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[[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 these analytic techniques help us break down complex concepts and understand causal processes, but the complexity of the models can introduce substantial variability in the results depending on the presence or absence of conventional control variables, the sample size, and the variables of interest.<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> The use of experimental designs may address some of these doubts.<ref>{{Cite journal |last=Ng |first=Ted Kheng Siang |last2=Gan |first2=Daniel R.Y. |last3=Mahendran |first3=Rathi |last4=Kua |first4=Ee Heok |last5=Ho |first5=Roger C-M |date=September 2021
Today, SEM forms the basis of [[machine learning]] and (interpretable) [[Neural network (machine learning)|neural networks]]. Exploratory and confirmatory factor analyses in classical statistics mirror unsupervised and supervised machine learning.
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