A Framework of Statistical Tests For Comparing Mean and Covariance Structure Models

Area of Science:

• Statistics
• Psychometrics
• Structural Equation Modeling

Background:

• Statistical comparison of nested mean and covariance structure models is established.
• Tests for non-nested models are less developed and often lack accessibility.
• Existing non-nested model tests are not integrated into common maximum likelihood estimation frameworks.

Purpose of the Study:

• To develop a general statistical framework for comparing non-nested mean and covariance structure models.
• To unify concepts of model equivalence, relation, and comparison.
• To provide an accessible and broadly applicable method within maximum likelihood estimation.

Main Methods:

• Building upon Vuong's (1989) general theory and Raykov & Penev's (1999) techniques.
• Developing a unified paradigm for statistical testing of competing models.
• Integrating hierarchical and non-hierarchical model comparisons.

Main Results:

• A general statistical framework for comparing mean and covariance structure models is presented.
• The framework accommodates both nested and non-nested models.
• Key aspects of model comparison are unified, enhancing accessibility.

Conclusions:

• The proposed framework offers a unified and accessible approach to statistical model comparison.
• It extends existing methods to non-nested models within maximum likelihood estimation.
• This work facilitates more robust statistical analyses in structural equation modeling.