A Statistical Test for Comparing Nonnested Covariance Structure Models.

While statistical procedures are well known for comparing hierarchically related (nested) covariance structure models, statistical tests for comparing nonhierarchically related (nonnested) models have proven more elusive. While isolated attempts have been made, none exists within the commonly used maximum likelihood estimation framework, thereby compromising these methods accessibility and general applicability. The current work builds on a distance measure originally proposed by C. Rao (1945; 1949), and its application to distances between covariance structure models (A. Kumar and S. Sharma, 1999), thereby proposing a method for conducting a statistical test of such distances in order to assess formally the distinctness between modelsnested or nonnested. An illustration is presented, and simulation evidence is provided to validate the performance of the proposed method. Two appendixes contain an illustration of the model for data generation and a program to compute distances between covariance matrices. (Contains 1 table, 2 figures, and 28 references.) (Author/SLD)