Blavaan testing moderation / mediation / independent effects differences

[Carolien T.]

Hi there,

I want to compare three models but I wonder how to do it the cleanest way. It is a mediator, moderator and independent effects model with two covariates which I specified as follows:

H1 moderator: Model1 <- "

 BAG_z ~ gender_beh + age_cen_within
 COG_z ~ CRxBAG_z + BAG_z + CR_z + gender_beh + age_cen_within
"

H2: mediator: Model2 <- "
  BAG_z ~ a*CR_z + gender_beh + age_cen_within
  COG_z ~ b*BAG_z + c*CR_z + gender_beh + age_cen_within

  indirect := a*b
  total    := c + (a*b)
"
H3: independent effects: Model3 <- "
 BAG_z ~  gender_beh + age_cen_within
 COG_z ~ CR_z + BAG_z + gender_beh + age_cen_within
"

I wonder about the covariate specification here, because I only added it to models 1 and 3 to make it more comparable to model 2 in terms of N parameters, but it is actually not NEEDED for the models, because in this model COG_z is the only dependent variable. So I feel like I am including a regression line which is not actually necessary, but without it, I have a different nuisance structure in models 1 and 3 vs. model 2. This is especially relevant, since I am using the multigroup function (with three groups) and I need to constrain the regression paths between those groups except for the covariates (so age and gender effects are allowed and expected to vary between groups while constraining the other paths, and then in a next step also comparing constrained vs. an all  unconstrained model...)

What would you advise? Remove them and accept the rather large difference in parameters or leave them in?

I hope my questions are a bit clear. The comparisons are basically done with z elpd (from loo).

Thanks so much for your advise.

Carolien Torenvliet