Structural equation modeling: Difference between revisions

Revision as of 23:13, 15 November 2024

Revision as of 21:36, 11 December 2024

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Traces of the historical convergence of the factor analytic and path analytic traditions persist as the distinction between the measurement and structural portions of models; and as continuing disagreements over model testing, and whether measurement should precede or accompany structural estimates.<ref name="HG00a">Hayduk, L.; Glaser, D.N. (2000) "Jiving the Four-Step, Waltzing Around Factor Analysis, and Other Serious Fun". Structural Equation Modeling. 7 (1): 1-35.</ref><ref name="HG00b">Hayduk, L.; Glaser, D.N. (2000) "Doing the Four-Step, Right-2-3, Wrong-2-3: A Brief Reply to Mulaik and Millsap; Bollen; Bentler; and Herting and Costner". Structural Equation Modeling. 7 (1): 111-123.</ref> Viewing factor analysis as a data-reduction technique deemphasizes testing, which contrasts with path analytic appreciation for testing postulated causal connections – where the test result might signal model misspecification. The friction between factor analytic and path analytic traditions continue to surface in the literature.

Wright's path analysis influenced Hermann Wold, Wold's student Karl Jöreskog, and Jöreskog's student Claes Fornell, but SEM never gained a large following among U.S. econometricians, possibly due to fundamental differences in modeling objectives and typical data structures. The prolonged separation of SEM's economic branch led to procedural and terminological differences, though deep mathematical and statistical connections remain.<ref name="Westland15">Westland, J.C. (2015). Structural Equation Modeling: From Paths to Networks. New York, Springer.</ref><ref>{{Cite journal|last=Christ|first=Carl F.|date=1994|title=The Cowles Commission's Contributions to Econometrics at Chicago, 1939-1955|url=https://www.jstor.org/stable/2728422|journal=Journal of Economic Literature|volume=32|issue=1|pages=30–59|jstor=2728422|issn=0022-0515}}</ref> TheDisciplinary economicdifferences versionin of SEMapproaches can be seen in SEMNET discussions of endogeneity, and in thediscussions heat produced as Judea Pearl's approach toon causality via directed acyclic graphs (DAG'sDAGs) rubs against economic approaches to modeling.<ref name="Pearl09"/> Discussions comparing and contrasting various SEM approaches are available<ref name="Imbens20">Imbens, G.W. (2020). "Potential outcome and directed acyclic graph approaches to causality: Relevance for empirical practice in economics". Journal of Economic Literature. 58 (4): 11-20-1179.</ref><ref name="BP13">{{cite book | doi=10.1007/978-94-007-6094-3_15 | chapter=Eight Myths About Causality and Structural Equation Models | title=Handbook of Causal Analysis for Social Research | series=Handbooks of Sociology and Social Research | date=2013 | last1=Bollen | first1=Kenneth A. | last2=Pearl | first2=Judea | pages=301–328 | isbn=978-94-007-6093-6 }}</ref> buthighlighting disciplinary differences in data structures and the concerns motivating economic models make reunion unlikely. Pearl<ref name=Pearl09 /> extended SEM from linear to nonparametric models, and proposed causal and counterfactual interpretations of the equations. Nonparametric SEMs permit estimating total, direct and indirect effects without making any commitment to linearity of effects or assumptions about the distributions of the error terms.<ref name=BP13 />

[[Judea Pearl]]<ref name="Pearl09" /> extended SEM from linear to nonparametric models, and proposed causal and counterfactual interpretations of the equations. Nonparametric SEMs permit estimating total, direct and indirect effects without making any commitment to linearity of effects or assumptions about the distributions of the error terms.<ref name="BP13" />

SEM analyses are popular in the social sciences because computer programs make it possible to estimate complicated causal structures, but the complexity of the models introduces substantial variability in the quality of the results. Some, but not all, results are obtained without the "inconvenience" of understanding experimental design, statistical control, the consequences of sample size, and other features contributing to good research design.{{Citation needed|date=July 2023}}

SEM analyses are popular in the social sciences because computer programs make it possible to estimate complicated causal structures, but the complexity of the models introduces substantial variability in the results, with or without experimental design, depending on the use of conventional statistical control, the consequences of sample size, and the variables of interests.<ref>{{Citation |last=Bollen |first=Kenneth A. |title=Eight Myths About Causality and Structural Equation Models |date=2013 |work=Handbooks of Sociology and Social Research |pages=301–328 |url=https://doi.org/10.1007/978-94-007-6094-3_15 |access-date=2024-12-11 |place=Dordrecht |publisher=Springer Netherlands |isbn=978-94-007-6093-6 |last2=Pearl |first2=Judea}}</ref>

== General steps and considerations ==

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* the set of variables to be employed,

* what is known about the variables,

* what is presumedtheorized or hypothesized about the variables' causal connections and disconnections,

* what the researcher seeks to learn from the modeling, and

* the instances of missing values and/or the need for imputation.

* and the cases for which values of the variables will be available (kids? workers? companies? countries? cells? accidents? cults?).

Structural equation models attempt to mirror the worldly forces operative for causally homogeneous cases – namely cases enmeshed in the same worldly causal structures but whose values on the causes differ and who therefore possess different values on the outcome variables. Causal homogeneity can be facilitated by case selection, or by segregating cases in a multi-group model. A model's specification is not complete until the researcher specifies:

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* {{Annotated link|Causal model}}

* {{Annotated link|Graphical model}}

* [[Judea Pearl]]

* {{Annotated link|Multivariate statistics}}

* {{Annotated link|Partial least squares path modeling}}