Compare Missing-Value Strategies for Linear Models

# 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? ### What a Strong Answer Covers - Marginal-distribution and relationship changes caused by each method - The value and limitation of a missingness indicator - MCAR, MAR, and MNAR assumptions - Leakage-free preprocessing, uncertainty, and evaluation by missingness cohort ### Follow-up Questions 1. Why does random marginal imputation not restore the feature's relationship with the target? 2. When can a missingness indicator become a shortcut that fails after deployment? 3. What would multiple imputation add for statistical inference? ```hint 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. ```