Pearl's D-Separation: One More Step Into Causal Thinking

Hayduk, Leslie A.; Cummings, Greta G.; Stratkotter, Rainer; Nimmo, Melanie; Grygoryev, Kostyantyn; Dosman, Donna; Gillespie, Michael; Pazderka, Hannah; Boadu, Kwame

doi:10.1207/s15328007sem1002_8

Cited by 88 publications

(35 citation statements)

References 3 publications

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“…To acknowledge the potential endogeneity of ELMX and SLMX, we also performed a generalized version of the Hausman (1978) test; in this model, we constrained the residual covariances of ELMX and SLMX with OCB and work performance to zero (and only estimated the residual covariance between ELMX and SLMX, as well as that of OCB with work performance). The results of this Wald test (χ² [4] = 8.10, p = 0.09) indicated that ELMX and SLMX may not be endogenous with respect to work performance and OCB in our specification; thus, we can assume that they have been "d-separated" (Hayduk, et al, 2003). When removing the cluster means controls, the model failed to fit the data χ² [67] = 106.88, p < 0.001.…”

Section: Resultsmentioning

confidence: 96%

Economic and social leader–member exchange relationships and follower performance

Kuvaas

Buch

Dysvik

et al. 2012

The Leadership Quarterly

101

195

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Section: Resultsmentioning

confidence: 96%

Economic and social leader–member exchange relationships and follower performance

Kuvaas

Buch

Dysvik

et al. 2012

The Leadership Quarterly

101

195

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“…For an additional introduction to d-separation for social Correspondence should be sent to Felix Thoemmes, Cornell University, MVR G62A, Ithaca, NY 14853. E-mail: felix.thoemmes@ cornell.edu scientists, see, for example, Hayduk et al (2003). Models without latent variables or bidirected arrows (also called ''Markovian'' models) are in the same equivalence class, if and only if the two models have the same d-separation constraints (Pearl, 2000).…”

Section: Cornell Universitymentioning

confidence: 99%

Reversing Arrows in Mediation Models Does Not Distinguish Plausible Models

Thoemmes

2015

Basic and Applied Social Psychology

193

136

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Reversing arrows in the classic tri-variate X-M-Y mediation models as a test to check whether one mediation model is superior to another is inadmissible. Presenting evidence that one tri-variate mediation model yields a significant indirect effect, whereas one with some reversed arrows does not, is not proof or even evidence that one model should be preferred. In fact, the significance of the indirect or any other effect can never be used to infer whether one model should be preferred over another, if the models are in the same so-called equivalence class. The practice of running several mediation models with reversed arrows to decide which model to prefer should be abandoned. The only way to choose among equivalent models is through assumptions that are either fulfilled by design features or invoked based on theory. Similar arguments about reversing arrows in mediation models have been made before, but this current work is the first to derive this result analytically for the complete (Markovian) equivalence class of the tri-variate mediation model.A mediator M in the tri-variate X-M-Y mediation model cannot be statistically distinguished from a confounder (Fiedler, Schott, & Meiser, 2011;MacKinnon, Krull, & Lockwood, 2000). In fact, as we show, it cannot be distinguished from a common cause, common effect, or a mediator in the reverse direction using statistics alone. However, there is still a persistent belief that it can be helpful to test alternative mediation models by switching arrows and comparing size and significance of the indirect effects. Without wanting to single out specific publications or authors, this practice can be seen in published work; for example, Fredrickson, Tugade, Waugh, and Larkin (2003) used this technique to argue that one mediation model (the one with the significant effect) was more plausible than two alternative models (the ones without significant effects). Anecdotally, the author can also attest that it is not uncommon that reviewers (or editors) request that in addition to a presented mediation model, some arrows should be reversed, and the model tested again, presumably to gain insight into which model is preferred.The (erroneous) thought behind this practice is that if the mediated effect of one model is significant, but the other model has no significant mediated effect, then the mediation model with the significant indirect effect is more plausible. However, none of the six models that one could form by reversing the three directed arrows in the tri-variate mediation model can be preferred on the basis of the significance of any of the resulting effects. 1

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“…(See Hayduk, 1987, pp. 150-154 [with the fifth-last and second-last "Yes's" on p. 152 corrected to being "No's" as per an addendum available from the author]; Hayduk, 1996, p. 6;Hayduk et al, 2003;Pearl, 2000. ) The implications of potential indirectness of measurement for the understanding of validity are substantial.…”

Section: Does Valid Measurement Require a Direct Effect Of The Latentmentioning

confidence: 99%

The Weird World, and Equally Weird Measurement Models: Reactive Indicators and the Validity Revolution

Hayduk

Pazderka²,

Cummings

et al. 2007

Structural Equation Modeling: A Multidisciplinary Journal

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Researchers using structural equation modeling (SEM) aspire to learn about the world by seeking models with causal specifications that match the causal forces extant in the world. This quest for a model matching existing worldly causal forces constitutes an ontology that orients, or perhaps reorients, thinking about measurement STRUCTURAL EQUATION MODELING, 14(2), validity. This article illustrates several ways the seemingly innocuous quest for structural equation models that mirror "the world beyond" confronts entrenched notions of measurement validity. The article begins by considering simple measurement models and ends by "discovering" a new class of indicators called reactive indicators. Reactive indicators act as both the cause and effect of an underlying latent variable. The identifiability of a simple model containing a reactive indicator is proven and a research example illustrating the use of a reactive indicator is provided. However, the real challenge is to understand how an indicator can be both a cause and effect of the latent it measures. The understanding does not come from complying with the traditional rules for reliability and validity, but from focusing on the quest to make the structural equation model match the structuring of the worldly forces we seek to understand. Valid measurement in the context of a weirdly structured world requires an equally weird structural equation model. SEM RESEARCH ONTOLOGYMost structural equation modeling (SEM) researchers do not doubt the existence of an underlying causally structured world. For them, the issue is not whether a causal world exists but which particular causal forces provided the data at their fingertips. The ontological commitment to seek the structure of an existing causal world is buttressed by multiple epistemological commitments concerning the most trustworthy methodological means via which researchers can come to know the extant world. The epistemological commitments include the methodological admonitions: to avoid contradictory causal claims, to seek logical implications of one's causal claims, to seek evidence relevant to those implications, and to be diligent in making observations that test one's causal understandings.This article does not pursue measurement and validity in the context of epistemology or methodological diligence (attentiveness to gathering and handling data). Nor does it pursue the philosophy of whether the world's causal structure is fundamental, or merely coincidentally parallel because it floats on some unfathomably deeper sea of "structures that produce causal structuring." Instead, the consequences of the research quest to supplant the current hazy and incomplete understanding of the worldly forces is pursued by locating, representing, and encapsulating the actual worldly causal forces within a structural equation model. The article examines the consequences of making an ontological commitment to the structured existence of underlying causal forces as producing the values of observed variables-namely the research co...

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Pearl's D-Separation: One More Step Into Causal Thinking

Cited by 88 publications

References 3 publications

Economic and social leader–member exchange relationships and follower performance

Economic and social leader–member exchange relationships and follower performance

Reversing Arrows in Mediation Models Does Not Distinguish Plausible Models

The Weird World, and Equally Weird Measurement Models: Reactive Indicators and the Validity Revolution

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