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Outlier Analysis (Standardized Residuals)

Outlier Analysis (Standardized Residuals)

Overview

Definition

Outliers are data points that deviate significantly from the rest of the observations.

  • Standardized Residuals: The model errors divided by their standard deviation. This puts errors on a Z-score scale.
Rule of Thumb

  • |Z|>2: Suspect. (Occurs 5% of time).
  • |Z|>3: Outlier. (Occurs 0.3% of time).

1. Python Implementation

import numpy as np

# 1. Get Standardized Residuals
influence = model.get_influence()
standardized_residuals = influence.resid_studentized_internal

# 2. Filter Outliers (|Z| > 3)
outliers = np.where(np.abs(standardized_residuals) > 3)[0]
print(f"Outlier Indices: {outliers}")

2. R Implementation

# 1. Get Standardized Residuals (rstandard)
res_std <- rstandard(model)

# 2. Identify
outliers <- which(abs(res_std) > 3)
print(outliers)

# 3. Plot
plot(model, 3) # Scale-Location plot helps see them