Causal Analysis in Theory and Practice

September 15, 2016

Summer-end Greeting from the UCLA Causality Blog

Filed under: Uncategorized — bryantc @ 4:39 am

Dear friends in causality research,
—————————————
This greeting from UCLA Causality blog contains news and discussion on the following topics:

1. Reflections on 2016 JSM meeting.
2. The question of equivalent representations.
3. Simpson’s Paradox (Comments on four recent papers)
4. News concerning Causal Inference Primer
5. New books, blogs and other frills.

1. Reflections on JSM-2016
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For those who missed the JSM 2016 meeting, my tutorial slides can be viewed here: http://bayes.cs.ucla.edu/jsm-august2016.ppt

As you can see, I argue that current progress in causal inference should be viewed as a major paradigm shift in the history of statistics and, accordingly, nuances and disagreements are merely linguistic realignments within a unified framework. To support this view, I chose for discussion six specific achievements (called GEMS) that should make anyone connected with causal analysis proud, empowered, and mighty motivated.

The six gems are:
1. Policy Evaluation (Estimating “Treatment Effects”)
2. Attribution Analysis (Causes of Effects)
3. Mediation Analysis (Estimating Direct and Indirect Effects)
4. Generalizability (Establishing External Validity)
5. Coping with Selection Bias
6. Recovering from Missing Data

I hope you enjoy the slides and appreciate the gems.

2. The question of equivalent representations
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One challenging question that came up from the audience at JSM concerned the unification of the graphical and potential-outcome frameworks. “How can two logically equivalent representations be so different in actual use?”. I elaborate on this question in a separate post titled “Logically equivalent yet way too different.” http://causality.cs.ucla.edu/blog/index.php/2016/09/12/

3. Simpson’s Paradox: The riddle that would not die
(Comments on four recent papers)
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If you search Google for “Simpson’s paradox”, as I did yesterday, you would get 111,000 results, more than any other statistical paradox that I could name. What elevates this innocent reversal of associations to “paradoxical” status, and why it has captured the fascination of statisticians, mathematicians and philosophers for over a century are questions that we discussed at length on this (and other) blogs. The reason I am back to this topic is the publication of four recent papers that give us a panoramic view at how the understanding of causal reasoning has progressed in communities that do not usually participate in our discussions.  http://causality.cs.ucla.edu/blog/index.php/2016/08/24/

4. News concerning Causal Inference – A Primer
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We are grateful to Jim Grace for his in-depth review on Amazon: https://www.amazon.com/gp/customer-reviews/R2T3OB4WRGRRC0/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=1119186846

For those of you awaiting the solutions to the study questions in the Primer, http://bayes.cs.ucla.edu/PRIMER/ I am informed that the Solution Manual is now available (to instructors) from Wiley. To obtain a copy, see page 2 of: http://bayes.cs.ucla.edu/PRIMER/CIS-Manual-PUBLIC.pdf However, rumor has it that a quicker way to get it is through your local Wiley representative, at https://professor.wiley.com/CGI-BIN/LANSAWEB?PROCFUN+PROF1+PRFFN15

If you encounter difficulties, please contact us at causality.ucla@gmail.com and we will try to help. Readers tell me that the solutions are more enlightening than the text. I am not surprised, there is nothing more invigorating than seeing a non-trivial problem solved from A to Z.

5. New books, blogs and other frills
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5.1
We are informed that a new book by Joseph Halpern, titled “Actual Causality”, is available now from MIT Press. (https://www.amazon.com/Actual-Causality-Press-Joseph-Halpern/dp/0262035022). Readers familiar with Halpern’s fundamental contributions to causal reasoning will not be surprised to find here a fresh and comprehensive solution to the age-old problem of actual causality. Not to be missed.

5.2
Adam Kelleher writes about an interesting math-club and causal-minded blog that he is orchestrating. See his post, http://causality.cs.ucla.edu/blog/index.php/2016/09/11/

5.3
Glenn Shafer just published a review paper: “A Mathematical Theory of Evidence turn 40” celebrating the 40th anniversary of the publication of his 1976 book “A Mathematical Theory of Evidence” http://www.glennshafer.com/assets/downloads/MathTheoryofEvidence-turns-40.pdf I have enjoyed reading this article for nostalgic reasons, reminding me of the stormy days in the 1980’s, when everyone was arguing for another calculus of evidential reasoning. My last contribution to that storm, just before sailing off to causality land, was this paper: http://ftp.cs.ucla.edu/pub/stat_ser/r136.pdf. Section 10 of Shafer’s article deals with his 1996 book “The Art of Causal Conjecture” My thought: Now, that the causal inference field has matured, perhaps it is time to take another look at the way Shafer views causation.

Wishing you a super productive Fall season.

J. Pearl

September 12, 2016

Logically equivalent yet way too different

Filed under: Uncategorized — bryantc @ 2:50 am

Contributor: Judea Pearl

In comparing the tradeoffs between the structural and potential outcome frameworks, I often state that the two are logically equivalent yet poles apart in terms of transparency and computational efficiency. (See Slide #34 of the JSM tutorial). Indeed, anyone who examines how the two frameworks solve a specific problem from begining to end (See, e.g., Slides #35-36 ) would find the differences astonishing.

The question naturally arises: How can two equivalent frameworks differ so substantially in actual use.

The answer is that epistemic equivalence does not mean representational equivalence. Two representations of the same information may highlight different aspects of the problem and thus differ substantially in how easy it is to solve a given problem.  This is a recurrent theme in complexity analysis, but is not generally appreciated outside computer science. We saw it in our discussions with Guido Imbens who could not accept the fact that the use of graphical models is a mathematical necessity not just a matter of taste. (http://causality.cs.ucla.edu/blog/index.php/2014/10/27/are-economists-smarter-than-epidemiologists-comments-on-imbenss-recent-paper/)

The examples usually cited in complexity analysis are combinatorial problems whose solution times depend critically on the initial representation. I hesitated from bringing up these examples, fearing that they will not be compelling to readers on this blog who are more familiar with classical mathematics.

Last week I stumbled upon a very simple example that demonstrates representational differences in no ambiguous terms; I would like to share it with readers.

Consider the age-old problem of finding a solution to an algebraic equation, say
y(x) = x3 + ax2 + bx + c = 0

This is a tough problem for those of us who do not remember Tartalia’s solution of the cubic.  (It can be made much tougher once we go to quintic equation.)

But there are many syntactic ways of representing the same function y(x) . Here is one equivalent representation:
y(x) = x(x2+ax) + b(x+c/b) = 0
and here is another:
y(x) = (x-x1)(x-x2)(x-x3) = 0,
where x1, x2, and x3 are some functions of a, b, c.

The last representation permits an immediate solution, which is:
x=x1, x=x2, x=x3.

The example may appear trivial, and some may even call it cheating, saying that finding x1, x2, and x3 is as hard as solving the original problem. This is true, but the purpose of the example was not to produce an easy solution to the cubic. The purpose was to demonstrate that different syntactic ways of representing the same information (i.e., the same polynomial) may lead to substantial differences in the complexity of computing an answer to a query (i.e., find a root).

A preferred representation is one that makes certain desirable aspects of the problem explicit, thus facilitating a speedy solution. Complexity theory is full of such examples.

Note that the complexity is query-dependent. Had our goal been to find a value x that makes the polynomial y(x) equal 4, not zero, the representation above y(x) = (x-x1)(x-x2)(x-x3) would offer no help at all. For this query, the representation
y(x) = (x-z1)(x-z2)(x-z3) + 4  
would yield an immediate solution
x=z1, x=z2, x=z3,
where z1, z2, and z3 are the roots of another polynomial:
x3 + ax2 + bx + (c-4) = 0

This simple example demonstrates nicely the principle that makes graphical models more efficient than alternative representations of the same causal information, say a set of ignorability assumptions. What makes graphical models efficient is the fact that they make explicit the logical ramifications of the conditional-independencies conveyed by the model. Deriving those ramifications by algebraic or logical means takes substantially more work. (See http://ftp.cs.ucla.edu/pub/stat_ser/r396.pdf for the logic of counterfactual independencies)

A typical example of how nasty such derivations can get is given in Heckman and Pinto’s paper on “Causal Inference after Haavelmo” (Econometric Theory, 2015). Determined to avoid graphs at all cost, Heckman and Pinto derived conditional independence relations directly from Dawid’s axioms and the Markov condition (See https://en.wikipedia.org/wiki/Graphoid.) The results are pages upon pages of derivations of independencies that are displayed explicitly in the graph. http://ftp.cs.ucla.edu/pub/stat_ser/r420.pdf

Of course, this and other difficulties will not dissuade econometricians to use graphs; that would rake a scientific revolution of Kuhnian proportions. (see http://ftp.cs.ucla.edu/pub/stat_ser/r391.pdf) Still, awareness of these complexity issues should give inquisitive students the ammunition to hasten the revolution and equip econometrics with modern tools of causal analysis.

They eventually will.

February 12, 2016

Winter Greeting from the UCLA Causality Blog

Friends in causality research,
This greeting from the UCLA Causality blog contains:

A. An introduction to our newly published book, Causal Inference in Statistics – A Primer, Wiley 2016 (with M. Glymour and N. Jewell)
B. Comments on two other books: (1) R. Klein’s Structural Equation Modeling and (2) L Pereira and A. Saptawijaya’s on Machine Ethics.
C. News, Journals, awards and other frills.

A.
Our publisher (Wiley) has informed us that the book “Causal Inference in Statistics – A Primer” by J. Pearl, M. Glymour and N. Jewell is already available on Kindle, and will be available in print Feb. 26, 2016.
http://www.amazon.com/Causality-A-Primer-Judea-Pearl/dp/1119186846
http://www.amazon.com/Causal-Inference-Statistics-Judea-Pearl-ebook/dp/B01B3P6NJM/ref=mt_kindle?_encoding=UTF8&me=

This book introduces core elements of causal inference into undergraduate and lower-division graduate classes in statistics and data-intensive sciences. The aim is to provide students with the understanding of how data are generated and interpreted at the earliest stage of their statistics education. To that end, the book empowers students with models and tools that answer nontrivial causal questions using vivid examples and simple mathematics. Topics include: causal models, model testing, effects of interventions, mediation and counterfactuals, in both linear and nonparametric systems.

The Table of Contents, Preface and excerpts from the four chapters can be viewed here:
http://bayes.cs.ucla.edu/PRIMER/
A book website providing answers to home-works and interactive computer programs for simulation and analysis (using dagitty)  is currently under construction.

B1
We are in receipt of the fourth edition of Rex Kline’s book “Principles and Practice of Structural Equation Modeling”, http://psychology.concordia.ca/fac/kline/books/nta.pdf

This book is unique in that it treats structural equation models (SEMs) as carriers of causal assumptions and tools for causal inference. Gone are the inhibitions and trepidation that characterize most SEM texts in their treatments of causation.

To the best of my knowledge, Chapter 8 in Kline’s book is the first SEM text to introduce graphical criteria for parameter identification — a long overdue tool
in a field that depends on identifiability for model “fitting”. Overall, the book elevates SEM education to new heights and promises to usher a renaissance for a field that, five decades ago, has pioneered causal analysis in the behavioral sciences.

B2
Much has been written lately on computer ethics, morality, and free will. The new book “Programming Machine Ethics” by Luis Moniz Pereira and Ari Saptawijaya formalizes these concepts in the language of logic programming. See book announcement http://www.springer.com/gp/book/9783319293530. As a novice to the literature on ethics and morality, I was happy to find a comprehensive compilation of the many philosophical works on these topics, articulated in a language that even a layman can comprehend. I was also happy to see the critical role that the logic of counterfactuals plays in moral reasoning. The book is a refreshing reminder that there is more to counterfactual reasoning than “average treatment effects”.

C. News, Journals, awards and other frills.
C1.
Nominations are Invited for the Causality in Statistics Education Award (Deadline is February 15, 2016).

The ASA Causality in Statistics Education Award is aimed at encouraging the teaching of basic causal inference in introductory statistics courses. Co-sponsored by Microsoft Research and Google, the prize is motivated by the growing importance of introducing core elements of causal inference into undergraduate and lower-division graduate classes in statistics. For more information, please see http://www.amstat.org/education/causalityprize/ .

Nominations and questions should be sent to the ASA office at educinfo@amstat.org . The nomination deadline is February 15, 2016.

C.2.
Issue 4.1 of the Journal of Causal Inference is scheduled to appear March 2016, with articles covering all aspects of causal analysis. For mission, policy, and submission information please see: http://degruyter.com/view/j/jci

C.3
Finally, enjoy new results and new insights posted on our technical report page: http://bayes.cs.ucla.edu/csl_papers.html

Judea

UAB’s Nutrition Obesity Research Center — Causal Inference Course

Filed under: Announcement,Uncategorized — bryantc @ 1:03 am
We received the following announcement from Richard F. Sarver (UAB):

UAB’s Nutrition Obesity Research Center invite you to join them at one or both of our five-day short courses at the University of Alabama at Birmingham.

June: The Mathematical Sciences in Obesity Research The mathematical sciences including engineering, statistics, computer science, physics, econometrics, psychometrics, epidemiology, and mathematics qua mathematics are increasingly being applied to advance our understanding of the causes, consequences, and alleviation of obesity. These applications do not merely involve routine well-established approaches easily implemented in widely available commercial software. Rather, they increasingly involve computationally demanding tasks, use and in some cases development of novel analytic methods and software, new derivations, computer simulations, and unprecedented interdigitation of two or more existing techniques. Such advances at the interface of the mathematical sciences and obesity research require bilateral training and exposure for investigators in both disciplines. July: Strengthening Causal Inference in Behavioral Obesity Research Identifying causal relations among variables is fundamental to science. Obesity is a major problem for which much progress in understanding, treatment, and prevention remains to be made. Understanding which social and behavioral factors cause variations in adiposity and which other factors cause variations is vital to producing, evaluating, and selecting intervention and prevention strategies. In addition, developing a greater understanding of obesity’s causes, requires input from diverse disciplines including statistics, economics, psychology, epidemiology, mathematics, philosophy, and in some cases behavioral or statistical genetics. However, applying techniques from these disciplines does not involve routine well-known ‘cookbook’ approaches but requires an understanding of the underlying principles, so the investigator can tailor approaches to specific and varying situations. For full details of each of the courses, please refer to our websites below: Mon 6/13/2016 – Fri 6/17/2016: The Mathematical Sciences in Obesity, http://www.soph.uab.edu/energetics/shortcourse/third Mon 7/25/2016 – Fri 7/29/2016: Strengthening Causal Inference in Behavioral Obesity Research, http://www.soph.uab.edu/energetics/causal_inference_shortcourse/second Limited travel scholarships are available to young investigators. Please apply by Fri 4/1/2016 and be notified of acceptance by Fri 4/8/2016. Women, members of underrepresented minority groups and individuals with disabilities are strongly encouraged to apply. We look forward to seeing you in Birmingham this summer!

January 1, 2000

About

Filed under: Uncategorized — bryantc @ 12:01 am

Thank you for visiting the Causal Analysis in Theory and Practice. We welcome participants from all backgrounds and views to post questions, opinions, or results for other visitors to chew on and respond to. Specific topics of interest include:

  • Questions regarding the basic principles of causal analysis including its meaning and historical development.
  • Views on the controversial status of causation (if any).
  • Reviews of current books and papers related to causal inference and its application
  • Discussion and comparison of various approaches and representations.
  • Development of practical applications in economics, social science, health sciences, political science, law, and other disciplines based on understanding of cause-effect relationships.

Submissions will be reviewed and posted on this blog anonymously unless the author gives permission to include the his/her name. The purpose of moderation is not to censor differing views, but rather, to ensure that the discussion remains relevant and professional.

To submit a topic or question for discussion, please complete a simple form. A reply will be sent upon receipt of a submission, and if a submission is not posted, a reason will be given. We appreciate your interest in causality and hope to hear your views on this subject.

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