In general, imputations are predictions for the missing values, based on an explicit or implicit model. In some cases, however, imputations can also be derived directly from the values that were observed in the same record, using derivation rules that do not contain any parameters to be estimated, such as is the case in models.
For instance: suppose that businesses are asked in a survey to report their total turnover (T), turnover from the main activity (T1), and turnover from sideline activities (T2). If the value of one of these variables is missing, and if it may be assumed that the two observed values are correct, then the missing value can be calculated using the rule: T1 + T2 = T.
The above imputation rule is an example of deductive or logical imputation. In this imputation method, one identifies cases where it is possible, based on logical or mathematical relationships between the variables, to unambiguously derive the value of one or more missing variables from the values that were observed, under the assumption that the observed values are correct. For the missing variables for which this is possible, the uniquely derived value is the deductive imputation. The assumption that all observed values are correct requires that all erroneous values in the original data have been removed in a previous process step.
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