Running head: Test For Nonnested Models 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) Reproductions supplied by EDRS are the best that can be made from the original document Test For Nonnested Models 1 Running head: Test For Nonnested Models A Statistical Test For Comparing Nonnested Covariance Structure Models Roy Levy and Gregory R. Hancock University of Maryland, College Park [Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL, April 2003] U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) GI This document has been reproduced as received from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY