Hi,

Imagine you have measured two variables X and Y at two points in time. You want to predict Y2 from X1 and also control for the autoregressive effect (= temporal stability) of Y1 and control for the correlation of X1 and Y1. My question: Is there any statistical reason that makes it necessary and/or advantageous to implement a full CLP, that is to include the pathes X1 -> X2, Y1 -> X2, and the correlation X2 Y2?

I am not interested in reciprocal relations between X and Y. I just wonder whether including these additional pathes has an impact on my path of interest (X1 -> Y2) and if so, why? I'd also be glad if oyu could provide a reference.