I'm trying to examine the developmental trajectory of construct A, but I'm also interested in knowing how the developmental trend of construct A is related to the longitudinal changes in construct B. Both constructs were measured at 4 time points.
My question is: should I treat construct B as a time-variant covariate, or use parallel analyses to model growth of both constructs? How would the interpretation of the results differ for those two methods?
Those are two quite different approaches but both are relevant. With parallel growth modeling, you let the two sets of growth factors relate to each other (e.g. correlate) and the two sets of observed variables are related to each other only via their growth factors. With time-varying covariates for construct B, you are saying that there are direct relationships between the two sets of observed variables; this approach is less parsimonious but may fit data better. A hybrid is of course also possible.