Imputation

A technique replacing missing data values with estimated substitutes, ranging from simple mean substitution to sophisticated multiple imputation approaches.

Source: Rubin 1987

Imputation fills the gaps left by missing values in a dataset, replacing each with an estimated substitute so that the analysis can use the whole sample rather than discarding incomplete records. Methods range from simply inserting the average, which understates uncertainty, to multiple imputation, which creates several plausible completed datasets and combines them to reflect the doubt about what was missing. All of it rests on assumptions about why the data were missing. Supplying principled substitutes for missing data is its purpose. Little and Rubin (2002) describe these techniques.

Source: Little & Rubin 2002

The types of imputation include single imputation methods, such as mean substitution or replacing a value with a prediction from other variables, which fill each missing value once; and multiple imputation, which creates several completed datasets with different plausible imputed values, analyses each, and combines the results to reflect the uncertainty. So imputation ranges from simple single methods to multiple imputation, with single methods being easy but often understating uncertainty and potentially biasing results, and multiple imputation being more principled because it accounts for the uncertainty in the missing values, which is why multiple imputation is generally preferred for valid inference.

Source: Rubin 1987

Multiple imputation is preferred over single imputation because single methods fill each missing value with one estimate, treating it as known and thereby understating the uncertainty, which leads to standard errors that are too small and inference that is over-confident. Multiple imputation creates several plausible completed datasets and combines them, propagating the uncertainty about the missing values. So multiple imputation is preferred because it reflects the uncertainty inherent in imputing missing data, giving valid standard errors and confidence intervals, whereas single imputation can bias estimates and falsely inflate precision, which is why multiple imputation is the standard principled approach when data are missing at random.

Source: Rubin 1987

Imputation relies on assumptions about why the data are missing, most commonly that the data are missing at random, meaning the probability of missingness depends only on observed data, which allows the observed data to be used to impute the missing values validly. If data are missing not at random, standard imputation can be biased. So imputation depends on the missing data mechanism, with multiple imputation generally valid under missing at random, and its results are interpreted with attention to whether that assumption is plausible, since imputation cannot fully recover information when missingness depends on the unobserved values themselves, which may require sensitivity analyses.

Source: Rubin 1976

The limitations of imputation include that it relies on assumptions about the missing data mechanism, usually missing at random, which cannot be verified; that simple single methods understate uncertainty and can bias results; and that even multiple imputation depends on the imputation model being adequate. So imputation is applied and interpreted with care, since it cannot create genuine information about the missing values and its validity rests on assumptions and on a well-specified imputation model, which is why the missing data mechanism is considered, principled methods such as multiple imputation are used, and sensitivity analyses examine whether conclusions hold under different assumptions about the missingness.

Source: Rubin 1987