Representing general theoretical concepts in structural equation models: the role of composite variables
 James B. Grace,
 Kenneth A. Bollen
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Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoreticallybased probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling heterogeneous concepts of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partiallyreducedform models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influence of suites of variables are often of interest.
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 Title
 Representing general theoretical concepts in structural equation models: the role of composite variables
 Journal

Environmental and Ecological Statistics
Volume 15, Issue 2 , pp 191213
 Cover Date
 20080601
 DOI
 10.1007/s1065100700477
 Print ISSN
 13528505
 Online ISSN
 15733009
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Composites
 Constructs
 Construct models
 Latent variables
 Structural equation modeling
 Theoretical concepts
 Authors

 James B. Grace ^{(1)}
 Kenneth A. Bollen ^{(2)}
 Author Affiliations

 1. U.S. Geological Survey, 700 Cajundome Blvd, Lafayette, LA, 70506, USA
 2. Department of Sociology, Odum Institute for Research in Social Science, University of North Carolina, CB 3210 Hamilton Hall, Chapel Hill, NC, 275993210, USA