Figure 5.
The estimated causal effect of X on Y in the IV-CLPM (Figure 1(C)) and the CLPM (Figure 1(A)) at varying time intervals between study waves, given different levels of the first-order (i.e., at ) causal effect of X on Y (A,B), first-order autoregression (AR1) of predictor X (C,D), and AR1 of outcome Y (E,F) in the data-generating model (Figure 2). For ease of display, the time intervals are shown up to 40 units, by which point all parameter estimates are close to their asymptotes. (A,B) The first-order causal effect does not impact the rate at which the distal effect decays with increasing time intervals in either model. However, a larger first-order causal effect size does lead to larger causal estimates in both models (as expected). Note, though, that the distal effect in the IV-CLPM approaches zero at longer intervals, regardless of the first-order causal effect size. (C,D) A larger AR1 parameter (i.e., greater stability over time) of the predictor variable leads to a larger distal effect in the CLPM across time intervals, as well as slower decay of the distal effect with increasing intervals. On the contrary, the degree of AR1 in the predictor has minimal impact on the causal estimates in the IV-CLPM. Note that in panel C, the two curves for the Proximal Effect at Wave 1 have fully overlapped, so only one of the two curves is visible. (E,F) The AR1 parameter of the outcome variable impacts the causal estimates in both models: a higher level of outcome AR1 leads to larger causal estimates and slower decay of the distal effect in both models.