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Data Analysis with R - Second Edition by Tony Fischetti

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Stochastic regression imputation

As far as unsophisticated approaches go, stochastic regression is fairly evolved. This approach solves some of the issues of regression imputation and produces unbiased estimates of the mean, variance, covariance, and regression coefficients under MCAR and MAR. It does this by adding a random (stochastic) value to the predictions of regression imputation. This random added value is sampled from the residual (error) distribution of the linear regression which, if you remember, is assumed to be a normal distribution. This restores the variability in the missing values (that we lost in regression imputation), which those values would have had if they weren't missing.

However, as far as subsequent analysis and ...

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