How do multiple imputation techniques handle missing data?

• A. Create a single imputed dataset and analyze once.
• B. Delete cases with missing data and analyze the rest.
• C. Replace missing values with fixed guesses and pool results.
• D. Create multiple complete datasets with imputed values reflecting uncertainty, analyze each, and combine results using Rubin's rules.

Answer: (D)

When data are missing, the idea is to acknowledge that we don’t know the true values and to reflect that uncertainty in the analysis. Multiple imputation does this by creating several complete datasets, each with plausible values for the missing entries drawn from predictive distributions based on the observed data. You then analyze each dataset separately, producing estimates and their standard errors. The results are combined using Rubin’s rules: you take the average of the point estimates across imputations and you combine the within-imputation variance with the between-imputation variance to get a final standard error that properly accounts for the uncertainty due to missing data. This approach preserves the information in the observed data, avoids the bias that can come from deleting cases, and avoids underestimating variability that occurs with single imputation.

Why the other approaches aren’t as good: using a single imputed dataset ignores the uncertainty about what the missing values could be, leading to overly optimistic (too precise) inferences; deleting cases discards data and can bias results if the missingness relates to the outcome; replacing with fixed guesses treats imputed values as known and also underestimates variance, giving confidence intervals that are too narrow.