The Logic of Causal Inference

Transcription

1 The Logic of Causal Inference Judea Pearl University of California, Los Angeles Computer Science Department Los Angeles, CA, , USA September 13, Introduction The role of causality in behavioral research is widely perceived to be, on the one hand, of pivotal methodological importance (Maxwell, 2010) and, on the other hand, confusing, enigmatic and controversial (Freedman, 1987;?; Rubin, 2009; Kraemer et al., 2008; Fleming and DeMets, 1996; Green et al., 2010). The traditional approach to causal analysis, based need on Structural Equation Modeling (SEM), (Bollen, 1989; Bentler, 2006; Steiger, 2001; Shrout freedman and Bolger, 2002), though it has gone through several cycles of reformation and consolidation, is still viewed with suspicion and confusion by many researchers (Sørensen, 1998; 2010 Berk, 2004; Sobel, 2008; Rubin, 2010) To witness, a recent issue of Psychological Methods, whose goal was to introduce the works Donald Campbell and Donald Rubin to psychologists, (Maxwell, 2010), remains totally silent on how these two approaches compare to the traditional methodology based on SEM. The impression is thus created that traditional methods This research was supported in parts by NIH grant #1R01 LM , NSF grant #IIS , and ONR grant #N

2 are either orthogonal, or inferior to those of Campbell and Rubin s when, in fact, they subsume the latter (Pearl, 2009, pp ) and provide a formal setting for the former. This confusion is further exposed, for example, in the influential report of Wilkinson and Task Force s (1999) on Statistical Methods in Psychology Journals: Guidelines and Explanations. After warning readers against the false premise that, while correlation does not prove causation causal modeling does, the report reaches a surprising conclusion: The use of complicated causal-modeling software [read SEM] rarely yields any results that have any interpretation as causal effects. The implication being that the entire enterprise of causal modeling, from Sewell Wright (1921) to Blalock (1964) and Duncan (1975), the entire literature in econometric research, including modern advances in graphical and non-parametric structural models have all been misguided, for they have been chasing parameters that have no causal interpretation. The absurdity of such conclusions notwithstanding, readers may rightly ask: If SEM methods do not prove causation, how can they yield results that have causal interpretation? Put another way, if the structural coefficients that SEM researchers labor to estimate can legitimately be interpreted as causal effects then, unless these parameters are grossly misestimated, why deny SEM researchers the honor of establishing causation or at least of deriving some useful claims about causation. The answer is that a huge logical gap exists between establishing causation, which requires manipulative experiments, and interpreting parameters as causal effects, which may be based on scientific knowledge or on previously conducted experiments. One can legitimately be in a possession of a parameter that stands for a causal effect and still be unable, using statistical means alone, to determine the magnitude of that parameter given non-experimental data. As a matter of fact, we know that no such statistical means exists; that is, causal effects in observational studies can only be substantiated from a combination of data and untested, theoretical assumptions; not from the data alone. Thus, if reliance on theoretical assumptions disqualifies SEM s parameters from having an interpretation as causal effects, no method whatsoever can endow any parameter with such interpretation, and science is not prepared to accept this limitation. But then, if the parameters estimated by SEM methods are legitimate carriers of causal

3 claims, and if those claims cannot be proven valid by the data alone, what is the empirical content of those claims? What good are the numerical values of the parameters? Can they inform prediction, decision or scientific understanding? Are they not merely fiction of one s fancy, comparable say to horoscopic speculations? The aim of this chapter is to lay a coherent logical framework for answering these foundational questions. Following a brief historical account of how the causal interpretation of SEM was obscured (Section??), we will explicate the empirical content of SEM s claims (Section??), and describe the tools needed for solving most (if not all) problems involving causal relationships (Sections?? and??). The tools are based on non-parametric structural equation models a natural generalization of those used by econometricians and social scientists in the s, which will serve as an Archimedean Point to liberate SEM from its parametric blinders and illucidate its causal content. In particular we will introduce 1. Tools of reading and explicating the causal assumptions embodied in SEM models as well as the set of assumptions that support each individual causal claim. 2. Methods of identifying the testable implications (if any) of the assumptions in (1), and ways of testing, not the model in its entirety, but the testable implications of the assumptions behind each individual causal claim. 3. Methods of deciding, prior to taking any data, what measurements ought to be taken, whether one set of measurements is as good as to another, and which measurements tend to bias our estimates of the target quantities. 4. Methods for devising critical statistical tests by which two competing theories can be distinguished. 5. Methods of deciding mathematically if the causal relationships of interest are estimable from the data and, if not, what additional assumptions, measurements or experiments would render them estimable, 6. Methods of recognizing and generating equivalent models which solidify, extend, and amend the heuristic methods of Stelzl (1986) and Lee and Hershberger (1990)

4 7. Generalization of SEM to categorical data and non-linear interactions, including a solution to the so called Mediation Problem, (Baron and Kenny, 1986; MacKinnon, 2008). still to cite???: Shadish (2010); West and Thoemmes (2010); Imbens (2010); Cook and Steiner (2010) References Baron, R. and Kenny, D. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology Bentler, P. (2006). EQS Structural Equations Program Manual. Multivariate Software, Inc., Encino, CA, USA. Berk, R. (2004). Regression Analysis: A Constructive Critique. Sage, Thousand Oaks, CA. Blalock, H. (1964). Causal Inferences in Nonexperimental Research. University of North Carolina Press, Chapel Hill. Bollen, K. (1989). Structural Equations with Latent Variables. John Wiley, New York. Cook, T. and Steiner, P. (2010). Case matching and the reduction of selection bias in quasi-experiments: The relative importance of pretest measures of outcome, of unreliable measurement, and of mode of data analysis. Psychological Methods Duncan, O. (1975). Introduction to Structural Equation Models. Academic Press, New York. Fleming, T. and DeMets, D. (1996). Surrogate end points in clinical trials: are we being misled? Annals of Internal Medicine Freedman, D. (1987). As others see us: A case study in path analysis (with discussion). Journal of Educational Statistics

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