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:

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.

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#### Best Answer

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`

.

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