Causal Analysis in Theory and Practice

April 24, 2000

Simpson’s paradox and decision trees

Filed under: Decision Trees,Simpson's Paradox — moderator @ 12:14 am

From Nimrod Megiddo (IBM Almaden)

I do not agree that "causality" is the key to resolving the paradox (but this is also a matter of definition) and that tools for looking at it did not exist twenty years ago. Coming from game theory, I think the issue is not difficult for people who like to draw decision trees with "decision" nodes distinguished from "chance" nodes.

I drew two such trees on the attached Word document which I think clarify the correct decision in different circumstances.
Click here for viewing the trees.

Causality and the mystical error terms

Filed under: General,structural equations — moderator @ 12:00 am

From David Kenny (University of Connecticut) 

Let me just say that it is very gratifying to see a philosopher give the problem of causality some serious attention. Moreover, you discuss the concept as it used in contemporary social sciences. I have bothered by the fact that all too many social scientist try to avoid saying "cause" when that is clearly what they mean to say. Thank you!

I have not finished your book, but I cannot resist making one point to you. In 5.4, you discuss the meaning of structural coefficients, but you spend a good deal of time discussing the meaning of epsilon or e. It seems to me that e has a very straight-forward meaning in SEM. If the true equation for y is

y = Bx + Cz + Dq + etc + r where is r is meant to allow for some truly random component, then e = Cz + Dq + etc + r or the sum of the omitted variables. The difficulty in SEM is that usually, though not always, for identification purposes it must be assumed that e and x have a zero correlation. Perhaps this is the standard "omitted variables" explanation of e that you allude to, but it does not seem at all mysterious, at least to me.

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