Abstract
Causality was at the center of the early history of structural equation models (SEMs) which continue to serve as the most popular approach to causal analysis in the social sciences. Through decades of development, critics and defenses of the capability of SEMs to support causal inference have accumulated. A variety of misunderstandings and myths about the nature of SEMs and their role in causal analysis have emerged, and their repetition has led some to believe they are true. Our chapter is organized by presenting eight myths about causality and SEMs in the hope that this will lead to a more accurate understanding. More specifically, the eight myths are the following: (1) SEMs aim to establish causal relations from associations alone, (2) SEMs and regression are essentially equivalent, (3) no causation without manipulation, (4) SEMs are not equipped to handle nonlinear causal relationships, (5) a potential outcome framework is more principled than SEMs, (6) SEMs are not applicable to experiments with randomized treatments, (7) mediation analysis in SEMs is inherently noncausal, and (8) SEMs do not test any major part of the theory against the data. We present the facts that dispel these myths, describe what SEMs can and cannot do, and briefly present our critique of current practice using SEMs. We conclude that the current capabilities of SEMs to formalize and implement causal inference tasks are indispensible; its potential to do more is even greater.
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Notes
- 1.
The notation slightly departs from the LISREL notation in its representation of intercepts.
- 2.
The expected effect refers to the expected value of the effect of one η on another.
- 3.
This rules out a variable with a direct effect on itself.
- 4.
In his later years, however, Freedman came to embrace a causal modeling approach he called “response schedule” – “how one variable would respond, if you intervened and manipulated other variables…” (Freedman 2009: 87; Chap. 19 by Berk et al. this volume) – which is none other but the SEM’s interpretation of structural equations (Haavelmo 1943; Blau and Duncan 1967; Pearl 2011c).
- 5.
In light of our discussion, it is not surprising that we disagree with descriptions that equate regression models with SEMs or with attempts to dichotomize SEMs into “regular SEM” and “causal SEM” as in the Wang and Sobel (Chap. 12, this volume) chapter.
- 6.
Path diagrams, as well as all graphical models used in this chapter, are not to be confused with Causal Bayes Networks (Pearl 2009, Ch. 1) or the FRCISTG graphs of Robins (1986). The latter two are “manipulative” (Robins 2003), namely, they are defined by manipulative experiments at the population level. Structural equations, on the other hand, are defined pseudo-deterministically at the unit level (i.e., with the error term being the only stochastic element) and support counterfactuals (see Pearl 2009, Ch. 7).
- 7.
A researcher could use the specific effects techniques proposed in Bollen (1987) to eliminate indirect effects originating with or going through any “attributes” when performing effect decomposition.
- 8.
Integrals should replace summation when continuous variables are invoked.
- 9.
- 10.
The conceptualization of natural (or “pure”) effects goes back to Robins and Greenland (1992) who proclaimed them non-identifiable even in controlled experiments and, perhaps unintentionally, committed them to nine years of abandonment (Kaufman et al. 2009). Interest in natural effects rekindled when Pearl (2001) formalized direct and indirect effects in counterfactual notation and, using SEM logic, derived conditions under which natural effects can nevertheless be identified. Such conditions hold, for example, when (ε 1, ε 2, ε 3) are mutually independent (after adjusting for appropriate covariates) – this is the commonplace assumption of “no unmeasured confounders” that some authors express in “ignorability” vocabulary. (See Chap. 12 by Wang and Sobel’s Eqs. (12.17), (12.18), and (12.19), this volume, where Pearl’s original results are rederived with some effort.) Milder conditions for identifiability, not insisting on “sequential ignorability,” are given explicit graphical interpretation in (Pearl 2012b).
- 11.
Wang and Sobel (Chap. 12, this volume) demonstrate this discounting by first referring to Principal Strata as “an alternative approach to mediation” and then proceeding with an analysis of moderation, not mediation.
- 12.
The first part of the statement represents an earlier misunderstanding under point (1) above where critics have made the false claim that SEM researchers believe that they can derive causal theory from associations in the data alone. See our above discussion under Myth #1 that refutes this view. The second part that SEM does not test any major part of the causal theory (assumptions) is ambiguous in that we do not know what qualifies as a “major” part of the theory.
- 13.
If the means and intercepts of the model are included, then the null hypothesis includes a test of whether the population means of the observed variables equals the model implied means that are a function of the model parameters.
- 14.
If some parameters are not identifiable, then the estimator might fail to converge or the run might be interrupted by SEM software that detects the identification problem. It is sometimes possible to estimate values for those parameters and functions of parameters that are identified and to test the fit of the overidentified parts of the model (see Shapiro 1986). But for most researchers, it would be prudent to abandon the test unless they have sufficient expertise on the problem. An alternative is to use a tetrad or partial correlation test statistics for models that are underidentified as long as vanishing tetrad or vanishing partial correlation is implied by the structure (see Bollen and Ting 1993; Pearl 2000: 144–154).
- 15.
This issue is complicated in that the tests assume a large sample and that certain distributional assumptions are satisfied. Fortunately, there are distributionally robust corrections (e.g., Bollen and Stine 1993; Satorra and Bentler 1994) and some small sample corrections (e.g., Bentler and Yuan 1999). There also is discussion about how to take account of the approximate nature of most models when the null hypothesis is one of exact fit where fit indexes are often used to supplement the chi-square test.
- 16.
Exploratory tetrad analysis which is designed to look for the different models that are consistent with the data is more oriented to creating models rather than testing models. Generally, ETA uses tests of single tetrads rather than simultaneous tests of multiple tetrads. See, for example, Glymour et al. (1987).
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Acknowledgments
The authors would like to thank Shawn Bauldry, Stephen Cole, Keith Marcus, Cameron McIntosh, Stan Mulaik, Johannes Textor, and other researchers from SEMNET for their comments on and critiques of our chapter. Bollen’s work was partially supported by NSF SES 0617276. Pearl’s work was partially supported by grants from NIH #1R01 LM009961-01, NSF #IIS-0914211 and #IIS-1018922, and ONR #N000-14-09-1-0665 and #N00014-10-0933.
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Bollen, K.A., Pearl, J. (2013). Eight Myths About Causality and Structural Equation Models. In: Morgan, S. (eds) Handbook of Causal Analysis for Social Research. Handbooks of Sociology and Social Research. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6094-3_15
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