## The Causal Foundations of Structural Equation Modeling (2010)

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Citations: | 9 - 4 self |

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@MISC{Pearl10thecausal,

author = {Judea Pearl},

title = {The Causal Foundations of Structural Equation Modeling},

year = {2010}

}

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### Abstract

### Citations

7110 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
- Pearl
- 1988
(Show Context)
Citation Context ...tality of all seven assumptions implies that Z is unassociated with Y in every stratum of X. Such testable implications can be read off the diagrams using a graphical criterion known as d-separation (=-=Pearl, 1988-=-). Definition 3 (d-separation) AsetS of nodes is said to block a path p if either (1) p contains at least one arrow-emitting node that is in S, or(2)p contains at least one collision node that is outs... |

1448 | The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations
- Baron, Kenny
- 1986
(Show Context)
Citation Context ...heuristic methods of Stelzl (1986) and Lee and Hershberger (1990) 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). 22 SEM and Causality: A Brief History of Unhappy Encounters The founding fathers of SEM, from Sewall Wright (1923) and the early econometricians (Haavelmo, 1943; Simon, 1953; Mars... |

1132 |
Causality: Models, Reasoning, and Inference
- Pearl
(Show Context)
Citation Context ...ocedurally by simulating an intervention in a causal model M, as in equation (3). The following definition captures the requirement that Q be estimable from the data: Definition 1 (identifiability ) (=-=Pearl, 2000-=-, p. 77) AquantityQ(M) is identifiable, given a set of assumptions A, if for any two models M1 and M2 that satisfy A, we have P (M1) =P (M2) ⇒ Q(M1) =Q(M2) (5) In words, the functional details of M1 a... |

794 |
Structural equations with latent variables
- Bollen
- 1989
(Show Context)
Citation Context ...ng omitted factors, we encode in effect the presence of latent variables affecting both X and Y , as shown explicitly in Figure 2(c), which is the standard representation in the SEM literature (e.g., =-=Bollen, 1989-=-). If, however, our attention focuses on causal relations among observed rather than latent variables, there is no reason to distinguish between correlated errors and interrelated latent variables; it... |

484 |
Estimating Causal Effects of Treatments in Randomized and Non-randomized Studies
- Rubin
- 1974
(Show Context)
Citation Context ...th analysis. This expression may be somewhat dated, however, as it seems to appear less often in the literature nowadays” (Kline, 2005, p. 9). Relentless assaults from the potential-outcome paradigm (=-=Rubin, 1974-=-) have further eroded confidence in SEM’s adequacy to serve as a language for causation. Sobel (1996), for example, states that the interpretation of the parameters of SEM model as effects “do not gen... |

479 |
Principles and practices of structural equation modeling
- Kline
- 2005
(Show Context)
Citation Context ...ausal modeling, which is used mainly in association with the techniques of path analysis. This expression may be somewhat dated, however, as it seems to appear less often in the literature nowadays” (=-=Kline, 2005-=-, p. 9). Relentless assaults from the potential-outcome paradigm (Rubin, 1974) have further eroded confidence in SEM’s adequacy to serve as a language for causation. Sobel (1996), for example, states ... |

341 |
Experimental and quasi-experimental designs for generalized causal inference
- Shadish, Cook, et al.
- 2002
(Show Context)
Citation Context ...biotic approach by offering a simple solution to the mediation problem for models with categorical data. An issue that was not discussed in this chapter is the perennial problem of external validity (=-=Shadish et al., 2002-=-), namely, the conditions under which causal conclusions from a study on one population can safely be modified and transported to another. This problem has recently received a formal treatment using n... |

318 |
Statistics and causal inference
- Holland
- 1986
(Show Context)
Citation Context ...obability of causation” (Pearl, 2009, Ch. 9) quantifies “causes of effect,” as opposed to “effect of causes,” and was excluded, prematurely I presume, from the province of potential outcome analysis (=-=Holland, 1986-=-). 7 Such tables are normally used to explain the philosophy behind the potential outcome framework (e.g., West and Thoemmes (2010) in which Y1 and Y0 are taken as unexplained random variables. Here t... |

217 |
Equivalence and synthesis of causal models
- Verma, Pearl
- 1990
(Show Context)
Citation Context ...constraints can be imposed, beyond the d-separation conditions. 6 5.2 Equivalent Models D-separation also defines conditions for model equivalence that are easily ascertained in the Markovian models (=-=Verma and Pearl, 1990-=-) as well a semi-Markovian models (Ali et al., 2009). These mathematically proven conditions should supercede the heuristic (and occasionally faulty) rules prevailing in SEM’s research (Lee and Hershb... |

157 | Mediation in experimental and nonexperimental studies: New procedures and recommendations - Shrout, Bolger - 2002 |

147 | Correlation and causation - Wright - 1921 |

143 | Issues and opinion on structural equation modeling - Chin - 1998 |

100 |
Identifiability and Exchangeability for Direct and Indirect Effects
- JM, Greenland
- 1992
(Show Context)
Citation Context ...ine the direct effect DEx,x ′(Y )7 as the expected change in Y induced by changing X from x to x ′ while keeping all mediating factors constant at whatever value they would have obtained under do(x) (=-=Robins and Greenland, 1992-=-; Pearl, 2001). Accordingly, Pearl (2001) defined direct effect using counterfactual notation: DEx,x ′(Y )=E(Yx ′ ,Zx) − E(Yx). (9) Here, Yx ′ ,Zx represents the value that Y would attain under the op... |

98 |
The Statistical Implications of a System of Simultaneous Equations
- Haavelmo
- 1943
(Show Context)
Citation Context ... Problem,” (Baron and Kenny, 1986; MacKinnon, 2008). 22 SEM and Causality: A Brief History of Unhappy Encounters The founding fathers of SEM, from Sewall Wright (1923) and the early econometricians (=-=Haavelmo, 1943-=-; Simon, 1953; Marschak, 1950; Koopmans, 1953), to Blalock (1964) and Duncan (1975) have all considered SEM a mathematical tool for drawing causal conclusions from a combination of observational data ... |

98 | Comment: Graphical models, causality, and intervention - Pearl - 1993 |

79 | Direct and indirect effects
- Pearl
- 2001
(Show Context)
Citation Context ...′(Y )7 as the expected change in Y induced by changing X from x to x ′ while keeping all mediating factors constant at whatever value they would have obtained under do(x) (Robins and Greenland, 1992; =-=Pearl, 2001-=-). Accordingly, Pearl (2001) defined direct effect using counterfactual notation: DEx,x ′(Y )=E(Yx ′ ,Zx) − E(Yx). (9) Here, Yx ′ ,Zx represents the value that Y would attain under the operation of se... |

72 | Process analysis: Estimating mediation in treatment evaluations - Judd, Kenny - 1981 |

72 |
Causal Ordering and Identifiability
- Simon
- 1953
(Show Context)
Citation Context ...n and Kenny, 1986; MacKinnon, 2008). 22 SEM and Causality: A Brief History of Unhappy Encounters The founding fathers of SEM, from Sewall Wright (1923) and the early econometricians (Haavelmo, 1943; =-=Simon, 1953-=-; Marschak, 1950; Koopmans, 1953), to Blalock (1964) and Duncan (1975) have all considered SEM a mathematical tool for drawing causal conclusions from a combination of observational data and theoretic... |

69 |
Causal inference, path analysis, and recursive structural equations models
- Holland
- 1988
(Show Context)
Citation Context ...otential Outcome Framework Definition 2 constitutes the bridge between SEM and a framework called “potential outcome” (Rubin, 1974) which is often presented as a “more principled alternative” to SEM (=-=Holland, 1988-=-; Sobel, 1996, 2008). Such claims are misleading and misinformed; the two frameworks have been proven to be a logically equivalent differing only in the language in 11which researchers are permitted ... |

68 | Introduction to structural equation models - Duncan - 1975 |

67 | Axiomatizing causal reasoning
- Halpern
- 1998
(Show Context)
Citation Context ...g restrictions,” and ways of reading them from the graph. 3 In other words, a complete axiomization of structural counterfactuals in recursive systems consists of (7) and a few non essential details (=-=Halpern, 1998-=-). 4 This nomenclature may be misleading because, as shown in Figure 1, testability and identificablity have little to do with each other. 125.1 The d-separation criterion Although each causal assump... |

61 | Probabilistic evaluation of sequential plans from causal models with hidden variables - Pearl, Robins - 1995 |

59 | A general identification condition for causal effects - Tian, Pearl - 2002 |

57 |
Counterfactuals and Causal Inference: Methods and Principles for Social Research
- Morgan, Winship
- 2007
(Show Context)
Citation Context ...t al., 2006; VanderWeele and Robins, 2007; Hafeman and Schwartz, 2009; Joffe and Green, 2009; VanderWeele, 2009; Kaufman, 2010) and is making its way slowly toward the social and behavioral sciences (=-=Morgan and Winship, 2007-=-; Imai et al., 2010). 29better without strengthening the assumptions. Acknowledgments This paper has benefited from discussions with Elias Barenboim, Peter Bentler, Ken Bollen, James Heckman, Jeffrey... |

48 | Causal Necessity - Skyrms - 1980 |

47 | Causal inferences in non-experimental research - Blalock - 1964 |

45 | An axiomatic characterization of causal counterfactuals
- Galles, Pearl
- 1998
(Show Context)
Citation Context ... not be interpreted as effect.” Remarkably, formal analysis proves the exact opposite: structural and causal parameters are 3one and the same thing, and they should always be interpreted as effects (=-=Galles and Pearl, 1998-=-; see Section 4). Paul Holland, another advocate of the potential-outcome framework, unravels the root of the confusion: “I am speaking, of course, about the equation: {y = a + bx + ɛ}. What does it m... |

45 | Mediation analysis - MacKinnon, Fairchild, et al. - 2007 |

45 | Graphs, causality, and structural equation models
- Pearl
- 1998
(Show Context)
Citation Context ...erpreted as effect.” Remarkably, formal analysis proves the exact opposite: structural and causal parameters are 3one and the same thing, and they should always be interpreted as effects (Galles and =-=Pearl, 1998-=-; see Section 4). Paul Holland, another advocate of the potential-outcome framework, unravels the root of the confusion: “I am speaking, of course, about the equation: {y = a + bx + ɛ}. What does it m... |

43 | Identification of conditional interventional distributions - Shpitser, Pearl - 2006 |

42 | Counterfactuals and policy analysis in structural mod- els - Balke, Pearl - 1995 |

40 |
Limitations of the application of fourfold table analysis to hospital data
- Berkson
- 1946
(Show Context)
Citation Context ...UX will hold in the distribution, but UZ ⊥UX|Y may or may not hold. This special handling of collision nodes (or colliders, e.g., Z → X ← UX) reflects a general phenomenon known as Berkson’s paradox (=-=Berkson, 1946-=-), whereby observations on a common consequence of two independent causes render those causes dependent. For example, the outcomes of two independent coins are rendered dependent by the testimony that... |

40 | When moderation is mediated and mediation is moderated - Muller, Judd, et al. - 2005 |

37 | Counterfactuals and comparative possibility - Lewis - 1973 |

37 | Direct and indirect causal effects via potential outcomes
- Rubin
- 2004
(Show Context)
Citation Context ...blem is approached from an exclusivist potential-outcome viewpoint, void of the structural guidance of equation (6), counterintuitive definitions ensue, carrying the label “principal stratification” (=-=Rubin, 2004-=-, 2005), which are at variance with common understanding of direct and indirect effects. For example, the direct effect is definable only in units absent of indirect effects. This means that a grandfa... |

36 | Identification of joint interventional distributions in recursive semi-Markovian causal models - Shpitser, Pearl - 2006 |

35 | Identification, inference, and sensitivity analysis for causal mediation effects
- Imai, Keele, et al.
- 2010
(Show Context)
Citation Context ... adjustment for appropriate sets of covariates W may be necessary to achieve this independence (as in equation 11) and that integrals should replace summations when dealing with continuous variables (=-=Imai et al., 2008-=-). Combining (12) and (14), the expression for the indirect effect, IE, becomes IEx,x ′(Y )=∑ E(Y |x, z)[P (z|x ′ ) − P (z|x)] (16) z which provides a general formula for mediation effects, applicable... |

34 | Causal inference using potential outcomes: Design, modeling, decisions - Rubin - 2005 |

34 | Mediating instrumental variables - Pearl - 1993 |

29 | An introduction to causal inference - Pearl |

29 | Cause and counterfactual - Simon, Rescher - 1966 |

27 | Causal inference in statistics: An overview - Pearl |

25 | 2005), “Identifiability of Path-Specific Effects - Avin, Shpitser, et al. |

23 |
Identification of Causal Parameters in Randomized Studies with Mediating Variables
- Sobel
(Show Context)
Citation Context ...ream literature. It is an essential tool to ward off critiques who view counterfactuals as an exclusive property of the potentialoutcome framework (Holland, 1988; Wilkinson et al., 1999; Rubin, 2004; =-=Sobel, 2008-=-; Imbens, 2010). This capacity can be demonstrated by a simple example, using a 3-variable linear model; the same one used by Holland (1988) and Sobel (2008) to “prove” that structural models do not h... |

23 |
Marginal Structural Models for the Estimation of Direct and Indirect Effects.’’ Epidemiology 20
- VanderWeele
(Show Context)
Citation Context ...meters separately (e.g., by regression or maximum likelihood methods), insert the parametric approximation into (16) and estimate its two conditional expectations (over z) to get the mediated effect (=-=VanderWeele, 2009-=-). Let us examine what the Mediation Formula yields when applied to the linear version of Figure 6(a), which reads x = uX z = b0 + b1x + uZ (17) y = c0 + c1x + c2z + uY 19with uX,uY ,anduZ uncorrelat... |

23 |
The Tariff on Animal and Vegetable Oils
- Wright
- 1928
(Show Context)
Citation Context ...niques may be invoked, for example, instrumental variables. 5.3.3 Recognizing Instrumental Variables Instrumental variables is one of the oldest identification technique available for linear systems (=-=Wright, 1928-=-). The method relies on finding a variable Z that is correlated with X and is deemed uncorrelated with the error term in an equation (see Pearl, 2009, pp. 242–48, for formal definition). While no stat... |

22 | Estimation of direct causal effects - Petersen, Sinisi, et al. - 2006 |

21 | The scientific model of causality - Heckman - 2005 |

19 | Four types of effect modification: A classification based on directed acyclic graphs
- VanderWeele, Robins
- 2007
(Show Context)
Citation Context ...sal-inference engine that takes qualitative causal assumptions, data and queries as inputs and produces 8 Such symbiosis is now standard in epidemiology research (Robins, 2001; Petersen et al., 2006; =-=VanderWeele and Robins, 2007-=-; Hafeman and Schwartz, 2009; VanderWeele, 2009) and is making its way slowly toward the social and behavioral sciences. 22data-fitness ratings to a few statistical tests, together with quantitative ... |

18 | As Others See Us: A Case Study in Path Analysis (with Discussion - Freedman - 1987 |