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Regression Imputation
An imputation method that predicts each missing value from a regression model fit on other, fully observed variables correlated with it, preserving relationships between variables better than mean imputation but still understating uncertainty if used as a single, deterministic fill-in.
In Plain English
Regression imputation improves on mean imputation by using other information you do have about a respondent to make a smarter guess about what their missing value probably was. If income is missing but you know the person's education, occupation, and age, all of which correlate with income, you can fit a regression model of income on those other variables using everyone who did report income, and then use that fitted model to predict the missing income values from each person's own known characteristics. This preserves genuine relationships between variables far better than just plugging in the overall average, but the basic (deterministic) version still has a real flaw: every predicted value falls exactly on the fitted regression line, understating the natural scatter real observations would have around it, which is why a stochastic version, adding random noise back into each prediction, or full multiple imputation is generally preferred in careful analysis.
Definition
Regression imputation predicts each missing value of a variable from a regression model, , fit using cases with observed and predictors measured, then applies the fitted model to each case with missing to generate a predicted fill-in value from that case's own observed predictor values. Deterministic regression imputation, using the fitted value directly, better preserves relationships between the imputed variable and its predictors than mean imputation does, but still understates the variable's true variance, since every imputed value falls exactly on the regression surface with none of the natural residual scatter real data would exhibit; stochastic regression imputation addresses this by adding a randomly drawn residual to each predicted value, , restoring realistic variability, and is a closer precursor to full multiple imputation, which further replicates this stochastic imputation process multiple times to also propagate the imputation uncertainty into final standard errors.
Formula
Properties
- Deterministic regression imputation's core flaw, that imputed values fall exactly on the fitted regression surface with no natural scatter, produces artificially high apparent predictive relationships and understated residual variance, a subtler version of the same variance-distortion problem that afflicts mean imputation, just less severe.
- Stochastic regression imputation, adding a randomly drawn residual back to each fitted prediction, directly addresses the deterministic version's variance-understatement problem and is generally preferred whenever regression imputation is used as a single (rather than multiple) imputation method.
- Regression imputation is the conceptual bridge between simple deterministic imputation methods and multiple imputation, multiple imputation can be understood as repeating a stochastic regression-imputation-like process many times, generating several plausible complete datasets, and combining results across them to also capture the imputation model's own uncertainty.
At a Glance