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Re: st: details of how the impute command work


From   wgould@stata.com (William Gould, StataCorp LP)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: details of how the impute command work
Date   Wed, 07 Nov 2007 08:37:17 -0600

Tim Hale <timhale@mindspring.com> writes, 

> I am trying to figure out exactly what the -impute- command in Stata
> does to estimate missing values.

-impute y x1 x2 ..., gen(yhat)-= creates 

        yhat_j = y_j            in observations j for which y_j<.
               = prediction_j   otherwise

Each prediction_j is the predicted value from a linear regression, said 
linear regression using the subset of variables of x1, x2, ..., that do not 
contain missing in observation j.

Consider the following dataset:

        . list y x1 x2 

             +-------------+
             | y   x1   x2 |
             |-------------|
          1. | 1    2    3 |
          2. | 4    5    6 |
          3. | 5    5    8 |
          4. | 5    6    6 |
          5. | .    5    6 |
             |-------------|
          6. | .    .    3 |
             +-------------+

and the command 

        . impute y x1 x2, gen(yhat)

Then yhat in observation 5 would be based on a regression of y on x1 and x2, 
because both x1 and x2 are not missing in observation 5.  This amounts to

        . regress y x1 x2
        . predict prediction 
        . replace yhat = prediction in 5

The yhat in observation 6 would be based on a regression of y on x2, because 
x1 in missing in observation 6.  This amounts to 

        . regress y x2 
        . prediction prediction 
        . replace yhat = prediction in 6

-- Bill
wgould@stata.com
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