Preacher and Hayes (2008) show how to analyze models with multiple mediators in SPSS and SAS, how
can I analyze multiple mediators in Stata?

Here is the full citation:

Preacher, K.J. and Hayes, A.F. 2008. Asymptotic and resampling strategies for assessing and
comparing indirect effects in multiple mediator models. Behavioral Research Methods, 40, 879-891.

NOTE: If running the code on this page, please copy it all into a do-file and
run all of it.

Mediator variables are variables that sit between independent variable and dependent variable
and mediate the effect of the IV on the DV. A model with two mediators is shown in the figure
below.

In the figure above a1 represents the regression coefficient for the IV when the MV is regressed on
the IV while b is the coefficient for the MV when the DV is regressed on MV and IV. The symbol
c’ represents the direct effect of the IV on the DV.
Generally, researchers want to determine
the indirect effect of the IV on the DV through the MV. One common way to compute the indirect
effect is by using the product of the coefficients method. This method determines the
indirect effect by multiplying the regression coefficients, for example, a1*b1 = a1b1.
In addition to computing the indirect
effect we also want to obtain the standard error of a1b1. Further, we want to be able to do
this for each of the mediator variables in the model.

Thus, we need the a and b coefficients for each of the mediator variable in the model. We
will obtain all of the necessary coefficients using the sureg (seemingly unrelated regression)
command as suggested by Maarten Buis on the Statalist. The general form of the sureg
command will look something like this:

sureg (mv1 iv)(mv2 iv)(dv mv1 mv2 iv)

Example 1

The hsb2 dataset with science as the dv,
math as the iv and read and write as the two mediator variables.

We will need the coefficients for read on math and write
on math as well as the coefficients for science on read and write from
the equation that also includes math.

use https://stats.idre.ucla.edu/stat/data/hsb2, clear

sureg (read math)(write math)(science read write math)

Seemingly unrelated regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
read              200      1    7.662848    0.4386     156.26   0.0000
write             200      1    7.437294    0.3812     123.23   0.0000
science           200      3    6.983853    0.4999     199.96   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
read         |
        math |    .724807   .0579824    12.50   0.000     .6111636    .8384504
       _cons |   14.07254   3.100201     4.54   0.000     7.996255    20.14882
-------------+----------------------------------------------------------------
write        |
        math |   .6247082   .0562757    11.10   0.000     .5144099    .7350065
       _cons |   19.88724   3.008947     6.61   0.000     13.98981    25.78467
-------------+----------------------------------------------------------------
science      |
        read |   .3015317   .0679912     4.43   0.000     .1682715     .434792
       write |   .2065257   .0700532     2.95   0.003     .0692239    .3438274
        math |   .3190094   .0759047     4.20   0.000      .170239    .4677798
       _cons |   8.407353   3.160709     2.66   0.008     2.212476    14.60223
------------------------------------------------------------------------------

Now we have all the coefficients we need to compute the indirect effect coefficients and their
standard errors. We can do this using the nlcom (nonlinear combination) command.
We will run nlcom three times: Once for each of the two
specific indirect effects for read and write and once for the total
indirect effect.

To compute an indirect direct we specify a product of coefficients. For example,
the coefficient for read on math is [read]_b[math] and the coefficient for
science on read is [science]_b[read]. Thus, the product is
[read]_b[math]*[science]_b[read]. To get the total indirect effect we just add the
two product terms together in the nlcom command.

/* indirect via read */

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 |   .2185523     .05229     4.18   0.000     .1160659    .3210388
------------------------------------------------------------------------------

/* indirect via write */

nlcom [write]_b[math]*[science]_b[write]

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

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .1290183   .0452798     2.85   0.004     .0402715    .2177651
------------------------------------------------------------------------------

/* total indirect */

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

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

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .3475706   .0594916     5.84   0.000     .2309693    .4641719
------------------------------------------------------------------------------

The results above suggest that each of the separate indirect effects as well as the total
indirect effect are significant. From the above results it is also possible to compute
the ratio of indirect to direct effect and the proportion due to the indirect effect.
These computations require an estimate of the direct effect, which can be found in the sureg
output. In this example the direct effect is given by the coefficient for math in the last
equation (.3190094). Here are the manual computations for the ratio of indirect to direct and the
proportion of total effect that is mediated.

/* ratio of indirect to direct */

display .3475706/.3190094

1.0895309

/* proportion of total effect that is mediated */

display .3475706/(.3475706+.3190094)

.52142369

nlcom computes the standard errors using the delta
method which assumes that the estimates of the indirect effect are normally distributed.
For many situations this is acceptable but it does not work well for the indirect effects
which are usually positively skewed and kurtotic. Thus the z-test and p-values for
these indirect effects generally cannot be trusted. Therefore, it is recommended
that bootstrap standard errors and confidence intervals be used.

Below is a short ado-program that is called by the bootstrap command. It computes the
indirect effect coefficients as the product of sureg coefficients (as before) but
does not use the nlcom command since the standard errors will be computed using the
bootstrap.

bootmm is an rclass program that produces three return values which we have called
“indread”, “indwrite” and “indtotal.” These are the local names for each of the indirect effect
coefficients and for the total indirect effect.

We run bootmm with the bootstrap command. We
give the bootstrap command the names of the three return values and select options
for the number of replications and to omit printing dots after each replication.

Since we selected 5,000 replications you may need to be a bit patient depending upon the speed
of your computer.

capture program drop bootmm
program bootmm, rclass
  syntax [if] [in]
  sureg (read math)(write math)(science read write math) `if' `in'
  return scalar indread  = [read]_b[math]*[science]_b[read]
  return scalar indwrite = [write]_b[math]*[science]_b[write]
  return scalar indtotal = [read]_b[math]*[science]_b[read]+[write]_b[math]*[science]_b[write] 
end

bootstrap r(indread) r(indwrite) r(indtotal), bca reps(5000): bootmm

Bootstrap results                               Number of obs      =       200
                                                Replications       =      5000

      command:  bootmm
        _bs_1:  r(indread)
        _bs_2:  r(indwrite)
        _bs_3:  r(indtotal)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .2185523   .0544617     4.01   0.000     .1118094    .3252953
       _bs_2 |   .1290183   .0498037     2.59   0.010     .0314048    .2266318
       _bs_3 |   .3475706   .0653076     5.32   0.000     .2195701    .4755711
------------------------------------------------------------------------------

We could use the bootstrap standard errors to see if the indirect effects are significant but
it is usually recommended that bias-corrected or percentile confidence intervals be used
instead. These confidence intervals are nonsymmetric reflecting the skewness of the
sampling distribution of the product coefficients. If the confidence interval does not contain
zero than the indirect effect is considered to be statistically significant.

estat boot, percentile bc bca

Bootstrap results                               Number of obs      =       200
                                                Replications       =      5000

      command:  bootmm
        _bs_1:  r(indread)
        _bs_2:  r(indwrite)
        _bs_3:  r(indtotal)

------------------------------------------------------------------------------
             |    Observed               Bootstrap
             |       Coef.       Bias    Std. Err.  [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .21855231  -.0009252   .05446169    .1116576   .3263005   (P)
             |                                       .1140179   .3286456  (BC)
             |                                       .1140179   .3286456 (BCa)
       _bs_2 |   .12901828   .0009822   .04980373    .0375536   .2286579   (P)
             |                                       .0375377     .22842  (BC)
             |                                       .0333511   .2264691 (BCa)
       _bs_3 |   .34757059    .000057    .0653076    .2181866   .4773324   (P)
             |                                       .2209776   .4805473  (BC)
             |                                       .2158857   .4752103 (BCa)
------------------------------------------------------------------------------
(P)    percentile confidence interval
(BC)   bias-corrected confidence interval
(BCa)  bias-corrected and accelerated confidence interval

In this example, the total indirect effect of math through read and write is
significant as are the individual indirect effects.

Example 2

What do you do if you also have control variables? You just add them to each of the equations in the
sureg model. Let’s say that socst is a covariate. Here is how the bootstrap
process would work.

capture program drop bootmm
program bootmm, rclass
  syntax [if] [in]
  sureg (read math socst)(write math socst)(science read write math socst) `if' `in'
  return scalar indread  = [read]_b[math]*[science]_b[read]
  return scalar indwrite = [write]_b[math]*[science]_b[write]
  return scalar indtotal = [read]_b[math]*[science]_b[read] + ///
                           [write]_b[math]*[science]_b[write] 
end

bootstrap r(indread) r(indwrite) r(indtotal), bca reps(5000) nodots: bootmm

Bootstrap results                               Number of obs      =       200
                                                Replications       =      5000

      command:  bootmm
        _bs_1:  r(indread)
        _bs_2:  r(indwrite)
        _bs_3:  r(indtotal)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .1561855    .040306     3.87   0.000     .0771872    .2351837
       _bs_2 |   .0890589   .0352121     2.53   0.011     .0200444    .1580733
       _bs_3 |   .2452443   .0477817     5.13   0.000     .1515939    .3388947
------------------------------------------------------------------------------

estat boot, percentile bc bca

Bootstrap results                               Number of obs      =       200
                                                Replications       =      5000

      command:  bootmm
        _bs_1:  r(indread)
        _bs_2:  r(indwrite)
        _bs_3:  r(indtotal)

------------------------------------------------------------------------------
             |    Observed               Bootstrap
             |       Coef.       Bias    Std. Err.  [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .15618546  -.0016606   .04030598    .0784972   .2359464   (P)
             |                                       .0836141   .2407494  (BC)
             |                                       .0838816   .2413034 (BCa)
       _bs_2 |   .08905886   .0000963    .0352121    .0241053    .163005   (P)
             |                                       .0274379   .1664222  (BC)
             |                                       .0260387    .164438 (BCa)
       _bs_3 |   .24524432  -.0015643    .0477817    .1536668    .341307   (P)
             |                                       .1581453   .3477974  (BC)
             |                                       .1581453   .3477974 (BCa)
------------------------------------------------------------------------------
(P)    percentile confidence interval
(BC)   bias-corrected confidence interval
(BCa)  bias-corrected and accelerated confidence interval

Although the total and individual indirect are much smaller in the model with the covariate, they
are still statistically significant using the 95% confidence intervals.