Impute

Impute is a verb with multiple related senses. In general usage, to impute something is to attribute or ascribe it to someone or something, often to assign responsibility or blame, or to credit an income or property to a person. In statistics and data analysis, imputation refers to the process of replacing missing values in a dataset with substituted values to produce a complete dataset for analysis.

Imputation is used to mitigate biases and inefficiencies caused by missing data. It can be performed as single imputation, where one value fills each missing entry, or as multiple imputation, where several plausible values are generated to reflect uncertainty and results are aggregated.

Common methods include mean or median imputation; regression imputation; hot-deck imputation; k-nearest neighbors (kNN) imputation; and model-based approaches such as multiple imputation by chained equations (MICE) or the expectation-maximization (EM) algorithm. The choice depends on the assumed missingness mechanism and the data structure.

Missing data mechanisms are typically categorized as MCAR (missing completely at random), MAR (missing at random), or MNAR (missing not at random). Imputation methods aim to reduce bias under MAR and MCAR, but improper imputation can distort distributions, reduce variance estimates, and overstate precision. Multiple imputation helps address uncertainty by creating several datasets and combining results.

Etymology: impute comes from Latin imputare, to count against or attribute. In statistical writing, the term has specialized usage; outside statistics, it refers to crediting or attributing traits or outcomes to a person or entity.