Multiple Imputation by Chained Equations

How MICE works

1. start with initial values: filling the missing values with initial values (e.g. mean)
2. iterate over each feature:
   1. Predict X1 using X2, X3 -> Replace missing X1
   2. Predict X2 using X1, X3 -> Replace missing X2
   3. Predict X3 using X1, X2 -> Replace missing X3
3. Repeat this cycle multiple times until convergence
4. Add randomness in predictions
5. Repeat whole process  for a number of iterations

Why “Multiple” Imputation

• opposite to single imputation which fills in each missing value once
• instead make missing value a distribution of plausible values

Key steps

1. create N different complete datasets
2. each dataset has slightly different plausible imputed values
3. train/analyze each dataset separately
4. combine results (average coefficients, adjust variance)

Why “Chained Equations”?

• In each iterative step, each feature with missing values is treated as a target to be predicted with other features

Why use MICE

Pros

• preserves statistical uncertainty
• preserves relationships between features
• allows flexible modeling:
  • Linear regression for continuous
  • Logistic regression for binary
  • Multinomial for categorical
  • Poisson for counts
  • Tree-based models (in some implementations)
• reduces bias, especially when
  • missingness rate is moderate (10–40%)
  • strong feature correlations exist
  • dataset is not extremely large

Cons

• assumes Missing At Random Handling Missing Data#^656f1e
• computationally heavier
• sensitive to model misspecification