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Suppose that a variable $Y_j$ has missing values. We can use regression to impute the data using the nonmissing observations:

$$Y_j = \beta_0+\beta_{1}Y_{1}+\beta_{2}Y_{2} + \dots + \beta_{(j-1)} Y_{(j-1)}$$

What are the disadvantages of this? When would it be better to impute the data from a distribution? For example, if a variable age has missing values, when would it be better to randomly sample from the overall distribution of the non-missing values of age ?

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True multiple-imputation methods return several sets of "complete" data, effectively imputing a distribution rather than a single estimate for each missing value. Your regression equation, in contrast, would provide only a single imputed value for each missing data point.

Downstream analysis of multiply-imputed data involves analyzing each of the data sets and pooling the results across the imputations, providing information about the variability arising from the imputation process. This approach is thus considered superior to simply examining a single set of imputations. This page provides a useful introduction to the concepts and links to software that implement the process.

You must, however, determine whether the necessary assumptions are met in your data. In particular, if the probability of a data point being missing depends on the value of the data point, then imputation will not be reliable.

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