Structural equation modeling: Difference between revisions

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[[File:Example SEM of Human Intelligence.png|alt=An example structural equation model pre-estimation|thumb|336x336px|Figure 2. An example structural equation model before estimation. Similar to Figure 1 but without standardized values and fewer items. Because intelligence and academic performance are merely imagined or theory-postulated variables, their precise scale values are unknown, though the model specifies that each latent variable's values must fall somewhere along the observable scale possessed by one of the indicators. The 1.0 effect connecting a latent to an indicator specifies that each real unit increase or decrease in the latent variable's value results in a corresponding unit increase or decrease in the indicator's value. It is hoped a good indicator has been chosen for each latent, but the 1.0 values do not signal perfect measurement because this model also postulates that there are other unspecified entities causally impacting the observed indicator measurements, thereby introducing measurement error. This model postulates that separate measurement errors influence each of the two indicators of latent intelligence, and each indicator of latent achievement. The unlabeled arrow pointing to academic performance acknowledges that things other than intelligence can also influence academic performance.]]

'''Structural equation modeling''' ('''SEM''') is a diverse set of methods used by scientists doingfor both observational and experimental research. SEM is used mostly in the social and behavioral sciencesscience fields, but it is also used in epidemiology,<ref name="BM08">{{cite book | doi=10.4135/9781412953948.n443 | chapter=Structural Equation Modeling | title=Encyclopedia of Epidemiology | date=2008 | isbn=978-1-4129-2816-8 }}</ref> business,<ref name="Shelley06">{{cite book | doi=10.4135/9781412939584.n544 | chapter=Structural Equation Modeling | title=Encyclopedia of Educational Leadership and Administration | date=2006 | isbn=978-0-7619-3087-7 }}</ref> and other fields. A common definition of SEM is, difficult"...a withoutclass referenceof methodologies that seeks to technicalrepresent languagehypotheses about the means, butvariances, and covariances of observed data in terms of a goodsmaller startingnumber placeof is'structural' theparameters namedefined itselfby a hypothesized underlying conceptual or theoretical model,"<ref>{{Cite web |title=Structural Equation Modeling - an overview {{!}} ScienceDirect Topics |url=https://www.sciencedirect.com/topics/neuroscience/structural-equation-modeling#:~:text=Structural%20equation%20modeling%20can%20be,underlying%20conceptual%20or%20theoretical%20model. |access-date=2024-11-15 |website=www.sciencedirect.com}}</ref>.

SEM involves a model representing how various aspects of some [[phenomenon]] are thought to [[Causality|causally]] connect to one another. Structural equation models often contain postulated causal connections among some latent variables (variables thought to exist but which can't be directly observed). Additional causal connections link those latent variables to observed variables whose values appear in a data set. The causal connections are represented using ''[[equation]]s'' but the postulated structuring can also be presented using diagrams containing arrows as in Figures 1 and 2. The causal structures imply that specific patterns should appear among the values of the observed variables. This makes it possible to use the connections between the observed variables' values to estimate the magnitudes of the postulated effects, and to test whether or not the observed data are consistent with the requirements of the hypothesized causal structures.<ref name="Pearl09">Pearl, J. (2009). Causality: Models, Reasoning, and Inference. Second edition. New York: Cambridge University Press.</ref>