Moderated mediation with latent moderator + mediator

[Onur Şahin]

Hi all,

I posted a question here a while ago, while Edward Rigton and Terrence Jorgerson took their time to help me (thanks guys!), it seems that my approach back then was not the best one.

I want to conduct a moderated mediation analysis with latent DV's, moderator and mediator. The IV's will not be latent, as they are single item. 

My issue is with the latent moderator. How does one approach this? The way I have it now, I calculate interaction terms before the SEM model, so I input the interaction terms in my model. Furthermore, I look at the moderation at -1 SD, mean and +1 SD of the moderator. I'm not sure whether this is possible with a latent variable. See my code below:

SEMdata$X1xW <- with(SEMdata, as.numeric(X1)*W) ## I need to create the interaction terms before the model, so I can use these new variables in the model. Not possible if I use a latent variable right? I think SEMtools has an option though, but is it possible for all these interactions? 

SEMdata$X2xW <- with(SEMdata, as.numeric(X2)*W)

SEMdata$X1xX2 <- with(SEMdata, as.numeric(X1)*as.numeric(X2))

SEMdata$X1xX2xW <- with(SEMdata, as.numeric(X1)*as.numeric(X2)*W)

mean_of_W <- mean(SEMdata$W, na.rm = T)

var_of_W <- var(SEMdata$W, na.rm = T)

model <- "

D1 =~ d11+ d12+ d13+ d14+ d15

D2 =~ d21+ d22+ d23+ d24+ d25

D3 =~ d31+ d32+ d33+ d34+ d35

D4 =~ d41+ d42+ d43+ d44+ d145

D5 =~ d51+ d52+ d53+ d54+ d55 

M =~ item1+item2+item3+item4+item4     ####(this is the mediator)

### Ideally I also would have:

# W =~ Witem1+Witem2 etc. but I have no idea how I can test the moderation in this way

M ~ a1*X1

M ~ a2*X2

D1 ~ b1*M

D2 ~ b2*M

D3 ~ b3*M

D4 ~ b4*M

D5 ~ b5*M

M~ a3*W  ### W is the moderator! I want this to be a latent variable as well but have no idea how to approach this

M~ a4*X1xW

M~ a5*X2xW

M~ a6*X1xX2

M~ a7*X1xX2xW

D1 ~ c1*X1

D1 ~ c6*X2

D2 ~ c2*X1

D2 ~ c7*X2

D3~ c3*X1

D3~ c8*X2

D4~ c4*X1

D4 ~ c9*X2

D5~ c5*X1

D5~ c10*X2

W ~ mean_of_W*1

W ~~ var_of_W*W

D1 ~ c11*W

D2 ~ c12*W

D3 ~ c13*W

D4 ~ c14*W

D5 ~ c15*W

X1xW ~~ X2xW ## I think these covariances are necessary, 

X1 ~~ X2

X1 ~~ X1xW

X2 ~~ X2xW

SD.below_X1_M := a1 + a4*(mean_of_W- sqrt(var_of_W)) ## This part can be ignored, but acts as an example to see how I test the moderation. I do this for all DV's as well

mean_X1_M := a1 + a4*(mean_of_W)

SD.above_X1_M := a1 + a4*(mean_of_W + sqrt(var_of_W))

[Terrence Jorgensen]

My issue is with the latent moderator. How does one approach this? 

Use Mplus.... sorry, but I think your model is already too large for product-indicators to be a viable solution.  Mplus is the only SEM package that enables LMS for latent interactions, except the R package nlsem (which you can try, but the syntax is difficult, and I was unable to make it work to estimate an interaction between latent and observed predictors).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Onur Şahin]

Thank you for taking the time to help me out, much appreciated. I think I'll just forget about the latent moderator.

Best,

Onur

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