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 of Chapter 27: 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.