I want to specify a path diagram with 7 (observed) variables. It includes the following two relationships:
b ~ a; c ~ a+b.
Analyzing these three variables separately, it is possible to define a simple moderator mediation model: b is both a mediator and a moderator of the relationship between 'a' and c (or 'a' is a moderator in the relationship between b and c). All variables are continuous.
I would like to include this moderator effect in the overall (bigger) path diagram, with seven variables, ie., I would like to define the interaction variable ab=a*b and to include the following relationship in the path diagram:
c ~ ab
My doubts are:
1) Does this variable/path make sense in the overall path diagram?
2) In the affirmative case, I would like to know whether it is necessary to include the correlations
ab ~~ a; ab ~~ b
and require 'fixed.x=FALSE' in the 'sem' function (as it happens in the simple moderated mediation model, according to https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4616155/pdf/nihms685520.pdf).
Can you please tell me your opinion?