2) Comparing to MI testing: “In fact, and in contrast to measurement invariance testing and related techniques … our similarity checking procedure is not tied to CFA or SEM at all, and can shed light on replication efforts involving any other model that can be estimated using Bayes’ theorem.”

What I like though about MI is there is a principled way of deciding what part of the model equivalence is actual being tested. But Obviously that could just be encoded into the priors and then you'd still not be tied to SEM/CFA! Dumb freuentist q, why beta for correlation? shouldn't it be [-1,1]?