Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure

Area of Science:

• Statistics
• Quantitative Psychology

Background:

• Traditional methods often focus on implied covariance structures from functional relationships.
• A need exists for flexible approaches to directly model covariance patterns.

Purpose of the Study:

• To demonstrate the utility and flexibility of structural equation modelling (SEM) for fitting direct covariance patterns.
• To illustrate the application of the MSTRUCT modelling language within SAS/STAT for covariance structure analysis.

Main Methods:

• Utilized the MSTRUCT modelling language in SAS/STAT (version 9.22 or later) for direct covariance pattern specification.
• Applied SEM framework to test basic patterns (sphericity, compound symmetry, multiple-group) and complex structures (circumplex, composite direct product).
• Incorporated numerical and computational examples for illustration.

Main Results:

• SEM provides a general and flexible framework for modelling direct covariance and correlation patterns.
• MSTRUCT syntax facilitates direct specification of covariance elements and parameters.
• Successfully illustrated the testing of various basic and complex covariance and correlation structures.

Conclusions:

• The SEM approach is a powerful and adaptable tool for analysing direct covariance and correlation structures.
• The MSTRUCT syntax, combined with SAS macros, offers an accessible interface for complex structure fitting, even with large datasets.