# coding: utf-8

# DO NOT EDIT
# Autogenerated from the notebook robust_models_0.ipynb.
# Edit the notebook and then sync the output with this file.
#
# flake8: noqa
# DO NOT EDIT

# # Robust Linear Models

import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.sandbox.regression.predstd import wls_prediction_std

# ## Estimation
#
# Load data:

data = sm.datasets.stackloss.load()
data.exog = sm.add_constant(data.exog)

# Huber's T norm with the (default) median absolute deviation scaling

huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())
hub_results = huber_t.fit()
print(hub_results.params)
print(hub_results.bse)
print(
    hub_results.summary(
        yname='y',
        xname=['var_%d' % i for i in range(len(hub_results.params))]))

# Huber's T norm with 'H2' covariance matrix

hub_results2 = huber_t.fit(cov="H2")
print(hub_results2.params)
print(hub_results2.bse)

# Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance
# matrix

andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave())
andrew_results = andrew_mod.fit(
    scale_est=sm.robust.scale.HuberScale(), cov="H3")
print('Parameters: ', andrew_results.params)

# See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale``
# for scale options
#
# ## Comparing OLS and RLM
#
# Artificial data with outliers:

nsample = 50
x1 = np.linspace(0, 20, nsample)
X = np.column_stack((x1, (x1 - 5)**2))
X = sm.add_constant(X)
sig = 0.3  # smaller error variance makes OLS<->RLM contrast bigger
beta = [5, 0.5, -0.0]
y_true2 = np.dot(X, beta)
y2 = y_true2 + sig * 1. * np.random.normal(size=nsample)
y2[[39, 41, 43, 45, 48]] -= 5  # add some outliers (10% of nsample)

# ### Example 1: quadratic function with linear truth
#
# Note that the quadratic term in OLS regression will capture outlier
# effects.

res = sm.OLS(y2, X).fit()
print(res.params)
print(res.bse)
print(res.predict())

# Estimate RLM:

resrlm = sm.RLM(y2, X).fit()
print(resrlm.params)
print(resrlm.bse)

# Draw a plot to compare OLS estimates to the robust estimates:

fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111)
ax.plot(x1, y2, 'o', label="data")
ax.plot(x1, y_true2, 'b-', label="True")
prstd, iv_l, iv_u = wls_prediction_std(res)
ax.plot(x1, res.fittedvalues, 'r-', label="OLS")
ax.plot(x1, iv_u, 'r--')
ax.plot(x1, iv_l, 'r--')
ax.plot(x1, resrlm.fittedvalues, 'g.-', label="RLM")
ax.legend(loc="best")

# ### Example 2: linear function with linear truth
#
# Fit a new OLS model using only the linear term and the constant:

X2 = X[:, [0, 1]]
res2 = sm.OLS(y2, X2).fit()
print(res2.params)
print(res2.bse)

# Estimate RLM:

resrlm2 = sm.RLM(y2, X2).fit()
print(resrlm2.params)
print(resrlm2.bse)

# Draw a plot to compare OLS estimates to the robust estimates:

prstd, iv_l, iv_u = wls_prediction_std(res2)

fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(x1, y2, 'o', label="data")
ax.plot(x1, y_true2, 'b-', label="True")
ax.plot(x1, res2.fittedvalues, 'r-', label="OLS")
ax.plot(x1, iv_u, 'r--')
ax.plot(x1, iv_l, 'r--')
ax.plot(x1, resrlm2.fittedvalues, 'g.-', label="RLM")
legend = ax.legend(loc="best")