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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>{{Citationcite |last1=Bollenjournal |first1=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|doi=10.1007/978-94-007-6094-3_15 |url-access=subscription }}</ref> The use of experimental designs may address some of these doubts.<ref>{{Citecite journal |last1=Ng |first1=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 |title=Social connectedness as a mediator for horticultural therapy's biological effect on community-dwelling older adults: Secondary analyses of a randomized controlled trial |url=https://doi.org/10.1016/j.socscimed.2021.114191 |journal=Social Science & Medicine |date=September 2021 |volume=284 |pages=114191 |doi=10.1016/j.socscimed.2021.114191 |pmid=34271401 |issn=0277-9536|url-access=subscription }}</ref>
Today, SEM forms part of a 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.
* Copulas {{citation needed|date=March 2024}}
* Deep Path Modelling <ref name="Ing2024"/>
* Exploratory Structural Equation Modeling <ref>{{Citecite journal |last1=Marsh |first1=Herbert W. |last2=Morin |first2=Alexandre J.S. |last3=Parker |first3=Philip D. |last4=Kaur |first4=Gurvinder |date=2014-03-28 |title=Exploratory Structural Equation Modeling: An Integration of the Best Features of Exploratory and Confirmatory Factor Analysis |url=https://www.annualreviews.org/doi/10.1146/annurev-clinpsy-032813-153700 |journal=Annual Review of Clinical Psychology |languagedate=en28 March 2014 |volume=10 |issue=1 |pages=85–110 |doi=10.1146/annurev-clinpsy-032813-153700 |pmid=24313568 |issn=1548-5943|url-access=subscription }}</ref>
* Fusion validity models<ref name="HEH19">{{doi|10.3389/psyg.2019.01139|doi-access=free}}{{dead link}}</ref>
* [[Item response theory]] models {{citation needed|date=July 2023}}
* [[Latent class models]] {{citation needed|date=July 2023}}
* Random intercepts models {{citation needed|date=July 2023}}
* Structural Equation Model Trees {{citation needed|date=July 2023}}
* Structural Equation [[Multidimensional scaling]]<ref>{{Citecite journal |last1=Vera |first1=José Fernando |last2=Mair |first2=Patrick |date=2019-09-03 |title=SEMDS: An R Package for Structural Equation Multidimensional Scaling |url=https://www.tandfonline.com/doi/full/10.1080/10705511.2018.1561292 |journal=Structural Equation Modeling: A Multidisciplinary Journal |languagedate=en3 September 2019 |volume=26 |issue=5 |pages=803–818 |doi=10.1080/10705511.2018.1561292 |issn=1070-5511|url-access=subscription }}</ref>
== Software ==
Structural equation modeling programs differ widely in their capabilities and user requirements.<ref>{{Citecite journal |lastlast1=Narayanan |firstfirst1=A. |date=2012-05-01 |title=A Review of Eight Software Packages for Structural Equation Modeling |url=https://doi.org/10.1080/00031305.2012.708641 |journal=The American Statistician |date=May 2012 |volume=66 |issue=2 |pages=129–138 |doi=10.1080/00031305.2012.708641 |s2cid=59460771 |issn=0003-1305|url-access=subscription }}</ref> Below is a table of available software.
{| class="wikitable sortable"
<!--<ref name="Boslaugh2008">{{cite book |doi=10.4135/9781412953948.n443 |chapter=Structural Equation Modeling |title=Encyclopedia of Epidemiology |year=2008 |isbn=978-1-4129-2816-8 |last1=Boslaugh |first1=Sarah |last2=McNutt |first2=Louise-Anne |hdl=2022/21973 }}</ref> -->
<ref name="Ing2024">{{cite journal |title=Integrating Multi-Modal Cancer Data Using Deep Latent Variable Path Modelling |author=Alex James Ing, Alvaro Andrades, Marco Raffaele Cosenza, Jan Oliver Korbel |journal=bioRxiv |date=2024-06-13 |url=https://www.biorxiv.org/content/10.1101/2024.06.13.598616v1 |doi=10.1101/2024.06.13.598616 |doi-access=free }}</ref>
}}
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