Hi , I have already run a whole bunch of OLS and found the following
Regress P= B1*L+e_1, found b1<0
Regress X= B2*L+e_2, found b2>0
Regress X= B3*P+e_3, found b3<0
I want to build a case with complex causal structure, in which there are two channels that L positively affects X.
1.Reducing P increases X
2.L positively affects X on its own
3.In addition, L positively affects X through the effect that increasing L reduces P, and we know reducing P increases X, thus this is the second channel that L positively affects X.
A. What OLS or other type of regression equations[I guess it takes more than 1 equation] should I run to prove my case, ie, to prove (if not possible to prove, strongly suggest) this whole system of causal strucuture?
B. What regression diagnostics should I use in SAS to show my logic behind the causal strcuture (L increases X through 2 channels )are ok?