rtol=1e-14)
# regression test for values
cr3 = np.array(
[ 1.22239215, 1.31551021, 1.52671069, 1.05003921, 0.89099323,
1.57405066, 1.03230092, 0.95844196, 1.15531836, 1.21963623,
0.87699564, 1.16707748, 1.10481391, 0.98839447, 1.08999334,
1.35680102, 1.46227715, 1.45966708, 1.13659521, 1.22799038])
assert_almost_equal(cr1, cr3, decimal=8)
def test_outlier_influence_funcs():
# smoke test
x = add_constant(np.random.randn(10, 2))
y = x.sum(1) + np.random.randn(10)
res = OLS(y, x).fit()
oi.summary_table(res, alpha=0.05)
res2 = OLS(y, x[:, 0]).fit()
oi.summary_table(res2, alpha=0.05)
infl = res2.get_influence()
infl.summary_table()
def test_outlier_influence_funcs():
#smoke test
x = add_constant(np.random.randn(10, 2))
y = x.sum(1) + np.random.randn(10)
res = OLS(y, x).fit()
oi.summary_table(res, alpha=0.05)
res2 = OLS(y, x[:,0]).fit()
oi.summary_table(res2, alpha=0.05)
infl = res2.get_influence()
infl.summary_table()
def test_outlier_influence_funcs(reset_randomstate):
x = add_constant(np.random.randn(10, 2))
y = x.sum(1) + np.random.randn(10)
res = OLS(y, x).fit()
out_05 = oi.summary_table(res)
# GH3344 : Check alpha has an effect
out_01 = oi.summary_table(res, alpha=0.01)
assert_(np.all(out_01[1][:, 6] <= out_05[1][:, 6]))
assert_(np.all(out_01[1][:, 7] >= out_05[1][:, 7]))
res2 = OLS(y, x[:, 0]).fit()
oi.summary_table(res2, alpha=0.05)
infl = res2.get_influence()
infl.summary_table()
def test_outlier_influence_funcs(reset_randomstate):
x = add_constant(np.random.randn(10, 2))
y = x.sum(1) + np.random.randn(10)
res = OLS(y, x).fit()
out_05 = oi.summary_table(res)
# GH3344 : Check alpha has an effect
out_01 = oi.summary_table(res, alpha=0.01)
assert_(np.all(out_01[1][:, 6] <= out_05[1][:, 6]))
assert_(np.all(out_01[1][:, 7] >= out_05[1][:, 7]))
res2 = OLS(y, x[:,0]).fit()
oi.summary_table(res2, alpha=0.05)
infl = res2.get_influence()
infl.summary_table()
def ols_sm(X_train, y_train, X_test):
X_train = sm.add_constant(
X_train) # adds col of ones for intercept coefficient in OLS model
ols = OLS(y_train, X_train).fit()
# with open('ols_model_summary.csv', 'w') as f:
# f.write(ols.summary().as_csv())
with open('ols_model_summary.txt', 'w') as f:
f.write(ols.summary().as_text())
# Plot True vs Predicted values to examine if linear model is a good fit
fig = plt.figure(figsize=(12, 8))
X_test = sm.add_constant(X_test)
plt.scatter(y_test, ols.predict(X_test))
plt.xlabel('True values')
plt.ylabel('Predicted values')
plt.title('True vs Predicted values')
plt.show()
plt.close()
# Add quadratic term to X or take log of y to improve
# Discern if a linear relationship exists with partial regression plots
fig = plt.figure(figsize=(12, 8))
fig = sm.graphics.plot_partregress_grid(ols, fig=fig)
plt.title('Partial Regression Plots')
plt.show()
plt.close()
# Identify outliers and high leverage points
# a. Identify outliers (typically, those data points with studentized residuals outside of +/- 3 stdev).
# Temporarily remove these from your data set and re-run your model.
# Do your model metrics improve considerably? Does this give you cause for more confidence in your model?
# b. Identify those outliers that are also high-leverage points (high residual and high leverage --> high influence).
fig, ax = plt.subplots(figsize=(12, 8))
fig = sm.graphics.influence_plot(ols, ax=ax, criterion="cooks")
plt.show()
fig, ax = plt.subplots(figsize=(8, 6))
fig = sm.graphics.plot_leverage_resid2(ols, ax=ax)
plt.show()
plt.close()
# Confirm homoscedasticity (i.e., constant variance of residual terms)
# If residuals exhibit a “funnel shaped” effect, consider transforming your data into logarithmic space.
studentized_residuals = ols.outlier_test()[:, 0]
y_pred = ols.fittedvalues
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(y_pred, studentized_residuals)
ax.axhline(y=0.0, color='k', ls='--')
ax.set_xlabel('Predicted y')
ax.set_ylabel('Studentized Residuals')
plt.show()
plt.close()
# Test if residuals are normally distributed in QQ plot
# plots quantile of the normal distribution against studentized residuals
# if sample quantiles are normally distributed, the dots will align with 45 deg line
fig, ax = plt.subplots()
sm.graphics.qqplot(studentized_residuals, fit=True, line='45', ax=ax)
plt.show()
plt.close()
# Find influencial points in data
# DFBETAS - standardized measure of how much each coefficient changes when that observation is left out
threshold = 2. / len(X_train)**.5
infl = ols.get_influence()
df = pd.DataFrame(infl.summary_frame().filter(regex="dfb"))
inf = df[df > threshold].dropna(axis=0, how='all')
print('Influencial points:\n', inf)
