I have a methodical question that might be better answered on SEMnet. Since I use lavaan, I hope it is okay anyway. I have a 2nd order construct (FX), several target variables (FY1, FY2) and a one-dimensional latent variable (FM). I want to test whether FM moderates the effects FX -> FY1 and FX -> FY2. Unfortunately I didn't find any literature on this problem, so I used the product indicator approach as I think it makes sense. My lavaan code is the following (mean centering and the calculation of the product indicators were done in the dataset with Excel):
#Moderator
FM =~ m1 + m2 + m3
#2nd order construct
FXD1 =~ x1 +x2 + x3 + x4
FXD2 =~ x5 + x6 + x7 + x8
…
FX =~ FXD1 + FXD2 + …
FXxFMD1 =~ x1xm1 + x2xm2 + x3xm3
FXxFMD2 =~ x5xm1 + x6xm2 + x7xm3
…
FXxMD =~ FXFMD1 + FXxFMD2 + …
x1xm1 ~~ x5xm1
x2xm2 ~~ x6xm2
x3xm3 ~~ x7m3
…
# Outcome variables
FY1 = y1 + y2 + y3 + y4
FY2 =~ y5 + y6 + y7 + y8
# Regressions
FY1 ~ FX + FM + FXxMD
FY2 ~ FX + FM + FXxMD + FY1
To get an impression if the results make sense, I calculated factor scores and did a simple moderator regression with PROCESS (the shame is on my side, something better didn't occur to me). Basically, the results seem to indicate that the procedure might work. Nevertheless, I would like to ask some questions:
(1) The dimensions of the second order construct are each measured with 4 indicators. The moderator with 3 indicators. As product indicators I used 3 variables (x1xm1 + x2xm2 + x3xm3). The selection of the indicators is of course arbitrary. Is there a "better" solution that is not over-complex?
(2) I'm not sure if this approach makes sense at all. It results in another 2nd order construct (FXxMD). Is there something better here?
(3) Is there possibly a completely different and better approach with lavaan?