International Statistical Review

Causality and Causal Models: A Conceptual Perspective

Benito V. Frosini

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Abstract

This paper aims at displaying a synthetic view of the historical development and the current research concerning causal relationships, starting from the Aristotelian doctrine of causes, following with the main philosophical streams until the middle of the twentieth century, and commenting on the present intensive research work in the statistical domain. The philosophical survey dwells upon various concepts of cause, and some attempts towards picking out spurious causes. Concerning statistical modelling, factorial models and directed acyclic graphs are examined and compared. Special attention is devoted to randomization and pseudo-randomization (for observational studies) in view of avoiding the effect of possible confounders. An outline of the most common problems and pitfalls, encountered in modelling empirical data, closes the paper, with a warning to be very cautious in modelling and inferring conditional independence between variables.

This paper is based on the President's Lecture, given at the Biennial Meeting of the Italian Statistical Society, Bari, June 2004.

Article information

Source
Internat. Statist. Rev., Volume 74, Number 3 (2006), 305-334.

Dates
First available in Project Euclid: 4 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.isr/1165245392

Keywords
Causality Causal models Directed acyclic graph Confounder Counterfactual

Citation

Frosini, Benito V. Causality and Causal Models: A Conceptual Perspective. Internat. Statist. Rev. 74 (2006), no. 3, 305--334. https://projecteuclid.org/euclid.isr/1165245392


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References

  • [1] Aickin, M. (2002). Causal Analysis in Biomedicine and Epidemiology. New York: Marcel Dekker.
  • [2] Anderson, J. (1938). The problem of causality. Australasian J. of Psychology and Philosophy, 16, 127-142.
  • [3] Andersson, S.A., Madigan, D. & Perlman, M.D. (1997). A characterization of Markov equivalence classes for acyclic digraphs. Ann. Statist., 25, 505-541.
  • [4] Aristotle (1928). Analytica Posteriora. In The Works of Aristotle, Ed. W.D. Ross, vol. 1. Oxford: Clarendon Press.
  • [5] Aristotle (1930). Physica. In The Works of Aristotle, Ed. W.D. Ross, vol. II. Oxford: Clarendon Press.
  • [6] Arjas, E. {& } Parner, J. (2004). Casual reasoning from longitudinal data (with discussion). Scand. J. Statist., 31, 171-201.
  • [7] Bentler, P. & Peeler, W. (1979). Models of female orgasm. Archives of Sexual Behavior, 8, 405-423.
  • [8] Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer.
  • [9] Blau, P. & Duncan, O. (1967). The American Occupational Structure. New York: Wiley.
  • [10] Bickel, P.J., Hammel, E.A. & O'Connell, J.W. (1977). Sex bias in graduate admissions: Data from Berkeley. In Statistics and Public Policy, Eds. W.B. Fairley and F. Mosteller. Reading, MA: Addison-Wesley.
  • [11] Carnap, R. (1950, 1962). Logical Foundations of Probability, Second Edition 1962. Chicago: University of Chicago Press.
  • [12] Copi, I.M. & Cohen, C. (1998). Logic, Tenth edition. Upper Saddle River, NJ: Prentice Hall.
  • [13] Cox, D.R. & Wermuth, N. (1993). Linear dependencies represented by chain graphs (with discussion). Statistical Science, 8, 204-218.
  • [14] Cox, D.R. & Wermuth, N. (1996). Multivariate Dependencies. London: Chapman and Hall.
  • [15] Cox, D.R. & Wermuth, N. (2004). Causality: a statistical view. Internat. Statist. Rev., 72, 285-305.
  • [16] Dawid, A.P. (1979). Conditional independence in statistical theory. J. Roy. Statist. Soc. B, 41, 1-31.
  • [17] Dawid, A.P. (2000). Causal inference without counterfactuals (with Discussion). J. Amer. Statist. Assoc., 95, 407-448.
  • [18] Dawid, A.P. (2002). Influence diagrams for causal modelling and inference. Internat. Statist. Rev., 70, 161-189.
  • [19] Edwards, D. (2000). Introduction to Graphical Modelling, Second Edition. New York: Springer.
  • [20] Eells, E. (1991). Probabilistic Causality. Cambridge: Cambridge University Press.
  • [21] Faliva, M. (1992). Recursiveness vs. interdependence in econometric models: a comprehensive analysis for the linear case. J. Ital. Statist. Soc., 1, 335-357.
  • [22] Faliva, M. & Zoia, M.G. (1994). Detecting and testing causality in linear econometric models. J. Ital. Statist. Soc., 3, 61-76.
  • [23] Fisher, R.A. (1959). Smoking: the Cancer Controversy. Edinburgh: Oliver and Boyd.
  • [24] Frangakis, C.E. & Rubin, D.B. (2002). Principal stratification in causal inference. Biometrics, 58, 21-29.
  • [25] Freedman, D. (1999). From association to causation: some remarks on the history of statistics. Statistical Science, 14, 243-258.
  • [26] Frosini, B.V. (1999). Conditioning, information, and frequentist properties. Statistica Applicata, 11, 165-184.
  • [27] Frosini, B.V. (2001). Metodi statistici. Roma: Carocci.
  • [28] Frosini, B.V. (2002). Le prove statistiche nel processo civile e nel processo penale. Milano: Giuffré.
  • [29] Frosini, B.V. (2004). On Neyman-Pearson theory: Information content of an experiment and a fancy paradox. Statistica, 64, 271-286.
  • [30] Frydenberg, M. (1990). The chain graph Markov property. Scand. J. Statist., 17, 333-353.
  • [31] Gail, M.H. (1986). Adjusting for covariates that have the same distribution in exposed and unexposed cohorts. In Modern Statistical Methods in Chronic Disease Epidemiology, Eds. S.H. Moolgavkar and R.L. Prentice, pp. 3-18. New York: Wiley.
  • [32] Götze, A. (1947). Old Babylonian Omen Texts. New Haven: Yale University Press.
  • [33] Goodman, L.A. (1973). The analysis of multidimensional contingency tables when some variables are posterior to others: A modified path analysis approach. Biometrika, 60, 179-192.
  • [34] Goodman, N. (1965-1983). Fact, Fiction, and Forecast, Fourth Edition. Cambridge, MA: Harvard University Press.
  • [35] Greenland, S., Pearl, J. & Robins, J.M. (1999). Confounding and collapsibility in causal inference. Statistical Science, 14, 29-46.
  • [36] Hempel, C.G. (1962). Deductive-Nomological vs Statistical Explanation. In Minnesota Studies in the Philosophy of Science, Eds. H. Feigl and G. Maxwell. Minneapolis: University of Minnesota Press.
  • [37] Hempel, C.G. (1965). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press.
  • [38] Hempel, C.G. (1966). Philosophy of Natural Science. Englewood Cliffs, NJ: Prentice Hall.
  • [39] Hempel, C.G. & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15, 135-175.
  • [40] Hill, A.B. (1965). The environment and disease; association or causation. Proceedings of the Royal Society of Medicine, 58, 295-300.
  • [41] Holland, P.W. (1986). Statistics and causal inference. J. Amer. Statist. Assoc., 81, 945-970.
  • [42] Hume, D. (1739-1888). A Treatise of Human Nature. Oxford: Clarendon Press.
  • [43] Jeffrey, R.C. (1969). Statistical explanation vs. statistical inference. In Essays in Honor of Carl G. Hempel, Ed. N. Rescher N. Dordrecht: D. Reidel.
  • [44] Laplace, P.S. (1840). Essai philosophique sur les probabilit\'{es}, Septième edition. Bruxelles: SociétéBelge de Librairie.
  • [45] Lauritzen, S.L. (1996). Graphical Models. Oxford: Clarendon Press.
  • [46] Lauritzen, S.L. (2001). Causal inference from graphical models. In Complex Stochastic Systems, Ed. O.E. Barndorff-Nielsen, pp. 63-107. London: Chapman and Hall.
  • [47] Lauritzen, S.L. (2004). Discussion on causality. Scand. J. Statist., 31, 189-192.
  • [48] Lauritzen, S.L., Dawid, A.P., Larsen, B.N. & Leimer, H.-G. (1990). Independence properties of directed Markov fields. Networks, 20, 491-505.
  • [49] Lindley, D.V. (1979). Discussion of Dawid's paper. J. Roy. Statist. Soc. B, 41, 15-16.
  • [50] Lindley, D.V. (2002). Seeing and doing: the concept of causation (with discussion). Internat. Statist. Rev., 70, 191-214.
  • [51] Mackie, J.L. (1965). On causes and conditions. American Philosophical Quarterly, pp. 245-255 and 261-264.
  • [52] Mackie, J.L. (1974). The Cement of the Universe: A Study of Causation. Oxford: Oxford University Press.
  • [53] Maldonado, G. & Greenland, S. (2002). Estimating causal effects. Int. J. Epidemiology, 31, 422- 429.
  • [54] Mill, J.S. (1843). A System of Logic. London: J.V. Parker.
  • [55] Neyman, J. (1923). Justification of applications of the calculus of probabilities to the solutions of certain questions in agricultural experimentation (Polish, German summary). Polish Forest Agric. Journal, 10, 1-51. (English translation of excerpts in Statistical Science, (1990) 5, 465-472).
  • [56] Pearl, J. (1995). Causal diagrams for empirical research. Biometrika, 82, 669-710.
  • [57] Pearl, J. (1996). Causation, action, and counterfactuals. In Computational Learning and Probabilistic Reasoning, Ed. A. Gammerman. Chichester: Unicom-Wiley.
  • [58] Pearl, J. (2000). Causality. Models, Reasoning, and Inference. Cambridge: Cambridge University Press.
  • [59] Pearson, K. (1900). The Grammar of Science, Second Edition. London: Adam and Charles Black.
  • [60] Prentice, R.L. (1989). Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine, 8, 431-440.
  • [61] Reichenbach, H. (1956). The Direction of Time. Berkeley: University of California Press.
  • [62] Robins, J.M. (1986). A new approach to casual inference in mortality studies with sustained exposure-Application to control of the healthy worker survivor effect. Math. Modelling, 7, 1393-1512.
  • [63] Robins, J.M. (1997). Causal inference from complex longitudinal data. In Latent Variable Modelling with Applications to Causality, Ed. M. Berkane, pp. 69-117. New York: Springer.
  • [64] Robins, J.M. (1998). Structural nested failure time models. In: The Encyclopedia of Biostatistics, Eds. P. Armitage and T. Colton, pp. 4372-4389. Chichester: Wiley.
  • [65] Rosenbaum, P.R. (1984). From association to causation in observational studies: The role of tests of strongly ignorable treatment assignment. J. Amer. Statist. Assoc., 79, 41-48.
  • [66] Rosenbaum, P.R. & Rubin, D.B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41-55.
  • [67] Rothman, K.J. (1976). Causes, American J. of Epidemiology. 104, 587-592.
  • [68] Rothman, K.J. (Ed.) (1988). Causal Inference. Chestnut Hill, MA: Epidemiology Resources.
  • [69] Rothman, K.J. & Greenland, S. (1998). Modern Epidemiology. Philadelphia: Lippincott-Raven.
  • [70] Rubin, D.B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. J. of Educational Psychology, 66, 688-701.
  • [71] Rubin, D.B. (1977). Assignment to treatment group on the basis of a covariate. J. of Educational Statistics, 2, 1-26.
  • [72] Rubin, D.B. (1978). Bayesian inference for causal effects: the role of randomization. Ann. Statist., 6, 34-58.
  • [73] Rubin, D.B. (1980). Discussion of Basu's paper. J. Amer. Statist. Assoc., 75, 591-593.
  • [74] Rubin, D.B. (2000). Comment on Dawid's paper. J. Amer. Statist. Assoc., 95, 435-438.
  • [75] Rubin, D.B. (2004). Direct and indirect causal effects via potential outcomes. Scand. J. Statist. 31, 161-170.
  • [76] Russell, B. (1913). On the notion of cause. Proceedings of the Aristotelian Society, 13, 1-26.
  • [77] Salmon, W.C. (1965). The status of prior probabilities in statistical explanation. Philosophy of Science, 32, 137-146.
  • [78] Salmon, W.C. (1978). Why ask ''Why''?: An inquiry concerning scientific explanation. Proceedings and Addresses of the American Philosophical Association, 5(6), 683-705
  • [79] Salmon, W.C. (1984). Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press.
  • [80] Scriven, M. (1959). Explanation and prediction in evolutionary theory. Science, 130, 477-482.
  • [81] Simpson, C. (1951). The interpretation of interaction in contingency tables. J. Roy. Statist. Soc. B, 13, 238-241.
  • [82] Speed, T.P. (1990). Introductory remarks on Neyman (1923). Statistical Science, 5, 463-464.
  • [83] Spirtes, P., Glymour, C. & Scheines, R. (2000). Causation, Prediction, and Search. Cambridge, MA: The MIT Press.
  • [84] Suppes, P. (1970). A Probabilistic Theory of Causality. Amsterdam: North Holland.
  • [85] van der Laan, M.J. {& } Robins, J.M. (2002). Unified Methods for Censored Longitudinal Data and Causality. New York: Springer.
  • [86] Verma, T. & Pearl, J. (1990). Equivalence and synthesis of causal models. In Uncertainty in Artificial Intelligence, Proceedings of the Sixth Conference, pp. 220-227. San Francisco: Morgan Kaufman.
  • [87] Wermuth, N. & Lauritzen, S.L. (1983). Graphical and recursive models for contingency tables. Biometrika, 70, 537-552.
  • [88] Wermuth, N. & Lauritzen, S.L. (1990). On substantive research hypotheses, conditional independence graphs and graphical chain models (with discussion). J. R. Statist. Soc. B, 52, 21-72.
  • [89] Wright, S. (1921). Correlation and causation. J. Agric. Res., 20, 557-585.
  • [90] Wright, S. (1934). The method of path coefficients. Ann. Math. Statist., 5, 161-215.
  • [91] Yule, G.U. (1903). Notes on the theory of association of attributes in Statistics. Biometrika, 2, 121-134.
  • [92] Zeisel, H. & Kaye, D. (1997). Prove it with Figures. New York: Springer.