A framework of statistical tests for comparing mean and covariance structure models

Although statistical procedures are well-known for comparing hierarchically related (nested) mean and covariance structure models, statistical tests for comparing non-hierarchically related (nonnested) models have proven more elusive. Although isolated attempts at statistical tests of non-hierarchically related models have been made, none exist within the commonly used maximum likelihood estimation framework, thereby compromising these methods' accessibility and general applicability. Building on general theory developed by Vuong (1989) and techniques for establishing the relation between covariance structure models (Raykov & Penev, 1999), this work provides a general paradigm for conducting statistical tests on competing mean and covariance structure models. The proposed framework is appropriate for hierarchically related models as well as non-hierarchically related models. In developing the structure of the framework, key aspects of model equivalence, relation, and comparison are unified. An illustration demonstrates its use.