Causal Analysis in Theory and Practice

October 22, 2008

Forthcoming 2nd Edition of Causality

Filed under: Announcement,Book (J Pearl) — moderator @ 11:00 pm

The new edition will (1) provide technical corrections, updates, and clarifications to all ten chapters in the original book; (2) add summaries of new developments at the end of each chapter; (3) elucidate subtle issues that readers have found perplexing in a new chapter.

Information about the upcoming release, including an updated table of contents, may be found here:

We welcome your comments.

February 22, 2007

Back-door criterion and epidemiology

Filed under: Back-door criterion,Book (J Pearl),Epidemiology — moderator @ 9:03 am

The definition of the back-door condition (Causality, page 79, Definition 3.3.1) seems to be contrived. The exclusion of descendants of X (Condition (i)) seems to be introduced as an after fact, just because we get into trouble if we dont. Why cant we get it from first principles; first define sufficiency of Z in terms of the goal of removing bias and, then, show that, to achieve this goal, you neither want nor need descendants of X in Z.

October 15, 2006

The validity of G-estimation

Filed under: Book (J Pearl),G-estimation — moderator @ 12:00 pm

From a previous correspondence with Eliezer S. Yudkowsky, Research Fellow, Singularity Institute for Artificial Intelligence, Santa Clara, CA

The following paragraph appears on p. 103, shortly after eq. 3.63 in my copy of Causality:

"To place this result in the context of our analysis in this chapter, we note that the class of semi-Markovian models satisfying assumption (3.62) corresponds to complete DAGs in which all arrowheads pointing to Xk originate from observed variables."

It looks to me like this is a sufficient, but not necessary, condition to satisfy 3.62. It appears to me that the necessary condition is that no confounder exist between any Xi and Lj with i < j and that no confounder exist between any Xi and the outcome variable Y. However, a confounding arc between any Xi and Xj, or a confounding arc between Li and Xj with i <= j, should not render the causal effect non-identifiable. For example, even if a confounding arc exists between X2 and X3 (but no other confounding arcs exist in the model), the causal effect on Y of setting X2=x2 and X3=x3 should be the same as the distribution on Y if we observe x2 and x3.

It is also not necessary that the DAG be complete.

May 8, 2006

Identifying conditional plans

Filed under: Book (J Pearl),Plans — moderator @ 12:00 am

Section 4.2 of the book (p. 113) gives an identification condition and estimation formula for the effect of a conditional action, namely, the effect of an action do(X=g(z)) where Z is a measurement taken prior to the action. Is this equation generalizable to the case of several actions, i.e., conditional plan?

The difficulty seen is that this formula was derived on the assumption that X does not change the value of Z. However, in a multi-action plan, some actions in X could change observations Z that are used to guide future actions. We do not have notation for distinguishing post-intevention from pre-intevention observations.

December 1, 2000

The causal interpretation of structural coefficients

Filed under: Book (J Pearl),structural equations — moderator @ 12:00 am

From L. H., University of Alberta and S.M., Georgia Tech 

In response to my comments (e.g., Causality, Section 5.4) that the causal interpretation of structural coefficients is practically unknown among SEM researchers, and my more recent comment that a correct causal interpretation is conspicuously absent from all SEM books and papers, including all 1970-1999 texts in economics, two readers wrote that the "unit-change" interpretation is common and well accepted in the SEM literature.

L.H. from the University of Alberta wrote:
"Page 245 of L. Hayduk, Structural Equation Modeling with LISREL: Essentials and Advances, 1986, has a chapter headed "Interpreting it All", whose first section is titled "The basics of interpretation," whose first paragraph, has a second sentence which says in italics (with notation changed to correspond to the above) that a slope can be interpreted as: the magnitude of the change in y that would be predicted to accompany a unit change in x with the other variables in the equation left untouched at their original values." … "Seems to me that O.D. Duncan, Introduction to Structural Equation Models 1975 pages 1 and 2 are pretty clear on b as causal. "More precisely, it [byx] says that a change of one unit in x … produces a change of b units in y" (page 2). I suspect that H. M. Blalock's book "Causal models in the social Sciences", and D. Heise's book "Causal analysis." probably speak of b as causal."

S.M., from Georgia Tech concurs:
"I concur with L.H. that Heise, author of Causal Analysis (1975) regarded the b of causal equations to be how much a unit change in a cause produced an effect in an effect variable. This is a well-accepted idea."

June 10, 2000

On functional models for predicting the effect of actions

Filed under: Book (J Pearl),General — moderator @ 12:00 am

From Dennis Lindley:

In the part of Chapter 1 that you kindly sent me, a functional, causal model is clearly defined by a set of equations in (1.40). The set provides a joint probability distribution of the variables using a specific order. That distribution may be manipulated to obtain an equivalent probability specification in any other order. I showed in my note that this probability structure could be described by a set of equations in an order different from that of (1.40). (That proof may be wrong, though on p. 31 you suggest the result was known in '93.) Consequently (1.40) can be replaced by a different set of equations. You tell us now to see what happens were a variable to be controlled; this in terms of the set, and I showed that different consequences flowed if different sets were used. How do I decide which set is correct?

May 18, 2000

Counterfactual notation

Filed under: Book (J Pearl),Counterfactual — moderator @ 12:00 am

From Jos Lehmann (University of Amsterdam):

Jos Lehmann noticed potential ambiguity in the notation used for counterfactual propositions. Capital letters, like "A" or "B," are sometimes used to denote propositional variables, and sometimes to denote propositions. For example, in the function A = C (Model M, page 209) "A" stands for the variable "whether rifleman-A shoots", and takes on values in {true, false}, while in statements S1-S5 (page 208), A stands for a proposition (e.g., "Fireman-A shot").

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