Hi:

Thanks to all those who have taken a look at this post. I'm not sure whether there have been no responses because it's obvious the model will make reasonable estimates, obvious it will make biased estimates, a silly question, or no one knows.

My feeling is that it will make reasonable estimates with the parameter for x1 capturing effects on y not operating through x2, and the parameter for x2 capturing the effects of x1 on y via x2 as well as x2's own effects on y.

Here's a quote from Kirkwood and Sterne (2003) that's actually about confounding but that supports the above: "Note that a variable that is part of the causal chain leading from E to D is not a confounder. That is, if E affects C, which in turn affects D, then we should not adjust for the effect of C in our analysis of the E-D association (unless we wish to estimate the effect of E on D which is not caused by the E-C association)".

In my case: E is x1, C is x2, and D is y. I want to capture the combined effects of x1 and x2 on y and the final bracketed text in the above quote seems to suggest this is fine.

If anyone has any thoughts on this I'd greatly appreciate hearing them.

Thanks