= Stata SEM Groups =

The '''`group`''' option is available only in `-gsem-`.

<<TableOfContents>>

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== Default and Implicit Behaviors ==

When groups are specified, paths are implicitly expanded such that the following two are equivalent. (Supposing that `gid` has 3 levels.)

{{{
... (x1 <- X) (x2 <- X), cov(e.x1*e.x2@c1) group(gid)
}}}

{{{
... (1: y <- x1) (2: y <- x1) (3: y <- x1) ///
    (1: y <- x2) (2: y <- x2) (3: y <- x2) ///
    cov(1: e.x1*e.x2@c1) cov(2: e.x1*e.x2@c1) cov(3: e.x1*e.x2@c1) ///
    group(gid)
}}}

If a group's path is overriden like:

{{{
... (y <- x) (2: y <- x@c1) (3: y <- x@c1), ///
    group(gid)
}}}

Then the path interpretter will see:

{{{
... (1: y <- x) (2: y <- x) (3: y <- x) (2: y <- x@c1) (3: y <- x@c1), ///
    group(gid)
}}}

The path interpretter will combine the duplicative paths automatically into:

{{{
... (1: y <- x) (2: y <- x@c1) (3: y <- x@c1), ///
    group(gid)
}}}

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== Covariance Structures ==

To constrain variance to be equal across groups, try:

{{{
... (x1 <- X), ///
    var(e.x1@c1) ///
    group(gid)
}}}

This expands out to:

{{{
... (1: x1 <- X) (2: x1 <- X) (3: x1 <- X), ///
    var(1: e.x1@c1) var(2: e.x1@c1) var(3: e.x1@c1) ///
    group(gid)
}}}

Which precisely achieves that constraint.

To instead constrain variance to be equal across some groups, try:

{{{
... (x1 <- X), ///
    var(e.x1@c2) var(2: e.x1@c1) var(3: e.x1@c1) ///
    group(gid)
}}}

(Supposing still that `gid` has 3 levels.) As `c2` only appears once in the expanded and combined interpretation, it is effectively unconstrained.



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CategoryRicottone