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I've often seen it mentioned that while SEM is generally used in relation to non-experimental designs it can be used in relation to experimental designs too. For example, Kline (2016) writes that

Most applications of SEM are in nonexperimental designs, but data from experimental or quasi-experimental designs can be analyzed, too. (p. 10)

I understand that a major point of SEM is to in some sense disconfirm causal hypotheses, and that with an experimental design one might be able to make causal inferences much more simply.

However, I am wondering under what circumstances it does, and does not, make sense to apply SEM to experimental designs. Are there rules of thumb that can tell me when applying SEM to an experimental design might be more or less advantageous?

Kline, R. B. (2016). Principles and practice of structural equation modeling. Guilford publications.

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The advantages of SEM over regression are to model multiple outcomes and to model latent variables. If you have either of those in an experiment, then you should use SEM.

For example, consider a mediation analysis. You have multiple outcomes (the mediator and the final outcome), and you can model those relationships using a system of simultaneous equation models. Assuming you do work to remove confounding of the mediator-outcome relationship, you can use SEM to make a causal mediation claim and estimate the causal mediation effects. There are other ways to estimate such effects (e.g., using conditional process or causal mediation techniques), but SEM is a straightforward method that follows directly from the research question.

Consider also an experiment with a latent outcome measured with a scale. You can use SEM to model the relationship between the experimental manipulation and the latent variable and between the latent variable and the indicators. You can then make a causal claim about the effect of the manipulation of the latent variable. SEM is the only framework that allows you to perform such an analysis validly.

Remember that SEM is not just about assessing causal hypotheses but also estimating specific effects. In experiments, one is often interested in estimating specific effects, and SEM provides a convenient and general framework for doing so.

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  • $\begingroup$ You mention that I should use SEM if I am going to "model multiple outcomes" or "model latent variables". Do you think it's fair to say that if neither of those conditions apply, there will be no advantage (although no harm either) in doing SEM? $\endgroup$ Aug 21, 2019 at 22:05
  • $\begingroup$ There's no other way to use it that is distinct from regression. If you're not doing one of those things, you're doing regression. How else could you think to use it in the context of an experiment? $\endgroup$
    – Noah
    Aug 21, 2019 at 22:39
  • $\begingroup$ I can't think of another way of using it in the context of an experiment, but in part I was wondering if expressing a linear regression as a special case of SEM would have advantages or disadvantages. I was initially thinking that it wouldn't make any difference, but searching a bit more I see there is an answer here from StasK that convincingly argues against expressing regression as a special case of SEM. $\endgroup$ Aug 21, 2019 at 23:20
  • $\begingroup$ StasK's argument is that SEM software shouldn't be used because software focused on regression provides more diagnostics relevant to regression. If all you care about is a treatment effect and its significance, there is no benefit to using an SEM or a regression software to perform the analysis. This is a bit similar to asking whether one should use a t-test or regression to compare group means; it doesn't matter, except that regression can do more, but if you don't want to do more, then one should do whichever is easiest for them. There is no theoretical reason for a preference. $\endgroup$
    – Noah
    Aug 21, 2019 at 23:45

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