How can I do mediation analysis with the sem command?

How can I do mediation analysis with the sem command?

By /

Mediation analysis is a statistical method used to explore the relationship between an independent variable and a dependent variable through the inclusion of a mediator variable. One way to conduct mediation analysis is by using the sem command in statistical software, such as SPSS or Stata. This command allows for the estimation of path coefficients and indirect effects, as well as significance testing of the mediation effect. It also allows for the examination of multiple mediator variables and the inclusion of control variables. By using the sem command, researchers can gain a deeper understanding of the underlying mechanisms and processes involved in their research relationship.

How can I do mediation analysis with the sem command? | Stata FAQ

The sem command introduced in Stata 12 makes the analysis of mediation models much easier
as long as both the dependent variable and the mediator variable are continuous
variables.

We will illustrate using the sem command with the hsbdemo dataset. The examples
will not demonstrate full mediation, i.e., the effect of the independent variable will not go
from being significant to being not significant. Rather, the examples will show partial
mediation in which there is a decrease in the direct effect.

A note about covariates

If your model contains control variables, i.e., covariates, you must include these in each of
the sem equations. Thus, your sem model will look something
like this:

sem (MV <- IV CV1 CV2)(DV <- MV IV CV1 CV2)

where DV stands for the dependent variable, IV stands for the independent variable,
MV stands for the mediator variable, and CVs stand for the covariates.

Simple mediation model

The simplest mediation model had one IV, one MV and a DV. Here is the symbolic version of the
model.

 sem (MV <- IV)(DV <- MV IV)

In our simple mediation example the independent variable is math, the
mediator variable is read and the dependent variable is science.

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

sem (read <- math)(science <- read math) 

Endogenous variables

Observed:  read science

Exogenous variables

Observed:  math

Fitting target model:

Iteration 0:   log likelihood = -2098.5822  
Iteration 1:   log likelihood = -2098.5822  

Structural equation model                       Number of obs     =        200
Estimation method  = ml
Log likelihood     = -2098.5822

-------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
Structural    |
  read        |
         math |    .724807   .0579824    12.50   0.000     .6111636    .8384504
        _cons |   14.07254   3.100201     4.54   0.000     7.996255    20.14882
  ------------+----------------------------------------------------------------
  science     |
         read |   .3654205   .0658305     5.55   0.000     .2363951    .4944459
         math |   .4017207   .0720457     5.58   0.000     .2605138    .5429276
        _cons |    11.6155   3.031268     3.83   0.000     5.674324    17.55668
--------------+----------------------------------------------------------------
   var(e.read)|   58.71925   5.871925                      48.26811    71.43329
var(e.science)|    50.8938    5.08938                      41.83548    61.91346
-------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .

estat teffects

Direct effects
------------------------------------------------------------------------------
             |                 OIM
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |    .724807   .0579824    12.50   0.000     .6111636    .8384504
  -----------+----------------------------------------------------------------
  science    |
        read |   .3654205   .0658305     5.55   0.000     .2363951    .4944459
        math |   .4017207   .0720457     5.58   0.000     .2605138    .5429276
------------------------------------------------------------------------------


Indirect effects
------------------------------------------------------------------------------
             |                 OIM
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |          0  (no path)
  -----------+----------------------------------------------------------------
  science    |
        read |          0  (no path)
        math |   .2648593   .0522072     5.07   0.000     .1625351    .3671836
------------------------------------------------------------------------------


Total effects
------------------------------------------------------------------------------
             |                 OIM
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |    .724807   .0579824    12.50   0.000     .6111636    .8384504
  -----------+----------------------------------------------------------------
  science    |
        read |   .3654205   .0658305     5.55   0.000     .2363951    .4944459
        math |     .66658     .05799    11.49   0.000     .5529217    .7802384
------------------------------------------------------------------------------

The total effect for math, .66658, is the effect we would find if there was no mediator
in our model. It is significant with a z of 11.49. The direct effect for math is
.4017207 which, while still significant (z = 5.58), is much smaller than the total effect.
The indirect effect of math that passes through read is .2648593 and is
also statistically significant.

It is often easier to interpret these values by computing ratios and proportions as
shown below.

proportion of total effect mediated = .2648593/.66658 = .3973406

ratio of indirect to direct effect = .2648593/.4017207 = .65931205

ratio of total to direct effect =  .66658/.4017207 =  1.6593121

We see above that the proportion of the total effect that is mediated is
almost .40 which is a respectable amount. The ratio of the indirect effect
to the direct effect is about .66 or almost 2/3 the size of the direct effect. And finally,
the total effect is about 1.66 times the direct effect.

Mediation with bootstrap standard errors and confidence intervals

If you are uncomfortable with the standard errors and confidence intervals produced directly
by sem, you can obtain the bootstrapped standard errors and confidence intervals in two ways.
First, by using the vce(boostrap) option after your sem command. Or second, by writing a small program that runs both the sem command and the estat teffects and then bootstrapping this program.

Let’s demonstrate the vce(boostrap) option. Here we will add the reps option and request 200 replications.

sem (read <- math)(science <- read math), vce(bootstrap,reps(200)) 
Bootstrap replications (200)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100
..................................................   150
..................................................   200

Structural equation model                       Number of obs     =        200
Estimation method  = ml                         Replications      =        200
Log likelihood     = -2098.5822

-------------------------------------------------------------------------------
              |   Observed   Bootstrap                         Normal-based
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
Structural    |
  read        |
         math |    .724807   .0581262    12.47   0.000     .6108818    .8387321
        _cons |   14.07254   3.092117     4.55   0.000     8.012099    20.13297
  ------------+----------------------------------------------------------------
  science     |
         read |   .3654205   .0802203     4.56   0.000     .2081915    .5226495
         math |   .4017207   .0875101     4.59   0.000     .2302041    .5732373
        _cons |    11.6155   2.707368     4.29   0.000     6.309158    16.92184
--------------+----------------------------------------------------------------
   var(e.read)|   58.71925    5.93704                      48.16332    71.58871
var(e.science)|    50.8938   5.496477                      41.18471    62.89176
-------------------------------------------------------------------------------

Adding this option provides us bootstrapped confidence intervals. You can now use estat teffects to obtain normal-based bootstrapped confidence intervals around the indirect effect.

estat teffects

Direct effects
------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |    .724807   .0581262    12.47   0.000     .6108818    .8387321
  -----------+----------------------------------------------------------------
  science    |
        read |   .3654205   .0802203     4.56   0.000     .2081915    .5226495
        math |   .4017207   .0875101     4.59   0.000     .2302041    .5732373
------------------------------------------------------------------------------


Indirect effects
------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |          0  (no path)
  -----------+----------------------------------------------------------------
  science    |
        read |          0  (no path)
        math |   .2648593   .0593311     4.46   0.000     .1485726    .3811461
------------------------------------------------------------------------------


Total effects
------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  read       |
        math |    .724807   .0581262    12.47   0.000     .6108818    .8387321
  -----------+----------------------------------------------------------------
  science    |
        read |   .3654205   .0802203     4.56   0.000     .2081915    .5226495
        math |     .66658   .0592669    11.25   0.000     .5504189    .7827411
------------------------------------------------------------------------------

However, you can also write a program to perform the bootstrapping. This enables us to obtain both percentile-based and bias-corrected confidence intervals as well as normal-based confidence intervals. Here is the program that we a calling indireff.ado.

program indireff, rclass
  sem (read <- math)(science <- read math)
  estat teffects
  mat bi = r(indirect)
  mat bd = r(direct)
  mat bt = r(total)
  return scalar indir  = el(bi,1,3)
  return scalar direct = el(bd,1,3)
  return scalar total  = el(bt,1,3)
end

So how do we know which elements of r(indirect), r(direct) and r(total)
we need? We will use the sem command and then quietly run estat teffects
followed by a matrix list to see the matrices of the coefficients.

sem (read <- math)(science <- read math)
quietly estat teffects

matrix list r(indirect)

r(indirect)[1,3]
         read:   science:   science:
            o.         o.           
         math       read       math
r1          0          0  .26485934

matrix list r(direct) 

r(direct)[1,3]
         read:   science:   science:
         math       read       math
r1  .72480697  .36542052  .40172068

matrix list r(total)

r(total)[1,3]
         read:   science:   science:
         math       read       math
r1  .72480697  .36542052  .66658002

We see that in each case the coefficient of interest is the third element.

Now that we know the correct matrix elements, we will run indireff for 200 bootstrap replications.
You may want to run more, say 2,000 to 5,000. We will then request the percentile and
biased corrected confidence intervals.

set seed 358395 

bootstrap r(indir) r(direct) r(total), reps(200): indireff 

Bootstrap replications (200)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100
..................................................   150
..................................................   200

Bootstrap results                               Number of obs     =        200
                                                Replications      =        200

      command:  indireff
        _bs_1:  r(indir)
        _bs_2:  r(direct)
        _bs_3:  r(total)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   .2648593   .0545941     4.85   0.000     .1578569    .3718618
       _bs_2 |   .4017207   .0872965     4.60   0.000     .2306228    .5728186
       _bs_3 |     .66658   .0576837    11.56   0.000      .553522    .7796381
------------------------------------------------------------------------------

Mediation with multiple IVs

What if you had multiple independent variables? You just need to have one equation for
each IV predicting the mediator variable. Here is the symbolic model.

sem (MV <- IV1)(MV <- IV2)(DV <- MV IV1 IV2)

For our example, we will use math
and ses as our independent variables. We will keep the same mediator and dependent variable
as before.

sem (read <- math)(read <- ses)(science <- read math ses) Endogenous variables

Observed:  read science

Exogenous variables

Observed:  math ses

Fitting target model:

Iteration 0:   log likelihood = -2306.1661  
Iteration 1:   log likelihood = -2306.1661  

Structural equation model                       Number of obs     =        200
Estimation method  = ml
Log likelihood     = -2306.1661

-------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
Structural    |
  read        |
         math |     .68845    .059519    11.57   0.000     .5717949     .805105
          ses |      1.726   .7698566     2.24   0.025     .2171093    3.234892
        _cons |   12.43962   3.147394     3.95   0.000     6.270842     18.6084
  ------------+----------------------------------------------------------------
  science     |
         read |   .3507374   .0663219     5.29   0.000     .2207487     .480726
         math |   .3905883   .0721193     5.42   0.000     .2492371    .5319395
          ses |   1.033732    .731092     1.41   0.157    -.3991816    2.466647
        _cons |   10.84415   3.065166     3.54   0.000     4.836532    16.85176
--------------+----------------------------------------------------------------
   var(e.read)|   57.27968   5.727968                      47.08476    69.68202
var(e.science)|   50.39009   5.039009                      41.42142    61.30067
-------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .

We note that the indirect effects of both math and ses are significant.

Because we have multiple independent variables, the computation of the ratios and proportions
is a bit more complex.

proportion of total math effect mediated = .2414651/.6320534 = .38203275
proportion of total ses effect mediated = .6053729/1.639105 = .36933137

ratio of math indirect to direct effect = .2414651/.3905883 = .61820874
ratio of ses indirect to direct effect = .6053729/1.033732 = .58561881

ratio of total math to direct effect = .6320534/.3905883 =  1.6182087
ratio of total ses to direct effect = 1.639105/1.033732 =  1.5856189

Mediation with multiple mediators

In this section we will consider the case in which there are multiple mediator variables.
This time there will be one equation for each mediator variable. The symbolic form of
the mode looks like this.

sem (MV1 <- IV)(MV2 <- IV)(DV <- MV1 MV2 IV)

For our example we will use read and write as the mediators.
We will go back to a single independent variable, math.

sem (read <- math)(write <- math)(science <- read write math) Endogenous variables

Observed:  read write science

Exogenous variables

Observed:  math

Fitting target model:

Iteration 0:   log likelihood = -2779.4174  
Iteration 1:   log likelihood = -2779.4174  

Structural equation model                       Number of obs     =        200
Estimation method  = ml
Log likelihood     = -2779.4174

-------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
Structural    |
  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
--------------+----------------------------------------------------------------
   var(e.read)|   58.71925   5.871925                      48.26811    71.43329
  var(e.write)|   55.31334   5.531334                      45.46841    67.28993
var(e.science)|   48.77421   4.877421                      40.09314    59.33492
-------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(1)   =     21.43, Prob > chi2 = 0.0000

The indirect effect for math, .345706, is the combination of the indirect via
read plus the indirect via write. We can compute these indirect paths manually.

indirect via read = .724807*.3015317 = .21855229

indirect via write = .6247082*.2065257 = .1290183

total indirect = .724807*.3015317 + .6247082*.2065257 = .21855229 + .1290183 = .34757059

The last computation shows that the indirect effect given by estat teffects is the combined
indirect effect.

We can use the values we just computed to get the ratios and proportions of interest.

proportion of total math effect mediated = .3475706/.66658 = .52142369
proportion of total math effect mediated via read = .21855229/.66658 = .32787106
proportion of total math effect mediated via write = .1290183/.66658 = .19355261

ratio of math indirect to direct effect = .3475706/.3190094 = 1.0895309
ratio of math indirect to direct effect via read = .21855229/.3190094 = .68509671
ratio of math indirect to direct effect via write = .1290183/.3190094 = .40443416

ratio of total math to direct effect = .66658/.3190094 = 2.0895309

 

 

Cite this article

stats writer (2024). How can I do mediation analysis with the sem command?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-can-i-do-mediation-analysis-with-the-sem-command/

stats writer. "How can I do mediation analysis with the sem command?." PSYCHOLOGICAL SCALES, 1 Jul. 2024, https://scales.arabpsychology.com/stats/how-can-i-do-mediation-analysis-with-the-sem-command/.

stats writer. "How can I do mediation analysis with the sem command?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/how-can-i-do-mediation-analysis-with-the-sem-command/.

stats writer (2024) 'How can I do mediation analysis with the sem command?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/how-can-i-do-mediation-analysis-with-the-sem-command/.

[1] stats writer, "How can I do mediation analysis with the sem command?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, July, 2024.

stats writer. How can I do mediation analysis with the sem command?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.

Download Post (.PDF)

Related terms:

  1. How can I perform moderated mediation analysis with a categorical moderator using the structural equation modeling (SEM) approach?
  2. How can I check measurement invariance using the sem command?
  3. What is the Success/Failure Condition in Statistics3. The output of the file command is: /home/ccuser/workspace/learn-the-command-line/file ASCII text
  4. How do you run a Monte Carlo power analysis for simple, serial, and parallel mediation models?
  5. How can I do mediation analysis with a categorical IV in Stata?
  6. How can I perform moderated mediation analysis in Stata?
  7. What are the differences between mixed and sem linear growth models in Stata?
  8. “What are the saturated and baseline models in SEM?”
  9. What is the annotated output for the Factor Analysis command in Stata?
  10. How can I perform mediation with multilevel data using Method 2?
Slide Up
x
PDF
Scroll to Top