Mehrfachimputation

Mehrfachimputation, or multiple imputation, is a statistical method for handling missing data by creating several plausible complete datasets, analyzing each one separately, and then combining the results to account for uncertainty due to missingness. The central idea is to replace every missing value with a set of plausible values drawn from a distribution conditional on the observed data, producing m complete datasets.

The typical workflow consists of four steps. First, specify an imputation model that captures the relations among variables and respects the data structure. Second, generate m imputations to create m complete datasets. Third, analyze each dataset with the intended statistical method. Fourth, pool the results across imputations using Rubin’s rules to obtain a single estimate and an associated standard error that reflect both within-imputation and between-imputation variability.

Imputation models can be parametric, such as joint modeling with a multivariate distribution, or semi-parametric, as in fully conditional specification (chained equations) or predictive mean matching. The method is most appropriate under missing at random (MAR) assumptions, meaning the probability of missingness may depend on observed data but not on unobserved values. Including relevant auxiliary variables in the imputation model helps satisfy MAR and reduce bias. Results are interpreted as incorporating uncertainty about missing values, with pooling yielding valid inferences under the imputation model.

Limitations include dependence on correct model specification, computational demands, and potential bias if data are missing not at random (MNAR) without sensitivity analyses. Mehrfachimputation has become a standard tool in many fields, enabling more efficient and less biased use of incomplete data.