Moderation mediation with latent Exogenous and a binary moderator

[Farideh Tavangar]

Hi all,

I am trying to run a Moderation mediation model with a latent  Exogenous and a binary moderator and binary/ continuous mediators with a binary Response using lavaan::sem.

 I have defined the equations for indirect and direct effects. I don't know how do we define the min and max of the interaction term, in this case, to calculate the indirect effect of X on response and test whether it is significant or not???? And also, how do we test whether the interaction term should be in the model or not?

Any guidance will be appreciated,

Farideh

# Exogenous= Latent variable X

            # Moderator= PnP ( A binary variable/0 AND 1), affects only the relationship between latent variable and mediators

            # Mediators are NSP (continuous), CAS and OS1 ( 0/1)

            # PATHS : X-->CAS-->STI; X-->OS1-->STI; X--NSP-->OS1-->STI; X-->NSP-->CAS-->STI

            # Endogenous variale= STI (0/1)

model <- '

              # Latent Variables

              X =~ TASP + TMT    ## TASP is a likert scale 1 to 6 and TMT is a continuous 2 to 37
             
              # Interaction term

              XP =~ X*PnP     ## How do we define the min and max of interaction term when a moderator is binary?


              # regressions


                             
               NSP ~ a1*X + a4*XP
               CAS ~ a2*X + a5*XP+d1*NSP

               OS1 ~ a3*X + a6*XP+d2*NSP

               STI ~ c*X + b2*CAS+ b3*OS1

               # residual covariances

               CAS ~~ OS1
               

               # define indirect effects of x on STI via CAS only   ; model: CAS= a2*X+a5*XP+d1*NSP    ; NSP= a1*X+a4*XP

               a5b2 := a5*b2*PnP     ## It was a5*b2*XP , I defined the slop as the indirect effect  ?????I think the problem is over here.
               a2b2 := a2*b2

               # define indirect effects of x on STI via OS1 only;   Model: OS1=a3*X+a6*XP+d2*NSP

               a6b3 := a6*b3*PnP
               a3b3 := a3*b3

               # define indirect effects of x on STI via CAS and OS1

               a1b2d1:= a1*b2*d1
               a1b3d2:= a1*b3*d2
               a4b2d1P:= a4*b2*d1*PnP
               a4b3d2P:= a4*b3*d2*PnP

               Indirect := a2b2 + a3b3+a5b2+a6b3+a1b2d1+a1b3d2+a4b2d1P+a4b3d2P
               Low_Indirect := a2b2 + a3b3+a5b2+a6b3+a1b2d1+a1b3d2                                     ## When moderator, PnP=0
               HI_Indirect := a2b2 + a3b3+a5b2+a6b3+a1b2d1+a1b3d2+1*a4b2d1+1*a4b3d2       ## When moderator, PnP=1

               Total_Indirect := HI_Indirect-Low_Indirect

               Total := c + Total_Indirect
               Prop  := Total_Indirect/Total'
 
      fit<-lavaan::sem(model, data=data, ordered=c("CAS","OS1","STI"))
 
      summary(fit,fit.measures=TRUE, modindices = TRUE )

Error in lav_partable_constraints_def(partable, con = LIST, debug = debug) :
  lavaan ERROR: unknown label(s) in variable definition(s): PnP a4b2d1 a4b3d2
In addition: Warning message:
In lav_data_full(data = data, group = group, cluster = cluster,  :
  lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
> 

[ryan chesnut]

Since your moderator is binary, have you considered using multiple group SEM? Here is a paper that might be useful to you if you decide to use that approach:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4616155/