Figure 7.

Likelihood-ratio tests (LRTs) of the causal estimates in the traditional CLPM and the IV-CLPM at varying time intervals between study waves. (A) CLPM: The non-centrality parameter (NCP) obtained from a 2-degrees-of-freedom (2df) test of bidirectional distal effects, and that obtained from a 1df LRT of a unidirectional distal effect (shown here is X to Y). (B) IV-CLPM: The NCP from a 6df omnibus test of bidirectional causal estimates of three types: the proximal effect at wave 1 (Proximal_W1), the distal effect, and the proximal effect at wave 2 (Proximal_W2). A significant omnibus test is followed up with a 3df LRT of the three causal effects in each direction, and, finally, the 1df LRTs of the three causal effects separately (in each direction of causation). The NCPs were obtained by fixing to zero the parameters of interest in models fitted to data with $N=1000,$ $b_{YX}=0.2,$ $b_{XY}=0.$2, $b_{X2X1}=0.7,$ $b_{Y2Y1}=0.7,$ and $r_{\mathit{exy}}=0.3.$