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I am trying to make a moderated mediation, where the moderator (W) is categorical and Y and X are latent variables. However, none of the approaches I found either here or in Pubmed.

Please consider the model from the paper linked:

enter image description here

Whose specification looks like:

> model7 <- “
+  del ~ cprime * male
+  del ~ b * respect
+  del ~ bprime * maleXResp
+  respect ~ a * male
+  respect ~~ maleXResp
+  male ~~ maleXResp
+
+  bmale:= b + bprime
+  indMale:= bmale * a
+  indFemale:= b * a
+  indDiff:= indMale – indFemale
+  ”
>
> fit7 <- sem(model7, data=d, fixed.x=FALSE,
+      se=“bootstrap”)
> summary(fit7)

Full citation for this paper is:

Jeremy N.V Miles, Magdalena Kulesza, Brett Ewing, Regina A Shih, Joan S Tucker, Elizabeth J D'Amico, (2015) "Moderated
mediation analysis: an illustration using the association of gender with delinquency and mental health", Journal of Criminal
Psychology, Vol. 5 Issue: 2, pp.99-123, https://doi.org/10.1108/JCP-02-2015-0010

In the data I have access to, both Deliquency and Respect are latent variables.

  • How would I specify the mediation in the case where deliquency and respect are latent variables?

In my attempt, lavaan complains of Respect not being an observed variable, I can't figure out how to approach this issue.

lf_araujo
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  • As specified/depicted, there's no indirect/mediated effect--you're only depicting the interaction between Male and Respect on Delinquency. Male can't serve as *both* a moderator and a predictor of a mediator within the same model, if that's what you were trying to do... – jsakaluk Oct 12 '17 at 21:52

1 Answers1

1

I found the answer and it is quite simple, but introduces new assumptions to the analysis.

One can create a multiplicative term using indProd() from semTools() like this:

dataset<-indProd(dataset, var1=c("item1","item2","item3"),
                      var2=c("second1","second2","second3"))

And then create a latent variable that regresses on this term:

model7 <- '
    ...
    interaction =~ item1.second1 + item2.second2 + item3.second3
    ...
'

The remainder of the model is similar to the one in the question, using a mediation approach but including interaction.

lf_araujo
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