counterfactual attribution, including a tool kit for estimation, is given in Pearl, Glymour, and Jewell (2016). An advanced formal treatment of actual causation can be found in Halpern (2016).

Matching techniques for estimating causal effects are used routinely by potential outcome researchers (Sekhon, 2007), though they usually ignore the pitfalls shown in our education-experience-salary example. My realization that missing-data problems should be viewed in the context of causal modeling was formed through the analysis of Mohan and Pearl (2014).

Cowles (2016) and Reid (1998) tell the story of Neyman’s tumultuous years in London, including the anecdote about Fisher and the wooden models. Greiner (2008) is a long and substantive introduction to “but-for” causation in the law. Allen (2003), Stott et al. (2013), Trenberth (2012), and Hannart et al. (2016) address the problem of attribution of weather events to climate change, and Hannart in particular invokes the ideas of necessary and sufficient probability, which bring more clarity to the subject.

References

Allen, M. (2003). Liability for climate change. Nature 421: 891–892. Balke, A., and Pearl, J. (1994a). Counterfactual probabilities: Computational methods, bounds, and applications. In Uncertainty in Artificial Intelligence 10 (R. L. de Mantaras and D. Poole, eds.). Morgan Kaufmann, San Mateo, CA, 46–54.

Balke, A., and Pearl, J. (1994b). Probabilistic evaluation of counterfactual queries. In Proceedings of the Twelfth National Conference on Artificial Intelligence, vol. 1. MIT Press, Menlo Park, CA, 230–237.

Cowles, M. (2016). Statistics in Psychology: An Historical Perspective. 2nd ed. Routledge, New York, NY.

Duncan, O. (1975). Introduction to Structural Equation Models. Academic Press, New York, NY.

Freedman, D. (1987). As others see us: A case study in path analysis (with discussion). Journal of Educational Statistics 12: 101–223. Greenland, S. (1999). Relation of probability of causation, relative risk, and doubling dose: A methodologic error that has become a social problem. American Journal of Public Health 89: 1166–1169. Greiner, D. J. (2008). Causal inference in civil rights litigation. Harvard Law Review 81: 533–598.

Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations. Econometrica 11: 1–12. Reprinted in D. F. Hendry and M. S. Morgan (Eds.), The Foundations of Econometric Analysis, Cambridge University Press, Cambridge, UK, 477–490, 1995.

Halpern, J. (2016). Actual Causality. MIT Press, Cambridge, MA. Hannart, A., Pearl, J., Otto, F., Naveu, P., and Ghil, M. (2016).

Causal counterfactual theory for the attribution of weather and climate-related events. Bulletin of the American Meteorological Society (BAMS) 97: 99–110.

Holland, P. (1986). Statistics and causal inference. Journal of the American Statistical Association 81: 945–960.

Hume, D. (1739). A Treatise of Human Nature. Oxford University Press, Oxford, UK. Reprinted 1888.

Hume, D. (1748). An Enquiry Concerning Human Understanding. Reprinted Open Court Press, LaSalle, IL, 1958.

Joffe, M. M., Yang, W. P., and Feldman, H. I. (2010). Selective ignorability assumptions in causal inference. International Journal of Biostatistics 6. doi:10.2202/1557-4679.1199.

Lewis, D. (1973a). Causation. Journal of Philosophy 70: 556–567. Reprinted with postscript in D. Lewis, Philosophical Papers, vol. 2, Oxford University Press, New York, NY, 1986.

Lewis, D. (1973b). Counterfactuals. Harvard University Press, Cambridge, MA.

Lewis, M. (2016). The Undoing Project: A Friendship That Changed Our Minds. W. W. Norton and Company, New York, NY. Mohan, K., and Pearl, J. (2014). Graphical models for recovering probabilistic and causal queries from missing data. Proceedings of Neural Information Processing 27: 1520–1528.

Morgan, S., and Winship, C. (2015). Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). 2nd ed. Cambridge University Press, New York, NY.

Neyman, J. (1923). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Statistical Science 5: 465–480.

Pearl, J. (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press, New York, NY.

Pearl, J. (2009). Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press, New York, NY.

Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics: A Primer. Wiley, New York, NY.

Reid, C. (1998). Neyman. Springer-Verlag, New York, NY.

Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66: 688–701.

Sekhon, J. (2007). The Neyman-Rubin model of causal inference and estimation via matching methods. In The Oxford Handbook of Political Methodology (J. M. Box-Steffensmeier, H. E. Brady, and D. Collier, eds.). Oxford University Press, Oxford, UK.

Shpitser, I., and Pearl, J. (2009). Effects of treatment on the treated: Identification and generalization. In Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, Montreal, Quebec, 514–521.

Stott, P. A., Allen, M., Christidis, N., Dole, R. M., Hoerling, M., Huntingford, C., Pardeep Pall, J. P., and Stone, D. (2013). Attribution of weather and climate-related events. In Climate Science for Serving Society: Research, Modeling, and Prediction Priorities (G. R. Asrar and J. W. Hurrell, eds.). Springer, Dordrecht, Netherlands, 449–484.

Tian, J., and Pearl, J. (2000). Probabilities of causation: Bounds and identification. Annals of Mathematics and Artificial Intelligence 28: 287–313.

Trenberth, K. (2012). Framing the way to relate climate extremes to climate change. Climatic Change 115: 283–290.

VanderWeele, T. (2015). Explanation in Causal Inference: Methods for Mediation and Interaction. Oxford University Press, New York, NY.

Глава 9. Опосредование: в поисках механизма действия

Annotated Bibliography

There are several books dedicated to the topic of mediation. The most up-to-date reference is VanderWeele (2015); MacKinnon (2008) also contains many examples. The dramatic transition from the statistical approach of Baron and Kenny (1986) to the counterfactual-based approach of causal mediation is described in Pearl (2014) and Kline (2015). McDonald’s quote (to discuss mediation, “start from scratch”) is taken from McDonald (2001).

Natural direct and indirect effects were conceptualized in Robins and Greenland (1992) and deemed problematic. They were later formalized and legitimized in Pearl (2001), leading to the Mediation Formula.

In addition to the comprehensive text of VanderWeele (2015), new results and applications of mediation analysis can be found in De Stavola et al. (2015); Imai, Keele, and Yamamoto (2010); and Muthén and Asparouhov (2015). Shpitser (2013) provides a general criterion for estimating arbitrary path-specific effects