Stata SEM Covariance Structure

Covariance structures are a major component to fitting an SEM. There are several tricky differences between -sem- and -gsem- in this category.

Default and Implicit Behaviors

Error variables are assumed to be independent.

Fixing Parameters

To specify that two variables have non-zero covariance, use the cov option. This is mainly useful for error variables, since the default behavior is to assume independence.

... (x1 <- X) (x2 <- X) (x3 <- X), cov(e.x1*e.x2)

The option can be repeated to indicate that other variables also covary. For example, add cov(e.x2*e.x3) to the above.

On the other hand, to specify that two variables have zero covariance, try:

... cov(Y*X@0)

-gsem- disallows configuring the covariances of observed exogenous variables.

Structure

Sometimes, the simplest way to declare covariances is with a systemic statement. The alternate covstructure option takes two arguments: a variable list and a structure name.

Valid structure names are:

• unstructured = all unrestructed
• diagonal = variances unrestricted, zero covariance
• exchangeable = equal (co)variance
• identity = equal variance, zero covariance
• zero = zero (co)variance

There are a few keywords that can be taken as a variable list on this option.

• _Ex = all exogenous variables

  • disallowed in -gsem-

• _OEx = all observed exogenous variables

  • disallowed in -gsem-

• _LEx = all latent exogenous variables

• e._En = all error variables

• e._OEn = all error variables associated with observed exogenous variables

• e._LEn = all error variables associated with latent exogenous variables

..., covstructure(_oexogenous, unstructured)

This option, like cov, can be repeated.

CategoryRicottone