5
$\begingroup$

I recently saw a case where someone fit a SEM with 20 latent variables (with many indicators each) predicting a single latent variable (of several indicators), and suggested it was evidence for some causal/theoretical model and called it a day. There were no indirect paths and they did not have multiple outcomes/DVs (i.e., multivariate). They also did not test multiple possible SEMs. This seems not so useful to me and does not seem to reflect the usefulness of SEM over regression. My understanding of SEM and it's advantages over multiple regression is:

  • Model Comparison: Contraining paths, or fixing paths to other estimates, or specifying other possible models to see which is better fit to the data
  • Multivariate: SEM, unlike multiple regression, can simultaneously estimate multiple outcomes
  • Combining Measurement and Structural Model: You can simultaneously estimate latent variables and the causal relationships among them
  • Error-Free: SEM uses latent variable models to account for measurement error

This is my cursory understanding of some of the major advantages of SEM over multiple regression for specific applications. With that being said, if someone takes a set of 20 questionnaires, puts them in an SEM as 20 latent variables, predicting another questionnaire as a latent variable, and stops there, that strikes me as providing no advantages over multiple regression. It is involving no model comparison (no constraining of paths, no testing of alternative models) and it is not multivariate (i.e., it has a single outcome). I suppose you could argue there are advantages to estimating the latent variables in the same model as the causal/path model, but I suspect this will be almost identical to estimating the means for each of these questionnaires, and estimating a linear regression model predicting the DV from the 20 IVs. Further, if you decided in advance what each of the indicators for each latent variable will be based on questionnaire they belong, it doesn’t seem that this measurement model provides all that many advantages.

I am aware of papers like this which suggest that calling multiple regression and SEM equivalent is a myth but I find this unconvincing for univariate regression cases with no model comparison. It seems like the inferences would and should be effectively identical in such a scenario.

My question broadly is-- When is there little to no advantage of SEM over multiple regression, and when is this a distinction without much of a difference? Further, when is the added obfuscation and complexity of SEM providing little benefit over a simpler, and easier to comprehend multiple regression model (e.g., the univariate case)?

References:

https://www.researchgate.net/post/What-is-the-difference-between-a-regression-analysis-and-SEM#:~:text=While%2C%20multiple%20regression%20is%20observed,based%20and%20variance%2Dbased%20methods.

http://faculty.cas.usf.edu/mbrannick/regression/SEM.html

Regression in SEM programs vs regression in statistical packages such as SPSS

https://www.quora.com/Which-is-better-regression-or-structural-equation-modeling-and-why

https://www.statisticssolutions.com/advantages-of-sem-over-regression/

https://www.youtube.com/watch?v=wHFrgp3SQMI&t=67s

$\endgroup$
1
  • $\begingroup$ "Multiple regression" is not well defined here. The overlaps include a lot of notable cases, possibly with multiple linear regressions, constraints, or derived values. For instance, the Baron Kenny test can be replicated in SEM as well as linear regression. In that way, SEM is a useful piece of software. Though latent variable models are seemingly unique to SEM, if we can call mixed effects regression "regression" even though we use EM to integrate over random effect distributions, why can't we use the same reasoning with a latent variable? $\endgroup$
    – AdamO
    Commented Nov 21, 2023 at 22:24

1 Answer 1

7
$\begingroup$

Relative to multiple regression (and assuming a single DV and only direct effects like you wrote), I see the main advantages of SEM in the possibility to test the model against the observed data (in particular: the measurement model) and that SEM corrects for measurement error. When you use regression with observed sum scores for each construct, you cannot test whether the measurement structure is adequate, and you do not correct for measurement error in the independent variables. One assumption of regression is that the independent variables are measured without error. This is probably an unrealistic assumption, at least for most social science constructs. When there is measurement error in the IVs, regression coefficients and their standard errors may be biased.

To answer your question, from this perspective, it would be OK to use regression with simple sum scores instead of SEM when you have a "proven" tau-equivalent (or Rasch/1-pl logistic IRT) measurement structure for each construct (so that a simple unweighted sum score is adequate for each construct), no cross-loadings between different constructs, and each scale's composite reliability was very close to perfect (1.0). Of course, there are other situations where you may have reasons to prefer regression (e.g., when your audience does not know or understand SEM).

$\endgroup$
2
  • 1
    $\begingroup$ Another reason to prefer regression in some cases may be sample size. Sometimes, the sample size may not be sufficient for a complex SEM with many measures and many predictors but it may be sufficient for regression. $\endgroup$ Commented Nov 18, 2023 at 14:46
  • $\begingroup$ Helpful-- Thank you! $\endgroup$
    – JElder
    Commented Nov 21, 2023 at 17:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.