Causal Analysis in Theory and Practice

The following problem was brought to our attention by Randy Verbrugge:

Randy writes:

Suppose the DAG is:
top row: unobserved U, with dotted arrows to X and Y.
bottom row: X –> W –> Y.

We can identify the causal effect of X on Y via the decomposition in the theorem. As I understand it, if we assume linearity, we regress Y on W and X and take the coefficient on W, call it b; then we regress W on X and take the coefficient, call it a; the causal effect is ab*x.

However, I wonder if we are (unavoidably) in a situation where X is a near-instrument for W, so that we will have a ton of bias.

Thanks for your help!

Randy

Judea replies:

Randy,
The danger of conditioning on an instrument or a near instrument only exists when we have some residual, uncontrolled bias. In our case, the W—>Y relation is completely deconfounded by conditioning on X, therefore, no bias-amplification can take place. The danger will resurface if there was a bi-directed arc between W and Y.

An important nuance: The capacity of an instrument to introduce bias where none existed (demonstrated in my paper) only pertains to situations where the zero bias is unstable, i.e., created by incidental cancellations. For example, if we had a bi-directed arc between W and Y that happened to cancel the bias created by the confounding path W<---X<--U-->Y, then the crude (regressional) estimate of the effect of W on Y would be unstably unbiased, and conditioning on W would introduce bias.

In general: The bias amplification phenomenon never conflicts with the rules of do-calculus.

Thanks for raising this question.

======Judea

Dear colleagues in causality research,

This is a Winter Greeting from the UCLA Causality blog, welcoming you back to a discussion on causality-related issues.

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

1. Topics under Discussion

1.1 Principal Stratification – A goal or a tool?’
http://ftp.cs.ucla.edu/pub/stat_ser/r382.pdf
http://escholarship.org/uc/item/4xj9d380#page-3

Was posted for discussion in the International Journal of Biostatistics (IJB) in March 2011, and has elicited response from eight discussants on whether studies based on Principal Stratification estimate quantities that researchers care about.

I am about to wrap up the discussion with a summary-rejoinder, so, if you have comments or insights that where not brought up, feel free to communicate them to the IJB’s Editor, “Nicholas P. Jewell” or/and, if you wish, cross-post them on this blog.

1.2 Comments and Controversies:
We are being warned again that graphical models can produce “incorrect” causal inferences. The warning comes again from Lindquist and Sobel (LS), entitled “Cloak and DAG”: http://www.sciencedirect.com/science/article/pii/S1053811911013085

A response to L&S is posted on our causality blog, proving them wrong, and questioning the wisdom of asking researchers to translate assumptions from a language where they stand out vividly and meaningfully into an Arrow-Phobic language where they can no longer be recognized, let alone justified. We have all the reason to suspect that L&S will come back.

1.3 The Match-Maker Paradox
An apparent paradox concerning the representation of matching designs in DAGs was posted by Pablo Lardelli and resolved by noting that matching involves unit-to-unit interaction and results in “persistent-unfaithfulness.”

1.4 An On-going Causal-Inference Discussions on SEMNET (Structural Equation Modeling Discussion Group
In the past four months I have spent time discussing modern approaches to causal inference with SEM researchers who, by and large, are still practicing the traditional methods associated with the acronym “SEM”. The discussions are fully documented and archived on http://bama.ua.edu/archives/semnet.html

Topics include:
a. the causal/statistical distinction.
b. the structural-regressional distinction
c. The residual/disturbance distinction
d. The assumptions conveyed by each structural equation.
e. The counterfactual reading of structural equations
f. What the Mediation Formula tells us about mediation and policy questions.
g. Mediators and Moderators.
h. d-separation, equivalent models and the testable implications of structural models
i. The logic of SEM as an inference engine.

Additionally, a weekly session is being conducted by Les Hayduk, going page by page over the R-370 chapter (http://ftp.cs.ucla.edu/pub/stat_ser/r370.pdf) and explaining it to novices in the field. It answers, I hope, all questions that rank and file researchers find perplexing when introduced to causal analysis.

1.5 Draft Chapter on Causality and SEM
Ken Bollen and I finished a draft chapter titled “Eight Myths about Causality and Structural Equation Models.” It covers the history of misconceptions about SEM, including recent assaults by the Arrow-Phobic Society.
see http://ftp.cs.ucla.edu/pub/stat_ser/r393.pdf

1.6 A Survey Paper on Adjustment
Greenland, S., and Pearl J., “Adjustments and their Consequences — Collapsibility Analysis using Graphical Models” http://ftp.cs.ucla.edu/pub/stat_ser/r369.pdf

The paper teaches researchers how to glance at a graph and determine when/if an adjustment for one variable modifies the relationship between two other variables. It is a simple exercise for graphical modellers but extremely difficult one for economists and other researchers who ask such questions routinely and have no graphs for guidance.

1.7 A New Introduction to Causal Calculus
An excellent introduction to causal diagrams and do-calculus was posted recently by bloggist-author Michael Nielsen, titled “If correlation doesn’t imply causation, then what does?” It can be accessed here: http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/

My response, together with thoughts on the psychology of Simpson’s Paradox is below http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-correlation-causation-and-the-psychology-of-simpsons-paradox/

1.8 Haavelmo and the Emergence of Causal Calculus
http://ftp.cs.ucla.edu/pub/stat_ser/r391.pdf

Presented at Haavelmo Centennial Symposium, in Oslo, last December, the paper describes the cultural barriers that Haavelmo’s ideas have had to overcome in the past six decades and points to the fact that modern economists are still unaware of the benefits that Haavelmo’s ideas bestow upon them.

2. New Results in Causal Inference

2.1 Interpretable Conditions for Identifying Natural Direct Effects.
http://ftp.cs.ucla.edu/pub/stat_ser/r389.pdf

The paper lists four conditions that are sufficient for the identification of natural direct and indirect effects. The conditions do not invoke “ignorability” jargon thus permitting more informed judgment of the plausibility of the assumptions. It also shows that conditions usually cited in the literature are overly restrictive, and can be relaxed without compromising identification.

2.2 Some Thoughts on Transfer Learning, with Applications to Meta-analysis and Data-sharing Estimation
http://ftp.cs.ucla.edu/pub/stat_ser/r387.pdf

Summary: How to combine data from multiple and diverse environments so as to take full advantages of that which they share in common.

2.3 Understanding Bias Amplification
http://ftp.cs.ucla.edu/pub/stat_ser/r386.pdf

This note sheds a new light on the phenomenon of “bias amplification” by considering the cumulative effect of conditioning on multiple “near instruments,” and shows that bias amplification may build up at a faster rate than bias reduction.

2.4 Local Characterizations of Causal Bayesian Networks
by Bareinboim, Brito and Pearl http://ftp.cs.ucla.edu/pub/stat_ser/r384.pdf

The standard definition of Causal Bayesian Networks (CBN) requires that every interventional distribution be decomposable into a truncated product, dictated by the graph. This paper replaces this “global” definition with three alternative ones, each invoking “local” aspects of conditioning and intervening.

3. Journals, Courses, Lectures and Conferences
3.1 Tutorial: Causal Inference in Statistics

I will be giving a tutorial (IOL) on causal inference at the upcoming JSM 2012 conference in San Diego California, July 29th, 4-5:50 PM. If any of your students or colleagues wishes to attend, the abstract and further details can be found on http://www.amstat.org/meetings/jsm/2012/onlineprogram/AbstractDetails.cfm?abstractid=304318

3.2 The Journal of Causal Inference
As reported in the last blog email, the Journal of Causal Inference (JCI) was launched on September 2011 and the website is open for submissions. http://www.bepress.com/jci

The first issue is planned for Summer of 2012 and, needless to state, 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 presenting their latest ideas, results and, yes, breakthroughs!

The Journal of Causal Inference will highlight both the uniqueness and interdisciplinary nature of causal research. and will publish both theoretical and applied research including survey and discussion papers.

3.3 Spring Workshop Graphical Causal Models
Friday 3/30/2012
Northwestern University, Chicago

This workshop will introduce graphical causal models, show how to simulate data from, and estimate such models in Tetrad, explain model search, and more….
Lecturers: Richard Scheines and Joseph Ramsey CMU
For details see chicagochapterasa@gmail.com
http://community.amstat.org/Chicago_Chapter/Calendar/20112012/NewItem6/

3.4 Conference: EVIDENCE AND CAUSALITY IN THE SCIENCE ECitS 2012
Centre for Reasoning, University of Kent, 5-7 September 2012
Organizers: Phyllis Illari and Federica Russo
http://www.kent.ac.uk/secl/philosophy/jw/2012/ecits/

3.5 New Software tool for Causal Inference
DAGitty: A Graphical Tool for Analyzing Causal Diagrams by Textor, Johannes; Hardt, Juliane; Kn|ppel, Sven
Epidemiology: September 2011 – Volume 22 – Issue 5 – p 745 doi: 10.1097/EDE.0b013e318225c2be

This paper announces the release of DAGitty, a graphical user interface for drawing and analyzing causal diagrams. DAGitty, offers several improvements over Kyono’s “COMMENTATOR” http://ftp.cs.ucla.edu/pub/stat_ser/r364.pdf among them efficient listing of all minimal sufficient adjustment sets. It is available under an open-source license obtained at www.dagitty.net and http://www.dagitty.net/manual.pdf

Best wishes,

=======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.

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.

From Sampsa Hautaniemi, NIH:

I am at the halfway of your book Causality, which I think to be excellent and instructive. What I am writing to you is that I browsed to homepage of Dr. Lotfi Zadeh and found out that he has a Word document whose subject is 'CAUSALITY IS UNDEFINABLE'. The page is http://www.cs.berkeley.edu/~nikraves/zadeh/Zadeh2.doc. I know you have answered many times reports like that, so if there is already discussion going on of this subject I would appreciate the URL/name of the journal as I am really interested in the subject.

From Professor Nozer Singpurwalla, from The George Washington University:

My basic point is that since causality has not been defined, the causal calculus is a technology which could use a foundation. However, the calculus does give useful insights and is thus valuable. Finally, according to my understanding of the causal calculus, I am inclined to state that the calculus of probability is the calculus of causality, notwithstanding Dennis' [Lindley] concerns about Suppes probabilistic causality.

Apart from the innate symmetricity of structural equation systems, the very definition for the conditional probability as well as Bayes's law of inverse probability unambiguously suggest the reversibility of cause-effect relationships. …
“A is a cause of B only when B can cause A.'' Amen.
(Quoted from Mr. Asha review of Causality, amazon.com, August 29, 2000)