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I'm currently looking into causal modeling (according to Pearl) and I'm having trouble understanding what exactly sets apart structural causal models (SCM) and structural equation models (SEM).

The only info I found to far is that for SCM [1]

The central idea is to exploit the invariant characteristics of structural equations without committing to a specific functional form.

Is that really, in essence, all that differentiates SCM and SEM?

Does that mean that everything we can do with SCM, we can also apply to SEM?

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2836213/

Johann
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2 Answers2

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It is the same thing, however SEM is not always interpreted as a causal model. Path model might be another closely related term. From Peters et a;. Elements of causal inference (which is free, if you want to read more about):

The idea of autonomy and invariance is deeply engrained in the concept of structural equation models (SEMs) or SCMs. We prefer the latter term, since the term SEM has been used in a number of contexts where the structural assignments are used as algebraic equations rather than assignments.

I am sure Pearl discuss it as well, but I don't have his book on hand

rep_ho
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I am late but anyways.
This is taken from the book Causality by Judea Pearl(2nd edition),Page 27.

A set of equations in the form of (1.40) and in which each equation represents an autonomous mechanism is called a structural model (a.k.a SEM); if each variable has a distinct equation in which it appears on the left-hand side (called the dependent variable), then the model is called a structural causal model or a causal model for short.

Equation 1.40,
X= some non-parametric function of (X1,...Xn,Ui), where (X1,..Xn) influence X and Ui represents error term.

If it is not clear let me know will expand on it.

yo wa
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