regresjonsimputation

Regresjonsimputation, or regression imputation, is a statistical method for handling missing data by filling in missing values with predictions from a regression model trained on observed data. The approach rests on the idea that the missing values can be inferred from related variables that are observed for all units.

Typically, a regression model is fitted using cases with complete data, and the model is then used to predict the missing entry. If a variable Y is missing for some units, a model Y ~ X1 + X2 + ... is estimated from units with observed Y, and predicted values Ŷ are substituted for the missing Y. In single imputation, the predicted values replace the missing values directly. In multiple imputation, several plausible values are drawn from the predictive distribution to create several complete datasets, and results are combined to reflect uncertainty.

Key assumptions include that the missing data mechanism is at least MAR (missing at random) and that the regression model is correctly specified for the relationships among variables. When these conditions hold, regression imputation can preserve relationships among variables and utilize information from observed data.

Advantages include simplicity and efficiency, especially when relationships are well captured by the model. Limitations include the tendency of single regression imputation to underestimate variability and standard errors, potential bias if the model is misspecified, and sensitivity to departures from missing-at-random assumptions. Regression imputation is commonly used as part of a broader imputation strategy, often within the framework of multiple imputation, to provide more reliable inferences. Related approaches include predictive mean matching and fully conditional specification methods that use regression models for each variable with missing values.