Causal Diagram and multiple regression I have 4 nodes:
A causes B and C, and C by itself causes D. However, C is not measurable, and my interest is to test the association between B and D. What would be the right causal diagram and multiple regression expression?
My guess is lm(D ~ B + A), because conditioning on A can remove the association between B and C, and therefore the estimated $\hat \beta_{B}$ reflects the realistic $\beta_B$, which is 0. Is my interpretation correct?


Your interpretation is correct. Conditioning on $A$ blocks the backdoor path $B\leftarrow A\to C\to D.$ Since $C$ is unavailable because it is unmeasured, you must condition on $A$ to block the backdoor path. Including $A$ on the RHS of your linear regression model is probably the most straight-forward way to condition on it. So I'd say your model, assuming it is correct, should provide the unbiased effect of $B$ on $D.$
