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# Re: st: Modeling control variables (covariates) in SEMs: What is the correct approach?

 From Joerg Luedicke To statalist@hsphsun2.harvard.edu Subject Re: st: Modeling control variables (covariates) in SEMs: What is the correct approach? Date Fri, 18 Jan 2013 14:51:31 -0500

```There seems to be some confusion going on. First, what you call
moderator variable rather looks like a mediator variable to me when
looking at the model you show under "approach 1". Second, when we
regress a on b, it means that we consider a as the outcome and b as
the predictor, not the other way round.

Now as for the modeling strategy, that always depends on what you want
to find out etc. In data analysis, there never is just one solution
for everything. That said, if you were interested in exploring
indirect effects of your main predictor of interest (IV) on your
outcome via the variable you call MV, then your first approach looks
reasonable. From judging without knowing any context here, I would say
that the second approach does not make much sense. Say you have only 3
variables, MV, IV, and DV. If you were interested in regressing DV on
MV while adjusting the effect for IV, then regressing DV and MV on IV
with two separate equations followed up by regressing DV on MV won't
get you there. You simply end up with three separate equations (with
possibly correlated errors) with which you cannot adjust the effect of
MV on DV with IV.

Joerg

On Fri, Jan 18, 2013 at 5:29 AM, Johannes Kotte
<johannes.kotte@st.ovgu.de> wrote:
> Hi everybody,
>
> regarding the use of control variables (covariates) in SEMs I have seen two
> different approaches and I am not sure which one is the correct one. Can
> anybody help me?
>
> Variables:
> IV ...independent variable
> MV ...moderator variable
> DV ...dependent variable
> CV1...control variable 1
> CV2...control variable 2
>
> *Approach 1* (http://www.ats.ucla.edu/stat/stata/faq/sem_mediation.htm) is
> to use the control variables in each of the equations:
>
> sem  (MV <- IV CV1 CV2) (DV <- MV IV CV1 CV2)
>
>
> *Approach 2* (used by a fellow researcher I know) is to regress CV1 and CV2
> on all other variables first and then do the rest of the regressions without
> control variables:
>
> sem (DV MV IV <- CV1 CV2) (MV <-IV) (DV<-MV)
>
> To me, this approach looks incorrect. What I find particularly confusing
> with this approach is that CV1 and  CV2 are also being regressed on IV.
>
> I am grateful for feedback. Thanks in advance!
>
>
> One more question comes to my mind: Some of my CVs are correlated at the 5%
> level, but their correlation coefficients are below 0.3. Would you exclude
> these CVs?
>
>
> Johannes
>
> --
> Johannes Kotte
> Otto-von-Guericke-Universität | Fakultät Wirtschaftswissenschaften |
> Lehrstuhl für Unternehmensführung und Organisation (Prof. Dr. Thomas
> Spengler) | Postfach 4120, 39016 Magdeburg | www.ufo.ovgu.de
>
> E-Mail: johannes.kotte@st.ovgu.de
>
>
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```