NOTE:  Code for this page was tested in Stata 12.

Computing indirect effects with multiply imputed data takes a few more step than for
a conventional non-imputed model.

Let’s begin by looking at the data.

use https://stats.idre.ucla.edu/stat/data/hsbmar, clear

sum science read math female

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
     science |       193    51.57513     9.86396         26         74
        read |       185    51.61622    10.19104         28         76
        math |       190    52.17895    9.246168         33         75
      female |       185    .5459459    .4992356          0          1

As you can see from the table above, all of
the variables have a different number of observations. For our example science
is the dependent variable, read is the mediator, math
is the independent variable and female is a covariate.

The method we will use to compute an indirect effect involves the sureg
and nlcom commands to get the product of coefficients.

So, what’s the problem?

Why not just impute the data and run the analyses. Well, sureg does not
work with imputed data unless we add the cmdok option to our mi estimate.
But then nlcom can’t find the results in the correct location. nlcom
looks for e(b) and e(V) but mi estimate
saves the results in e(b_mi) and e(V_mi).

We can move the results to the correct location by writing an eclass
program which we are calling called myeret.ado.
It makes use of the ereturn repost command.
Here is what the program looks like.

prog myeret, eclass
  ereturn repost b=b V=V
end

It has to be declared to be an eclass command. The repost
places matrix b into e(b) anf V into
e(V).

We saved the program in our ado/personal directory.

Now, let’s start our example analysis by running the multiple imputation.

mi set mlong

mi register imputed read math science female

set seed 485769

mi impute mvn read math science female = write, add(20)

Performing EM optimization:
  observed log likelihood = -1349.5408 at iteration 7

Performing MCMC data augmentation ... 

Multivariate imputation                     Imputations =       20
Multivariate normal regression                    added =       20
Imputed: m=1 through m=20                       updated =        0

Prior: uniform                               Iterations =     2000
                                                burn-in =      100
                                                between =      100

------------------------------------------------------------------
                   |               Observations per m             
                   |----------------------------------------------
          Variable |   Complete   Incomplete   Imputed |     Total
-------------------+-----------------------------------+----------
              read |        185           15        15 |       200
              math |        190           10        10 |       200
           science |        193            7         7 |       200
            female |        185           15        15 |       200
------------------------------------------------------------------
(complete + incomplete = total; imputed is the minimum across m
 of the number of filled-in observations.)

If you try to run mi estimate: sureg (read math female)(science read math female)
you will get an error message that sureg is not officially supported.
However if you add the cmdok option it will run just fine.

mi estimate, cmdok: sureg (read math female)(science read math female)

Multiple-imputation estimates                     Imputations     =         20
                                                  Number of obs   =        200
                                                  Average RVI     =     0.1236
                                                  Largest FMI     =     0.1816
DF adjustment:   Large sample                     DF:     min     =     594.26
                                                          avg     =    1602.26
                                                          max     =    3257.71

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
read         |
        math |   .7030755   .0627357    11.21   0.000     .5800272    .8261238
      female |  -.8018491   1.156265    -0.69   0.488    -3.068929    1.465231
       _cons |   15.58747   3.385455     4.60   0.000     8.949015    22.22592
-------------+----------------------------------------------------------------
science      |
        read |   .3661471   .0686624     5.33   0.000       .23146    .5008342
        math |    .411848    .077228     5.33   0.000     .2602325    .5634634
      female |  -1.772933   1.122191    -1.58   0.115    -3.976875    .4310101
       _cons |   12.17901   3.384061     3.60   0.000      5.53725    18.82077
------------------------------------------------------------------------------

Next, we need to copy the e(b_mi) and e(V_mi) matrices.

matrix b = e(b_mi)
matrix V = e(V_mi)

To get all of the pieces into the right place we quietly run sureg on the
imputation zero data followed by our myeret command that was shown above.

quietly sureg (read math female)(science read math female) if _mi_m == 0

myeret

We are finally able to use the nlcom command to get the product of the coefficients.

nlcom [read]_b[math]*[science]_b[read]

       _nl_1:  [read]_b[math]*[science]_b[read]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |    .257429   .0531467     4.84   0.000     .1532635    .3615946
------------------------------------------------------------------------------

To get the total effect of math just add the direct effect to the nlcom
command above.

nlcom [read]_b[math]*[science]_b[read] + [science]_b[math]

       _nl_1:  [read]_b[math]*[science]_b[read] + [science]_b[math]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |    .669277   .0617048    10.85   0.000     .5483379    .7902161
------------------------------------------------------------------------------

And that is how you can compute an indirect effect using multiply imputed data.