imputation

Imputation is the process of replacing missing data with substituted values to produce a complete dataset for analysis. It aims to preserve sample size and reduce bias from case-wise deletion while acknowledging uncertainty about the missing values. Imputation methods are broadly categorized as single imputation and multiple imputation.

Single imputation replaces each missing value with one plausible value. Techniques include mean or median substitution, regression-based imputation, hot-deck imputation, and k-nearest neighbors imputation. They are simple but can distort distributions and underestimate variability, leading to overconfident conclusions.

Multiple imputation treats missing values as random draws. Several complete datasets are created by drawing imputations from predictive distributions, analyses are conducted on each dataset, and results are combined to reflect imputation uncertainty. Methods include regression-based MI, multiple imputation by chained equations (MICE), and model-based approaches such as the expectation-maximization (EM) algorithm.

Imputation relies on assumptions about the missing data mechanism. Missing completely at random (MCAR) means missingness is independent of data; missing at random (MAR) means missingness depends on observed data; missing not at random (MNAR) means missingness depends on unobserved data. Imputation is more reliable under MCAR or MAR.

Applications span survey research, epidemiology, and genomics, among others. Imputation provides a principled way to handle missing data but requires careful method selection, diagnostics, and transparent reporting of uncertainty to avoid biased conclusions.