Now i need to know the aggregate effect (estimate and SE) of x on y2. I can do this in two ways:
1] Throw the indirect path out of the model. This will give me an estimate, but the error will be inflated, because the model doesn't "know" the information in the y1 predictor.
2] Calculate the aggregate. This would be: Estimate(y2 ON x) + Estimate(y1 ON x) * Estimate(y2 ON y1). This would result in the same estimate as above. However, I don't think I can do the same trick with the SE, since they might be correlated.
Am I correct in this, or can I simply calculate SE(y2 ON x) + SE(y1 ON x)*SE(y2 on y1) ?
If not, is there a way to calculate/estimate/simulate the aggregate SE?