Regression with complex causal structure

Question

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.

Two questions.

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?

Thanks.

Answer 1

It sounds like you might want to use Path Analysis, which I believe is a subset of Structural Equation Modeling (SEM). However, I'm pretty certain that there's no statistical method for proving (or even strongly suggesting) causality. Rather, you create a causal structure and make the case that it makes sense, then use statistical methods to show that your structure is not inconsistent with the data. If you can come up with several plausible causal structures, you may be able to statistically show that one is more consistent with the data than the others, which is more suggestive (depending on how well your set of causal structures seem to account for all plausible alternatives).

I don't know SAS, but I believe PROC CALIS (and perhaps PROC REG) is a good place to start.