I want to test a model with three sets of variables. Set A grows linearly but discontinuously: at a time-varying point, there is an increase in both intercept and slope. Set B follows the same pattern, but does so 1 time interval after A. Variable C (a single variable in this case) also follows the same pattern, but does so 1 time interval after B. I have seven waves of data to work with. I know how to model each growth pattern separately for A, B, and C. I would like to model them together, to show that A predicts B one interval later, and B predicts C one interval after that. Can I do that with 3parallel models? Do I want to show that A's i and s predict B, or do I want time-lagged time-varying covariates?
I'm not sure this is the solution to your problem, but one thing you might consider is defining the intercept growth factor for each process so that the points you want to relate have zero time scores. The time scores for your three growth processes might look like:
0 1 2 3
-1 0 1 2
-2 -1 0 1
where zero defines the intercept growth factor. Then you could regress i3 on i2 and i2 on i1.
Following your response: I think that, in addition to regressing i3 on i2 and i2 on i1, I want to regress s3 on s2 and s2 on s1. I want to show that variation in growth among my set A variables predicts variation in growth among my set B variables, and so on. Further, I have 4 variables in set A. My theory holds that 2 of the 4 slopes will predict slopes in a given set B variable, but the other two will add nothing to that prediction. So, can I regress a slope from set B on 4 slopes from set A simultaneously, so I can evaluate the incremental role of each slope over the other slopes? Thanks again.