Causal Analysis in Theory and Practice

December 4, 2012

Neyman-Rubin’s model and ASA Causality Prize

We received the following query from Megan Murphy (ASA):
Dr. Pearl,
I received the following question regarding the Causality in Statistics Education prize on twitter. I’m not sure how to answer this, perhaps you can help?

Would entries using Neyman-Rubin model even be considered? RT @AmstatNews: Causality in Statistics Education #prize…

Judea Answers:
“Of course! The criteria for evaluation specifically state: ‘in some mathematical language (e.g., counterfactuals, equations, or graphs)’ giving no preference to any of the three notational systems. The criteria stress capabilities to perform specific inference tasks, regardless of the tools used in performing the tasks.

For completeness, I re-list below the evaluation criteria:

• The extent to which the material submitted equips students with skills needed for effective causal reasoning. These include:

—1a. Ability to correctly classify problems, assumptions, and claims into two distinct categories: causal vs. associational

—1b. Ability to take a given causal problem and articulate in some mathematical language (e.g., counterfactuals, equations, or graphs) both the target quantity to be estimated and the assumptions one is prepared to make (and defend) to facilitate a solution

—1c. Ability to determine, in simple cases, whether control for covariates is needed for estimating the target quantity, what covariates need be controlled, what the resulting estimand is, and how it can be estimated using the observed data

—1d. Ability to take a simple scenario (or model), determine whether it has statistically testable implications, and apply data to test the assumed scenario

• The extent to which the submitted material assists statistics instructors in gaining an understanding of the basics of causal inference (as outlined in 1a-d) and prepares them to teach these basics in undergraduate and lower-division graduate classes in statistics.

Those versed in the Neyman-Rubin model are most welcome to submit nominations.

Note, however, that nominations will be evaluated on ALL four skills, 1a – 1d.

November 25, 2012

Conrad (Ontario/Canada) on SEM in Epidemiology

Filed under: Counterfactual,Epidemiology,structural equations — moderator @ 4:00 am

Conrad writes:

In the recent issue of IJE (, Tyler VanderWeele argues that SEM should be used in Epidemiology only when 1) the interest is on a wide range of effects 2) the purpose of the analysis is to generate hypothesis. However if the interest is on a single fixed exposure, he thinks traditional regression methods are more superior.

According to him, the latter relies on fewer assumptions e.g. we don’t need to know the functional form of the association between a confounder and exposure (or outcome) during estimation, and hence are less prone to bias. How valid is this argument given that some of (if not all) the causal modeling methods are simply a special case of SEM (e.g. the Robin’s G methods and even the regression methods he’s talking about).

Judea replies:

Dear Conrad,

Thank you for raising these questions about Tyler’s article. I believe several of Tyler’s statements stand the risk of being misinterpreted by epidemiologists, for they may create the impression that the use of SEM, including its nonparametric variety, is somehow riskier than the use of other techniques. This is not the case. I believe Tyler’s critics were aimed specifically at parametric SEM, such as those used in Arlinghaus etal (2012), but not at nonparametric SEMs which he favors and names “causal diagrams”. Indeed, nonparametric SEM’s are blessed with unequal transparency to assure that each and every assumption is visible and passes the scrutiny of scientific judgment.

While it is true that SEMs have the capacity to make bolder assumptions, some not discernible from experiments, (e.g., no confounding between mediator and outcome) this does not mean that investigators, acting properly, would make such assumptions when they stand contrary to scientific judgment, nor does it mean that investigators are under weaker protection from the ramifications of unwarranted assumptions. Today we know precisely which of SEM’s claims are discernible from experiments (i.e., reducible to do(x) expressions) and which are not (see Shpitser and Pearl, 2008)

I therefore take issue with Tyler’s statement: “SEMs themselves tend to make much stronger assumptions than these other techniques” (from his abstract) when applied to nonparametric analysis. SEMs do not make assumptions, nor do they “tend to make assumptions”; investigators do. I am inclined to believe that Tyler’s critics were aims at a specific application of SEM rather than SEM as a methodology.

Purging SEM from epidemiology would amount to purging counterfactuals from epidemiology — the latter draws its legitimacy from the former.

I also reject occasional calls to replace SEM and Causal Diagrams with weaker types of graphical models which presumably make weaker assumptions. No matter how we label alternative models (e.g., interventional graphs, agnostic graphs, causal Bayesian networks, FFRCISTG models, influence diagrams, etc.), they all must rest on judgmental assumptions and people think science (read SEM), not experiments. In other words, when an investigators asks him/herself whether an arrow from X to Y is warranted, the investigator does not ask whether an intervention on X would change the probability of Y (read: P(y|do(x)) = P(y)) but whether the function f in the mechanism y=f(x, u) depends on x for some u. Claims that the stronger assumptions made by SEMs (compared with interventional graphs) may have unintended consequences are supported by a few contrived cases where people can craft a nontrivial f(x,u) despite the equality P(y|do(x)) = P(y)). (See an example in Causality page 24.)

For a formal distinction between SEM and interventional graphs (also known as “Causal Bayes networks”, see Causality pages 23-24, 33-36). For more philosophical discussions defending counterfactuals and SEM against false alarms see:

I hope this help clarify the issue.

May 31, 2010

An Open Letter from Judea Pearl to Nancy Cartwright concerning “Causal Pluralism”

Filed under: Discussion,Nancy Cartwright,Opinion,structural equations — moderator @ 1:40 pm

Dear Nancy,

This letter concerns the issue of “causal plurality” which came up in my review of your book “Hunting Causes and Using Them” (Cambridge 2007) and in your recent reply to my review, both in recent issue of Economics and Philosophy (26:69-77, 2010).

My review:

Cartwright Reply:

I have difficulties understanding causal pluralism because I am a devout mono-theist by nature, especially when it comes to causation and, although I recognize that causes come in various shades, including total, direct, and indirect causes, necessary and sufficient causes, actual and generic causes, I have seen them all defined, analyzed and understood within a single formal framework of Structural Causal Models (SCM) as described in Causality (Chapter 7).

So, here I am, a mono-theist claiming that every query related to cause-effect relations can be formulated and answered in the SCM framework, and here you are, a pluralist, claiming exactly the opposite. Quoting:

“There are a variety of different kinds of causal systems; methods for discovering causes differ across different kinds of systems as do the inferences that can be made from causal knowledge once discovered. As to causal models, these must have different forms depending on what they are to be used for and on what kinds of systems are under study.

If causal pluralism is right, Pearl’s demand to tell economists how they ought to think about causation is misplaced; and his own are not the methods to use. They work for special kinds of problems and for special kinds of systems – those whose causal laws can be represented as Pearl represents them. HC&UT argues these are not the only kinds there are, nor uncontroversially the most typical.

I am very interested in finding out if, by committing to SCM I have not overlooked important problem areas that are not captured in SCM. But for this we need an example; i.e., an example of ONE problem that cannot be formulated and answered in SCM.

The trouble I have with the examples sited in your reply is that they are based on other examples and concepts that are scattered on many pages in your book and, thus, makes it hard to follow. Can we perhaps see one such example, hopefully with no more than 10 variables, described in the following format:

Example: An agent is facing a decision or a question.

Given: The agent assumes the following about the world: 1. 2. 3. ….
The agent has data about …., taken under the following conditions.
Needed: The agent wishes to find out whether…..

Why use this dry format, you may ask, when your book is full with dozens of imaginative examples, from physics to econometrics? Because if you succeed in showing ONE example in this concise format you will convert one heathen to pluralism, and this heathen will be grateful to you for the rest of his spiritual life.

And if he is converted, he will try and help you convert others (I promise) and, then, who knows? life on this God given earth would become so much more enlightened.

And, as Aristotle used to say (or should have) May clarity shine on causality land.


Judea Pearl

August 6, 2007

SEM and Dichotomous Variables

Filed under: structural equations — moderator @ 5:22 am

David Liu writes:

In Statistics and Causal Inference: A Review (Pearl 2003), it was said 'the bulk of SEM methodology was developed for linear analysis, and until recently, no comparable methodology has been devised to extend its capabilities to models involving dichotomous variables or nonlinear dependencies.'  Is it true by now?

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."

September 15, 2000

Reciprocal links in structural equations

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

From Dennis Lindley 

Equations (1.42) and (1.43) and the general issue of description by equations, still perplex me. It is incoherent to state both p(x|y) and p(y|x). (Try it with x and y binary, when these statements describe 4 values, whereas we know only 3 are needed for the joint distribution of x and y.) There are special cases, as with normal, linear regression, where the coherence is avoided. Generally I do not see how there can be two links between x and y.

April 24, 2000

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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