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Direct and Implied Covariance Patterns

You have seen how you can use PROC CALIS to test covariance patterns directly. Basically, you can specify the parameters
in the covariance and mean matrices directly by using the MSTRUCT modeling language, which is invoked by the MSTRUCT statement.
You can also use the COVPATTERN=
option to test some built-in covariance patterns in PROC CALIS. To handle more complicated covariance and mean structures
that are products of several model matrices, you can use the COSAN modeling language. The COSAN modeling language is too powerful
to consider in this introductory chapter, but see the COSAN
statement and the section The COSAN Model in ChapterĀ 29: The CALIS Procedure.

This section considers the fitting of patterned covariances matrix directly by using the MSTRUCT and the MATRIX statements
or by the COVPATTERN= option. However, in most applications of structural equation modeling, the covariance patterns are not
specified directly but are implied from the linear structural relationships among variables. The next few sections show how
you can use other modeling languages in PROC CALIS to specify structural equation models with implied mean and covariance
structures.