Robust and weighted fits in Python

RLM downweights outliers; WLS uses weights you supply.

import numpy as np
import statsmodels.api as sm

rng = np.random.default_rng(7)
x = np.linspace(0, 20, 60)
y = 5 + 2 * x + rng.normal(0, 1, size=60)
y[:3] += 60  # three wild outliers

X = sm.add_constant(x)
ols = sm.OLS(y, X).fit()
robust = sm.RLM(y, X, M=sm.robust.norms.HuberT()).fit()
weights = np.where(np.arange(60) < 3, 0.05, 1.0)
weighted = sm.WLS(y, X, weights=weights).fit()

print("ols     ", ols.params.round(3))
print("robust  ", robust.params.round(3))
print("weighted", weighted.params.round(3))

How it works

1. RLM with Huber loss resists a few bad points.
2. WLS weights each observation, usually by inverse variance.
3. Compare the slopes to see how much the outliers moved OLS.

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Step 2 of 2 in Diagnostics & robustness, step 8 of 19 in Statistics with statsmodels.

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