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Compare Missing-Value Strategies for Linear Models

Point72Quantitative Researcher · Online Assessment
MediumQuantitative ResearcherOnline AssessmentMachine Learning

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Compare mean, random empirical, and indicator-assisted imputation for linear models under MCAR, MAR, and MNAR without training leakage.

Compare Missing-Value Strategies for Linear Models

A continuous feature has missing values in a linear prediction problem. Compare three treatments: mean imputation, drawing an imputed value from the observed empirical distribution, and mean imputation plus a missingness indicator. Explain when each can work, how each affects bias, variance, covariance with other features, and what changes under MCAR, MAR, or MNAR missingness.

Constraints & Assumptions

  • Imputation statistics must be learned from training data only.
  • The same transformation is applied during training and serving.
  • Other features may predict both the missing value and the missingness process.
  • The goal is prediction, though coefficient interpretation also matters.

Clarifying Questions to Ask

  • Is missingness caused before or after the outcome is realized?
  • Are train and production missingness rates and mechanisms stable?
  • Is inference or prediction the primary objective?
  • Can a model-based multiple-imputation procedure be used?

Hints

Hint 1

Separate feature value from missingness: Ask what information is lost when the value is absent and whether the event of absence itself carries stable predictive signal.

Follow-up questions

  • Why does random marginal imputation not restore the feature's relationship with the target?
  • When can a missingness indicator become a shortcut that fails after deployment?
  • What would multiple imputation add for statistical inference?