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# imputation

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The process of replacing missing values in (usually) a large-scale social survey. Suppose, for example, that the salary information is missing for an individual who is known to be a doctor aged 55. One approach would be to determine the average salary of all 55-year-old doctors and to replace the missing value with this average value (or some estimate obtained, for example, by multiple regression of salary on other variables). There are two possible objections to this approach: (i) the imputed value might not be a salary actually obtained by any 55-year-old doctor, and (ii), if there are many doctors of this age with missing salary information and if each were given the same imputed salary, this would give a very misleading idea of salary variability.

The first objection can be met by insisting that the value imputed must be a real salary. Both objections can be met if the imputed value is taken to be the most recently encountered actual salary of a doctor of that age. This is called hot deck imputation, which refers to a time when the records on each individual were on a separate card. Imagine examining the deck of cards a card at a time, imputing missing values. The salary chosen for the doctor is that most recently encountered in the cards containing information on 55-year-old doctors. The alternative, in which all imputation takes place after all the cards have been examined, is called cold deck imputation—the most recently encountered value is used to replace all those missing (so that only the first objection is met).

Subjects: Probability and Statistics.

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