Causal Analysis in Theory and Practice

Stan Mulaik called my attention to a recent article by Grice, Shlimgen and Barrett (GSB) (linked here http://psychology.okstate.edu/faculty/jgrice/personalitylab/OOMMedForm_2011A.pdf ) which is highly critical of structural equation modeling (SEM) in general, and of the philosophy and tools that I presented in “The Causal Foundation of SEM” (Pearl 2011) ( http://ftp.cs.ucla.edu/pub/stat_ser/r370.pdf.)  In particular, GSB disagree with the conclusions of the Mediation Formula — a tool for assessing what portion of a given effect is mediated through a specific pathway.

I responded with a detailed account of the disagreements between us (copied below), which can be summarized as follows:

Summary

1. The “OOM” analysis used by GSB is based strictly on frequency tables (or “multi-grams”) and, as such, cannot assess cause-effect relations without committing to some causal assumptions. Those assumptions are missing from GSB account, possibly due to their rejection of SEM.

2. I define precisely what is meant by “the extent to which the effect of X on Y is mediated by a third variable, say Z,” and demonstrate both, why such questions are important in decision making and model building and why they cannot be captured by observation-oriented methods such as OOM.

3. Using the same data and a slightly different design, I challenge GSB to answer a simple cause-effect question with their method (OOM), or with any method that dismisses SEM or causal algebra as unnecessary.

4. I further challenge GSB to present us with ONE RESEARCH QUESTION that they can answer and that is not answered swiftly, formally and transparently by the SEM methodology presented in Pearl (2011). (starting of course with the same assumptions and same data.)

5. I explain what gives me the assurance that no such research question will ever be found, and why even the late David Friedman, whom GSB lionize for his staunch critics of SEM, has converted to SEM thinking at the end of his life.

6. I alert GSB to two systematic omissions from their writings and posted arguments, without which no comparison can be made to other methodologies:
(a) A clear statement of the research question that the investigator attempts to answer, and
(b) A clear statement of the assumptions that the investigator is willing to make about reality.

Click here for the full response.

=======Judea

Dear colleague in causality research,

At long last, I am pleased to bring to your attention the birth of a new journal, the Journal of Causal Inference — JCI, dedicated to building a rigorous cross-disciplinary dialogue in causality.

The first issue is planned for Fall 2011 and the website is now open for submissions.
http://www.bepress.com/jci

As most readers of this forum know, existing discipline-specific journals tend to bury causal analysis in the language and methods of traditional statistical methodologies, creating the inaccurate impression that causal questions can be handled by routine methods of regression, simultaneous equations or logical implications, and glossing over the special ingredients needed for causal analysis. In contrast, Journal of Causal Inference highlights both the uniqueness and interdisciplinary nature of causal research. The journal serves as a forum for the growing causal inference community to develop a shared language and to study the commonalities and distinct strengths of their various disciplines’ methods for causal analysis.

You are invited to submit your latest results, and to bring JCI to the attention of students and colleagues who might be seeking a forum for discussing their latest ideas, results and, yes, breakthroughs!

Submissions
Journal of Causal Inference encourages submission of applied and theoretical work from across the range of rigorous causal paradigms.

In addition to significant original research articles, Journal of Causal Inference also welcomes:
1)      Submissions that synthesize and assess cross-disciplinary methodological research
2)      Submissions that discuss the history of the causal inference field and its philosophical underpinnings
3)      Unsolicited short communications on topics that aim to highlight areas of emerging consensus and ongoing controversy, or to bring unorthodox perspectives to open questions
4)      Responses to published articles in causality

To read more about JCI, including its aims and scope and editorial board membership, please visit our website:
http://www.bepress.com/jci
Papers can be submitted electronically at:
http://www.bepress.com/cgi/submit.cgi?context=jci

The first issue is planned for Fall 2011.

Have a productive Fall quarter,
See you on JCI
=======Judea

Dear colleague in causality research,

This is an End-of-Winter Greetings from the UCLA Causality blog, welcoming you back to a spring-time discussion in causality-related issues.

This message contains
1. Topics under discussion
2. New results
3. Information on courses, lectures, and conferences.

1. Discussions inviting comments

1.1. “Principal Stratification – A goal or a tool?”
http://ftp.cs.ucla.edu/pub/stat_ser/r382.pdf
Posted for discussion by the International Journal of Biostatistics (IJB), this paper questions whether studies based on Principal Stratification target quantities that researchers truly care about.

If you have comments, ideas or objections, you are invited to communicate them to the IJB’s  Editor, “Nicholas P. Jewell” <mm-11332-3261687@bepress.com> or/and, if you wish, cross-post them on this blog.

1.2. “Comments and Controversies: Graphical models, potential outcomes and causal inference: Comment on Lindquist and Sobel”
http://ftp.cs.ucla.edu/pub/stat_ser/r380.pdf

This note comments on a paper published in NeuroImage which argues (yes, again) that the potential outcome model is somehow superior, more rigorous or more principled than the structural models used in fMRI research. To further illuminate the logic of such claims I have added a section (4.4.2) in this paper:
http://ftp.cs.ucla.edu/pub/stat_ser/r370.pdf
which demonstrates how potential outcomes can be generated, on demand, from a simple structural model, and no one can tell where they came from. Enjoy.

1.3. “The Causal Mediation Formula – A practitioner guide to the assessment of causal pathways”
http://ftp.cs.ucla.edu/pub/stat_ser/r379.pdf

This paper present mediation analysis to researchers in the tradition of Baron and Keney (1986), and shows through examples how “the percentage explained by mediation” and “the percentage owed to mediation” are estimated in nonlinear models with both continuous and categorical variables.

1.4. Simpson’s Paradox
Sander Greenland brought to my attention a recent paper in Synthese (Sept. 28, 2010) claiming that Simpson’s paradox is NOT rooted in causal, but in some other kind of illusion. I remain convinced of the former, and have accordingly modified the Simpson Paradox entry in Wikipedia to reinforce the causal illusion theory. You might wish to add your take on the subject.

1.5. “The ETT Paradox  (or, the curse of free will)”
This paradox would be appreciated by those who are fascinated, like me, by our ability to determine, from data alone, if one would have been better off acting differently than one actually did. This can lead to a cycle of inevitable regret, and provokes some naughty thoughts.
http://ftp.cs.ucla.edu/pub/stat_ser/r375.pdf

2. New Results

2.1. A newly posted paper, “Controlling Selection Bias in Causal Inference” http://ftp.cs.ucla.edu/pub/stat_ser/r381.pdf gives graphical and algebraic conditions for the removal of selection bias and the recovery of covariate-specific effect measures.

2.2. A new section (Section 5) in http://ftp.cs.ucla.edu/pub/stat_ser/r372.pdf generalizes the concept of transportability from experimental to observational studies,and shows how one can avoid re-learning things from scratch when moving to a new population, new domain, or a new environment.

2.3. After months of struggling with the literature of “surrogate endpoints” we feel that we now have a fairly satisfactory theory of surrogacy. It is based on the idea that a surrogate should serve not merely as a good predictor of outcomes, but also as ROBUST predictor of effects in the face of changing external conditions.  See section 6 in http://ftp.cs.ucla.edu/pub/stat_ser/r372.pdf

3. Courses, Lectures and Conferences

3.1. Causal Inference Course
Thomas Richardson and Michael Hudgens are once again teaching Causal Inference June 13-15, 2011 in the Summer Institute here at U Washington. They have funds to support tuition waivers and some travel for students and postdocs. The website is http://depts.washington.edu/sismid/

3.2. 2011 Atlantic Causal Conference
The 2011 Atlantic Causal Conference will take place at the University of Michigan School of Public Health in Ann Arbor, Michigan, Thursday May 19th and Friday May 20th. See
http://www.sph.umich.edu/biostat/2011acic/index.html for
Contact: Mike Elliott at mrelliot@umich.edu or Ben Hansen at ben.hansen@umich.edu

3.3. Errata for Causality (2010)
FYI, Cambridge University Press has come up with a new printing of my book Causality, which corrects a few errors in the 2009 edition. Please advise students to insist on a copy saying “reprinted 2010”.
If you have an older copy, you can find the corrections marked in red here:
http://bayes.cs.ucla.edu/BOOK-09/errata_scanned_pages7-28-10.pdf

3.4. Lecture Slides available
Slides of my lecture on “What’s New in Causal Inference” can be viewed on my home page, second line from top.
http://bayes.cs.ucla.edu/jp_home.html
You are welcome to use them in any way you choose. But usage for a good cause is recommended.

Looking forward to your postings, and may clarity prevail.

———Judea Pearl
UCLA

Dear colleague in causality research,

This is a belated End-of-Summer greeting from the UCLA Causality blog, welcoming you back to an open discussion of causality-related issues. Below please find four new postings and three hot topics for discussion.

1.  New postings:

Three new papers and several lecture videos have been posted on our website.

1.1. Pearl and Bareinboim, “Transportability across studies: A formal approach,” October 2010.

http://ftp.cs.ucla.edu/pub/stat_ser/r372.pdf

The paper introduces a formal representation for encoding differences between populations and derives procedures for deciding whether (and how) causal effects in the target environment can be inferred from experimental findings in another.

1.2. J. Pearl, “The Causal Foundations of Structural Equation Modeling,” August 2010.

http://ftp.cs.ucla.edu/pub/stat_ser/r370.pdf

The paper summarizes how traditional SEM methods can be enriched by modern advances in causal and counterfactual inference.

Click here to the full post.

As always, we welcome your views on this topic. To continue the discussion, please use the comment link below to add your thoughts. You can also suggest a new topic of discussion using our submission form by clicking here.

Dear friends in causality,

Below are a few items you might find to be of some interest and  possibly some challenge.

1.
A new book containing a collection of recent articles on causation, some tutorial in nature, is now available from College Publications (2010.) Title: Heuristics, Probability and Causality, Editors: R. Dechter, H. Geffner and J. Halpern.

For table of contents, preface and more information please click on:
http://bayes.cs.ucla.edu/TRIBUTE/pearl-tribute2010.htm
As you can see, I have had a natural indirect effect on the cover design, but zero controlled direct effect.

2.
A symposium on causality and related topics by some of the contributors to “Heuristics, Probabilities and Causality” was held at UCLA on March 12. Videos of lectures, by: C. Hitchcock, S. Greenland, T. Richardson, J. Robins, R. Scheines, J. Tian, Y. Shoham and J. Pearl, can be viewed here:
http://bayes.cs.ucla.edu/TRIBUTE/tribute-videos.htm
Videos of additional lectures will be posted in the near future.

3.
Recent entries on our Causality-Blog include:

3.1.
An open letter from Judea Pearl to Nancy Cartwright concerning “Causal Pluralism”, a topic central to a discussion of her book “Hunting Causes” which appeared recently in Economics and Philosophy 26:69-77. (Posted May 31, 2010), and
3.2.
A lively discussion by T. Richardson, J. Robins and J. Pearl on the structure of the causal hierarchy and the scientific roll of untestable counterfactual assumptions. (Posted May 3 and May 15, 2010)

Both are posted on http://causality.cs.ucla.edu/blog/.

4.
A recent posting on my web-page is a paper titled: “The Mediation Formula: A guide to the assessment of causal pathways in non-linear models” which explains why traditional methods of mediation analysis yield distorted results when applied to discrete data, even when correct parametric models are assumed and all parameters are known precisely. The Mediation Formula circumvents these difficulties.
http://ftp.cs.ucla.edu/pub/stat_ser/r363.pdf

5.
Another posting of potential interest is Technical Report R-364, by T. Kyono (Master Thesis), titled: “Commentator: A Front-End User-Interface Module for Graphical and Structural Equation Modeling”. It take a DAG as input and prints (1): all identifiable direct effects, (2) all identifiable causal effects, (3) all (minimal) sets of admissible covariates, (4) all instrumental variables, and (5) (almost) all testable implications of a model. The source code is available upon request. http://ftp.cs.ucla.edu/pub/stat_ser/r364.pdf

6.
Finally, I have received inquiries regarding a slide that I used at NYU, in which an instrumental variable poses as an innocent confounder and, upon adjustment, amplifies, rather than reduces confounding bias. The moral of the story was (and is) that “outcome assignment” is safer to model than “treatment assignment”. The pertinent paper is R-356, or http://ftp.cs.ucla.edu/pub/stat_ser/r356.pdf

7.
As always, your thoughts are welcome and will surely be put into some good cause when conveyed to other blog readers.

Best,
=======Judea Pearl
UCLA

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:
http://journals.cambridge.org/action/displayFulltext?type=1&fid=7402268&jid=&volumeId=&issueId=&aid=7402260

Cartwright Reply:
http://journals.cambridge.org/action/displayFulltext?type=1&fid=7402292&jid=&volumeId=&issueId=&aid=7402284

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.

Sincerely,

Judea Pearl

Judea Pearl writes:

Thomas’ latest posting triggered my curiosity to re-examine the causal hierarchy. Originally (see Causality chapter 1), I have characterized causal sentences into three categories:

1. probabilistic (i.e., non-causal, or what we can estimate from observational studies)
2. experimental (i.e., do-expressions, or what we can estimate from controlled, randomized experiments)
3. counterfactuals (i.e., subscripted sentences, or everything that can be computed from a fully specified structural model that is, a collection of functions with probabilities on the exogenous variables)

Click here for the full post.

—

As always, we welcome your views on this topic. To continue the discussion, please use the comment link below to add your thoughts. You can also suggest a new topic of discussion using our submission form by clicking here.

Opening remarks

A few days ago, Dan Sharfstein posed a question regarding the “well-defineness” of “direct effects” in situations where the mediating variables cannot be manipulated. Dan’s question triggered a private email discussion that has culminated in a posting by Thomas Richardson and Jamie Robins (below) followed by Judea Pearl’s reply.

We urge more people to join this important discussion.

Thomas Richardson and James Robins’ discussion:

Hello,

There has recently been some discussion of mediation and direct effects.

There are at least two issues here:

(1) Which counterfactuals are well defined.

(2) Even when counterfactuals are well defined, should we include assumptions that identify effects (ie the natural direct effect) that could never be confirmed even in principle by a Randomized Controlled Trial (RCT).

As to (1) it is clear to most that all counterfactuals are vague to a certain extent and can be made more precise by carefully describing the (quite possibly only hypothetical) intervention you want the counterfactual to represent. For this reason,  whether you take manipulation or causality as ontologically primary, we need to relate causation to manipulation to clarify and make more precise which counterfactual world we are considering.

On (2) we have just finished a long paper on the issue, fleshing out considerably an argument I (Jamie) made at the American Statistical Association (in 2005) discussing a talk by Judea on natural (pure and total) direct effects.

“Alternative Graphical Causal Models and the Identification of Direct Effects”

It is available at
http://www.csss.washington.edu/Papers/wp100.pdf.

Here is a brief summary:

Click here for the full post.

Best wishes,

Jamie Robins  and Thomas Richardson

Judea Pearl’s reply:

1.
As to the which counterfactuals are “well defined”, my position is that counterfactuals attain their “definition” from the laws of physics and, therefore, they are “well defined” before one even contemplates any specific intervention. Newton concluded that tides are DUE to lunar attraction without thinking about manipulating the moon’s position; he merely envisioned how water would react to gravitaional force in general.

In fact, counterfactuals (e.g., f=ma) earn their usefulness precisely because they are not tide to specific manipulation, but can serve a vast variety of future inteventions, whose details we do not know in advance; it is the duty of the intervenor to make precise how each anticipated manipulation fits into our store of counterfactual knowledge, also known as “scientific theories”.

2.
Regarding identifiability of mediation, I have two comments to make; ‘ one related to your Minimal Causal Models (MCM) and one related to the role of structural equations models (SEM) as the logical basis of counterfactual analysis.al basis of counterfactual analysis.

Click here for Judea’s reply.

M. Elizabeth Halloran from University of Washington writes:

A 2.5 day course on Causal Inference, with particular applications in infectious diseases,  including causal inference with interference,  is offered June 14-16, 2010, in Seattle at the University of Washington. The course is taught by Thomas Richardson and Michael Hudgens. It is Module 2 of the Summer Institute in Statistics and Modeling in Infectious Diseases.

We have funds to support students and postdocs for tuition waivers and travel. Please apply if possible by April 15, though we would likely consider applications after that.

More information and registration is available at http://depts.washington.edu/sismid

Dear blogger,

A few causality-related papers have recently been posted on my website:

• R-357: J. Pearl, “On Measurement Bias in Causal Inference,” http://ftp.cs.ucla.edu/pub/stat_ser/r357.pdf
• R-358: J. Pearl, “On the Consistency Rule in Causal Inference: An Axiom, Definition, Assumption, or a Theorem?,” http://ftp.cs.ucla.edu/pub/stat_ser/r358.pdf
• R-359: J. Pearl, “Physical and Metaphysical Counterfactuals,” http://ftp.cs.ucla.edu/pub/stat_ser/r359.pdf
• R-360: J. Pearl, “If Oswald Hadn’t Used Counterfactuals, My Robot Would Have,” http://ftp.cs.ucla.edu/pub/stat_ser/r360.pdf
• R-361: S. Greenland and J. Pearl, “Causal Diagrams,” http://ftp.cs.ucla.edu/pub/stat_ser/r361.pdf

As usual, comments, reservations and objections are most welcome, and can be posted on this forum.

And may that every brilliant thought be put to some good cause.