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I have been reading about SEM and latent variables. Now it seems usually that a latent variable is a function of observed manifest variables. But is there a SEM where a latent variable is a predctor of an outcome? So in my example, we have outcomes (y1, y2), observed independent variables (x1, x2), one latent l1, and two errors (e1, e2), over the same indviduals.

y1 = x1 + l1 + e1

y2 = x2 + l1 + e2

Would that work in lavaan?

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  • $\begingroup$ Indicators of a latent variable are the outcomes. The causal theory behind a common-factor model is that there is a common (set of) cause(s) of the "manifest" indicators. So your 2-equation system is in fact a 2-indicator factor model. $\endgroup$
    – Terrence
    Commented Mar 24, 2023 at 21:25

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The outcome variable in SEM most definitely can be a latent variable. A latent variable is just a bunch of observed variables together to represent a construct (usually a theory). I would familiarize with factor analysis first, before you dive into SEM. SEM is used when you want to use a latent variable (a factor) in a path analysis, usually (said with caution here) to attempt to show causality.

Yes, it can be a predictor. A latent variable can used anywhere in a SEM model.

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  • $\begingroup$ The post asked whether the latent variable can be a predictor, so this response doesn't really answer the question. $\endgroup$
    – Terrence
    Commented Mar 24, 2023 at 21:24
  • $\begingroup$ Thanks for clarifying. Added answer to response. $\endgroup$
    – nick
    Commented Mar 25, 2023 at 16:30

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