How can I do moderated mediation with a categorical moderator in Stata?

How can I do moderated mediation with a categorical moderator in Stata?

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Moderated mediation is a statistical technique used to examine the relationship between an independent variable, a mediator, and a dependent variable, while taking into account the influence of a moderator. In Stata, this can be achieved through the use of the “modmed” command. This command allows for the inclusion of a categorical moderator in the mediation analysis, thus allowing for a more comprehensive understanding of how the moderator affects the mediation process. By specifying the appropriate variables and model parameters, Stata can generate results that indicate the direct and indirect effects of the independent variable on the dependent variable, as well as the moderating effect of the categorical moderator. This can provide valuable insights into the underlying mechanisms of the relationship between variables and aid in the interpretation of the results.

How can I do moderated mediation with a categorical moderator in Stata? | Stata FAQ

This page is just an extension of How can I do moderated mediation
in Stata? to include a categorical moderator variable.
We will call that page modmed. If
you are unfamiliar with moderated mediation you should review the modmed
FAQ page before continuing on with this page.

We will to use the same data and the same abbreviated variable names as were used on the
modmed page.

use https://stats.idre.ucla.edu/stat/data/hsbdemo, clear
rename science y  /* dependent variable   */
rename math x     /* independent variable */
rename read m     /* mediator variable    */
rename prog w     /* moderator variable with 3 levels */

The modmed page presented five different models for moderated mediation.
We will select one of them, model 2, to illustrate the use of categorical moderators. The
diagram for model 2 looks like this:

Model 2
Image model2s-1

Using sureg with manual interactions

For our first pass we will manually create indicator variables and interactions.

tab w, gen(w)               //  create indicator variables
generate wx2=w2*x           //  moderator w2 by iv interaction 
generate wx3=w3*x           //  moderator w3 by iv interaction

In model 2 the effect of x on m is what is moderated.
So, the interaction terms need to go in the models for both m and
y. Thus the sureg command looks like this:

sureg (m x w2 w3 wx2 wx3)(y m x w2 w3 wx2 wx3)

Seemingly unrelated regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
m                 200      5    7.493404    0.4632     172.56   0.0000
y                 200      6    6.927073    0.5080     206.54   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
m            |
           x |   .4896411   .1517936     3.23   0.001     .1921311     .787151
          w2 |  -12.20637   9.068511    -1.35   0.178    -29.98032    5.567587
          w3 |  -2.822291   9.952575    -0.28   0.777    -22.32898     16.6844
         wx2 |    .270153   .1735662     1.56   0.120    -.0700305    .6103366
         wx3 |   .0222002   .2028633     0.11   0.913    -.3754045    .4198048
       _cons |   25.26262    7.67478     3.29   0.001     10.22033    40.30491
-------------+----------------------------------------------------------------
y            |
           m |   .3997664   .0653666     6.12   0.000     .2716503    .5278825
           x |   .5525436   .1439253     3.84   0.000     .2704552    .8346321
          w2 |   5.643216   8.421022     0.67   0.503    -10.86168    22.14812
          w3 |  -1.079664   9.202235    -0.12   0.907    -19.11571    16.95639
         wx2 |  -.1860791   .1614174    -1.15   0.249    -.5024513    .1302932
         wx3 |  -.0157907    .187537    -0.08   0.933    -.3833565    .3517751
       _cons |   4.914386   7.284383     0.67   0.500    -9.362742    19.19151
------------------------------------------------------------------------------

Next, we use the nlcom command to compute the conditional indirect effects
for each of the
levels of the moderator variable. For level one multiply each of the interaction terms,
wx2 and wx3 by zero. For level 2, multiply wx2
by one and wx3 by zero. For level 3, just reverse the zeros and ones.
Here is the code:

nlcom (_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]          //  for w = 1

       _nl_1:  (_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |    .195742   .0686054     2.85   0.004      .061278    .3302061
------------------------------------------------------------------------------

nlcom (_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]          // for w = 2

       _nl_1:  (_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .3037401   .0599894     5.06   0.000      .186163    .4213173
------------------------------------------------------------------------------

nlcom (_b[m:x]+0*_b[m:wx2]+1*_b[m:wx3])*_b[y:m]          // for w = 3

       _nl_1:  (_b[m:x]+0*_b[m:wx2]+1*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .2046169   .0633558     3.23   0.001     .0804418    .3287921
------------------------------------------------------------------------------

From these results we see that the indirect effect is strongest when w
= 2 (that is, for the academic program) followed by w = 3 (vocational program) and finally
w = 1 (general program). It is also possible to test whether the indirect
effects for the three levels differ from one another. We will demonstrate this by looking at
the difference between w = 2 and w = 1 (the biggest
difference). We do this by subtracting the two nlcom terms.


nlcom ((_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m])-((_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m])

This simplifies to:

nlcom (1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]   // w1 vs w2 

       _nl_1:  (1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .1079981   .0715978     1.51   0.131    -.0323311    .2483272
------------------------------------------------------------------------------

In this case the difference in the conditional indirect effects is not statistically significant.

In general, nlcom does a reasonably good job of estimating standard
errors and confidence intervals using the delta method. However, the delta method has
some fairly strong normality assumptions that may not hold for products of coefficients.
Many researchers prefer using the bootstrap to obtain confidence intervals.

Bootstrap confidence intervals

To obtain bootstrap confidence intervals for the conditional indirect effects we begin
by writing a program, which we have called bootmmcat and saving it as
an ado file called bootmmcat.ado. Here is the program:

capture program drop bootmmcat
program bootmmcat, rclass
  sureg (m x w2 w3 wx2 wx3)(y m x w2 w3 wx2 wx3)
  return scalar w1 = (_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]
  return scalar w2 = (_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]
  return scalar w3 = (_b[m:x]+0*_b[m:wx2]+1*_b[m:wx3])*_b[y:m]
 end

Now we can run bootmmcat using the bootstrap command. We will demonstrate
this using 500 bootstrap replications. You will want to use more, say 5,000 or 10,000 or more.

bootstrap r(w1) r(w2) r(w3), reps(500) nodots: bootmmcat

Bootstrap results                               Number of obs      =       200
                                                Replications       =       500

      command:  bootmmcat
        _bs_1:  r(w1)
        _bs_2:  r(w2)
        _bs_3:  r(w3)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |    .195742    .075913     2.58   0.010     .0469553    .3445288
       _bs_2 |   .3037401   .0604079     5.03   0.000     .1853429    .4221374
       _bs_3 |   .2046169   .0729526     2.80   0.005     .0616324    .3476015
------------------------------------------------------------------------------

By default the bootstrap command produces normal-based confidence
intervals. To get bias corrected or percentile confidence intervals use the
estat boot command.

estat boot, bc percentile

Bootstrap results                               Number of obs      =       200
                                                Replications       =       500

      command:  bootmmcat
        _bs_1:  r(w1)
        _bs_2:  r(w2)
        _bs_3:  r(w3)

------------------------------------------------------------------------------
             |    Observed               Bootstrap
             |       Coef.       Bias    Std. Err.  [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .19574204   .0015209   .07591302    .0623215   .3492891   (P)
             |                                       .0633699   .3669358  (BC)
       _bs_2 |   .30374014  -.0030653   .06040786    .1904437   .4215902   (P)
             |                                       .1981149   .4295833  (BC)
       _bs_3 |   .20461692   .0020635   .07295263    .0732974   .3612065   (P)
             |                                       .0818157   .3720523  (BC)
------------------------------------------------------------------------------
(P)    percentile confidence interval
(BC)   bias-corrected confidence interval

All of the examples above used the manually computed indicators and interactions.
The next section shows how to obtain the same results using factor variables.

Using sureg with factor variables

Since this section replicates the above analyses, we will run the commands in a single block
of code.

sureg (m c.x##w)(y m c.x##w)

Seemingly unrelated regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
m                 200      5    7.493404    0.4632     172.56   0.0000
y                 200      6    6.927073    0.5080     206.54   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
m            |
           x |   .4896411   .1517936     3.23   0.001     .1921311     .787151
             |
           w |
          2  |  -12.20637   9.068511    -1.35   0.178    -29.98032    5.567587
          3  |  -2.822291   9.952575    -0.28   0.777    -22.32898     16.6844
             |
       w#c.x |
          2  |    .270153   .1735662     1.56   0.120    -.0700305    .6103366
          3  |   .0222002   .2028633     0.11   0.913    -.3754045    .4198048
             |
       _cons |   25.26262    7.67478     3.29   0.001     10.22033    40.30491
-------------+----------------------------------------------------------------
y            |
           m |   .3997664   .0653666     6.12   0.000     .2716503    .5278825
           x |   .5525436   .1439253     3.84   0.000     .2704552    .8346321
             |
           w |
          2  |   5.643216   8.421022     0.67   0.503    -10.86168    22.14812
          3  |  -1.079664   9.202235    -0.12   0.907    -19.11571    16.95639
             |
       w#c.x |
          2  |  -.1860791   .1614174    -1.15   0.249    -.5024513    .1302932
          3  |  -.0157907    .187537    -0.08   0.933    -.3833565    .3517751
             |
       _cons |   4.914386   7.284383     0.67   0.500    -9.362742    19.19151
------------------------------------------------------------------------------

nlcom (_b[m:x]+0*_b[m:2.w#c.x]+0*_b[m:3.w#c.x])*_b[y:m]  // for w = 1 

       _nl_1:  (_b[m:x]+0*_b[m:2.w#c.x]+0*_b[m:3.w#c.x])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |    .195742   .0686054     2.85   0.004      .061278    .3302061
------------------------------------------------------------------------------

nlcom (_b[m:x]+1*_b[m:2.w#c.x]+0*_b[m:3.w#c.x])*_b[y:m]  // for w = 2 

       _nl_1:  (_b[m:x]+1*_b[m:2.w#c.x]+0*_b[m:3.w#c.x])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .3037401   .0599894     5.06   0.000      .186163    .4213173
------------------------------------------------------------------------------

nlcom (_b[m:x]+0*_b[m:2.w#c.x]+1*_b[m:3.w#c.x])*_b[y:m]  // for w = 3 

       _nl_1:  (_b[m:x]+0*_b[m:2.w#c.x]+1*_b[m:3.w#c.x])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .2046169   .0633558     3.23   0.001     .0804418    .3287921
------------------------------------------------------------------------------

Using the sureg command is not the only way to compute conditional indirect effects.
The next section will show how to do this using the sem command.

Using sem

Since sem does not support factor variables, we will go back to using
the manually created indicators and interactions.

sem (m 

Endogenous variables

Observed:  m y

Exogenous variables

Observed:  x w2 w3 wx2 wx3

Fitting target model:

Iteration 0:   log likelihood = -3316.2503  
Iteration 1:   log likelihood = -3316.2503  

Structural equation model                       Number of obs      =       200
Estimation method  = ml
Log likelihood     = -3316.2503

------------------------------------------------------------------------------
             |                 OIM
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  m  chi2 =      .

To see the names of each of the coefficients, just use the coeflegend option
with sem.

sem, coeflegend

Structural equation model                       Number of obs      =       200
Estimation method  = ml
Log likelihood     = -3316.2503

------------------------------------------------------------------------------
             |      Coef.  Legend
-------------+----------------------------------------------------------------
Structural   |
  m  chi2 =      .

As you can see, the names of the coefficients are the same as we used with the
sureg command. So, the nlcom commands would be
exactly the same.

nlcom (_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]          // for w = 1

       _nl_1:  (_b[m:x]+0*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |    .195742   .0686054     2.85   0.004      .061278    .3302061
------------------------------------------------------------------------------

nlcom (_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]          // for w = 2

       _nl_1:  (_b[m:x]+1*_b[m:wx2]+0*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .3037401   .0599894     5.06   0.000      .186163    .4213173
------------------------------------------------------------------------------

nlcom (_b[m:x]+0*_b[m:wx2]+1*_b[m:wx3])*_b[y:m]          // for w = 3

       _nl_1:  (_b[m:x]+0*_b[m:wx2]+1*_b[m:wx3])*_b[y:m]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .2046169   .0633558     3.23   0.001     .0804418    .3287921
------------------------------------------------------------------------------

The methods given on this page can be adapted to any of the other four models for moderated mediation
found on the modmed page.

Cite this article

stats writer (2024). How can I do moderated mediation with a categorical moderator in Stata?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-can-i-do-moderated-mediation-with-a-categorical-moderator-in-stata/

stats writer. "How can I do moderated mediation with a categorical moderator in Stata?." PSYCHOLOGICAL SCALES, 1 Jul. 2024, https://scales.arabpsychology.com/stats/how-can-i-do-moderated-mediation-with-a-categorical-moderator-in-stata/.

stats writer. "How can I do moderated mediation with a categorical moderator in Stata?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/how-can-i-do-moderated-mediation-with-a-categorical-moderator-in-stata/.

stats writer (2024) 'How can I do moderated mediation with a categorical moderator in Stata?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/how-can-i-do-moderated-mediation-with-a-categorical-moderator-in-stata/.

[1] stats writer, "How can I do moderated mediation with a categorical moderator in Stata?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, July, 2024.

stats writer. How can I do moderated mediation with a categorical moderator in Stata?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.

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