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What are good books that introduce causal analysis? I'm thinking of an introduction that both explains the principles of causal analysis and shows how different statistical methods could be used to apply these principles.

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You might try this article by Krider which has a simple graphical technique. Along the way, it has a fairly simple explanation of some causal techniques. I'm making this just a comment because this isn't exactly what you asked for. – zbicyclist Dec 16 '12 at 7:38
Judea Pearl. Causality: Models, Reasoning, and Inference. Cambridge Univ.Press, 2000. (ISBN 0521773628) – Deer Hunter Dec 16 '12 at 10:18
Chen & Pearl have a report on Regression and Causation: A Critical Examination Econometrics Textbooks – Jack Tanner Dec 17 '12 at 17:35

Try Morgan and Winship (2007) for a social science take or Hernan and Robins (forthcoming) for an epidemiological take. Although still in progress, this looks like it's going to be very good.

Morgan and Winship is particularly good on what must be assumed for causal interpretations of regression-type models.

Pearl (2000) is in no sense introductory, although ultimately a very good read. You may find some of his website and specific articles useful, particularly on interpreting structural equation models. They are mostly available as technical reports.

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I think M&W is actually 2007. – Dimitriy V. Masterov Dec 18 '12 at 21:54
Thanks @DimitriyV.Masterov Not sure how that date leaked in after I spent the last many w eeks teaching out of it! – conjugateprior Dec 19 '12 at 10:00

I have very high expectations for Austin Nichols' forthcoming book Causal Inference: Measuring the Effect of x on y. The expected publication date is 2013. In the mean time, his handout and paper provide a nice overview of panel methods, instrumental variables, propensity score matching/reweighting, and regression discontinuity. The comparisons between all these estimators (and RCTs) are especially useful, as well as the Stata mini-tutorials (that can be skipped if you're not a Stata user). Curated references are provided if you want to dig deeper. Unfortunately, there's not very much on structural equations here, though that is also true of the Morgan and Winship book. Their ARS paper is a shorter, though somewhat dated, overview.

I found Pearl to be an interesting, but difficult, introduction to this material. If it was my first exposure to these ideas, I don't know if I would have walked away after reading it knowing how to apply any of the methods very well.

Finally, here are video presentations and slides by economist James Heckman and Pearl from the 2012 Causal Inference Symposium at University of Michigan. Lots of stuff on structural models here.

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Cosma Shalizi's textbook Advanced Data Analysis from an Elementary Point of View has an excellent coverage of causation. (The textbook is still in draft form, and is available online as a pdf, so it has the added benefit of being free.)

You should decide, though, whether you are interested in methods for (a) estimating the size of causal effects, or (b) learning the structure of causal networks (i.e. learning which variables influence which others). There are many references for (a), I think Pearl's Causality is the best. There are few introductory references for (b); I think Cosma's textbook is the best, but it is not comprehensive.

CMU hosted some great introductory talks on causal structure learning in 2013. Richard Scheines presented a tutorial on causal inference using Tetrad, a long and gentle introduction to the basic concepts. Frederick Eberhardt presented All of Causal Discovery, a fast-paced overview of the state of the art. One or both of them may be helpful; Frederick's talk should give you plenty of ideas about where to go next.

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