Stata SEM Groups
The group option is available only in -gsem-.
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)
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.