Testing interaction effects in TSSEM

Dear Mike,

Thanks for being so helpful in previous instances that we've had a question about metaSEM. metaSEM has made it possible for us to conduct meta-analysis beyond anything we envisioned was possible 5 years ago.

We would like to test whether the exogenous variables in our model interact with each other with respect to each endogenous variable in our model.

There are four exogenous variables: UNIres, TTOres, REGres, and uSize

There are also four endogenous variables: LicRev, LicNum, Spin, and Perf

There are paths from all four exogenous variables to each of the four endogenous variables.

I would like to test whether UNIres, TTOres, and REGres interact with each other when predicting: (a) LicRev and (b) Perf. To this end, I created a latent construct named "Resources" and loaded UNIres & TTOres as indicators for the "Resources" latent variable. To test whether UNIres & TTOres interact with each other when predicting LicRev, LicRev is now predicted by: the latent construct "Resources" + REGres + uSize

We repeat this process once again to test the interaction of (a) TTOres & REGres, (b) UNIres & TTOres, and (c) TTOres, UNIres, & REG together, when predicting LicRev. This process is also repeated for another endogenous variable, Perf.

We then compare the parsimonious fit of (a) the baseline model with only direct paths from the four exogenous variables to the four endogenous variables with the fit of (b) each model where two variables interact through the latent construct. However, this process provides the same values for the measures of parsimonious fit we use BIC and AIC regardless of whether we are using the latent construct to predict LicRev or Perf. Thus, it seems that using a latent construct to test interaction between variables only measures whether variables interact with each other, but doesn't test whether they interact when predicting different endogenous variables in our model.

If so, what would be the best way for us to go about testing whether the exogenous variables in our model interact with each other when predicting each endogenous variable in our model in the context of TSSEM?

Thanks,
Sergio