Calculation of SE and p-values for complete indirect paths using SEM (similar to binary_mediation)

[Anne Chistensen]

Hi,
I am doing a mediation analysis using the SEM command (or the builder, both are fine) with only observed variables.
Using estat teffects I get all the "simple" (a and b paths) direct and indirect effects and their related p-values, but I would like a p-value for a test of the "complete" paths (from the predictor through the mediator to the outcome). I know that if one of the simple indirect paths are insignificant, the complete path won't be either, but I would still like an estimate, SE and p-value for these complete path.

For a simple example:
My command is: sem (lei <- sep sex age) (al <- let sp sex age)

That is, I am testing whether the effect of sep on al is mediated by lei, with sex and age as covariates.
Using estat teffects I get paths and p-values from sep to lei and from lei to al, and of course by multiplying these I can get the complete indirect effects but no p-value.
Is there some bootstrap-procedure I can use to get this?

For those of you familiar with the user-written binary_mediation command, there is a bootstrap-option that does this - the problem is, I need to use SEMs FIML option.

Please let me know if you need any more info to help me and thank you in advance.

[Roman Mostazir]

Use nlcom for nonlinear test (indirect paths). Here is a quick example with artificial data followed by bootstrapping the nonlinear effect:

sem (lei <- sep sex age) (al <- lei sep sex age),


Structural equation model                       Number of obs     =      1,000
Estimation method  = ml
Log likelihood     = -1457.8648

------------------------------------------------------------------------------
             |                 OIM
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural   |
  lei <-     |
         sep |   .0731329   .0319451     2.29   0.022     .0105218    .1357441
         sex |   .0092227   .0183664     0.50   0.616    -.0267749    .0452203
         age |  -.0601395   .0316345    -1.90   0.057     -.122142     .001863
       _cons |   .4835566    .026982    17.92   0.000     .4306728    .5364403
  -----------+----------------------------------------------------------------
  al <-      |
         lei |  -.0158457   .0323121    -0.49   0.624    -.0791762    .0474848
         sep |   .0495867   .0327268     1.52   0.130    -.0145567      .11373
         sex |    .000865   .0187692     0.05   0.963    -.0359219    .0376519
         age |  -.0116921   .0323824    -0.36   0.718    -.0751606    .0517763
       _cons |   .4700953   .0316898    14.83   0.000     .4079845    .5322062
-------------+----------------------------------------------------------------
   var(e.lei)|   .0839667   .0037551                      .0769201    .0916587
    var(e.al)|   .0876671   .0039206                        .08031    .0956981
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .


// Do the non-linear indirect paths test:

nlcom _b[lei:sep]*_b[al:lei]

       _nl_1:  _b[lei:sep]*_b[al:lei]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |  -.0011588   .0024167    -0.48   0.632    -.0058955    .0035778
------------------------------------------------------------------------------

//For Bootstrapping the non-linear effect:

capture program drop boots
    program boots, rclass
    sem (lei <- sep sex age) (al <- lei sep sex age),
    return scalar est1 =  _b[lei:sep]*_b[al:lei]
end

bootstrap r(est1), reps(15) : boots //Use your own number of replications, for demostration purpose 15 is given here.


Bootstrap replications (15)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
...............

Bootstrap results                               Number of obs     =      1,000
                                                Replications      =         15

      command:  boots
        _bs_1:  r(est1)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |  -.0011588   .0021683    -0.53   0.593    -.0054086    .0030909
------------------------------------------------------------------------------

[Anne Chistensen]

Thank you so much Roman! I will try it for myself when I have my data tomorrow. Is this a user-written command or do you know where I might find more info about this?

[Anne Chistensen]

Okay found it, sorry I can't seem to find anything about using the mlmv method option for this - do you know if they are compatible if I use mlmv in the first sem command?

[Roman Mostazir]

Just use the 'mlmv' option after the 'sem' command.