By Gregory R. Hancock, Ralph O. Mueller
Subsidized by way of the yankee academic study Association's exact curiosity crew for tutorial Statisticians This quantity is the second one variation of Hancock and Mueller's highly-successful 2006 quantity, with all the unique chapters up-to-date in addition to 4 new chapters. the second one version, just like the first, is meant to function a didactically-oriented source for graduate scholars and study pros, masking a vast variety of complex issues usually no longer mentioned in introductory classes on structural equation modeling (Sem). Such issues are very important in furthering the knowledge of foundations and assumptions underlying Sem in addition to in exploring Sem, as a possible device to deal with new varieties of learn questions that may now not have arisen in the course of a primary path. Chapters concentrate on the transparent clarification and alertness of subject matters, instead of on analytical derivations, and include fabrics from well known Sem software program.
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Extra info for Structural Equation Modeling: A Second Course (2nd ed.)
Vp)′ to represent a set of p observed variables with a population covariance matrix Σ and sample covariance matrix S, θ the vector of parameters of a proposed structural equation ˆ(q) the population covariance matrix implied by the model model M, and S ˆ(q) for some q, the basis for most M at θ. Under the null hypothesis H0 : S = S fit indices used in SEM is the discrepancy between the sample covariance matrix of the observed variables (S) and the covariance matrix of these variˆ ). , S Using numerical algorithms, parameter estimates describing the structure ˆ of a model M are generated that produce an implied covariance matrix S The Problem of Equivalent Structural Models 5 with least discrepancy from the observed sample covariance matrix S.
L. HERSHBERGER and G. A. MARCOULIDES Strategies for Identifying Equivalent Models Two general categories of strategies for approaching the problem of equivalent models that have been considered in the literature are those that occur either before data collection or after data collection. It is our opinion that researchers should be strongly urged to at least try and detect models that are equivalent to one’s theoretical model before hefty resources have been spent on a particular project. Thus, an ideal time for such an activity would be before data collection begins, when the study is still in the planning stage.
Breckler, 1990; Hershberger, 1994; Lee & Hershberger, 1990; Levy & Hancock, 2007; Luijben, 1991; MacCallum, Wegener, Uchino, & Fabrigar, 1993; Marcus, 2002; McDonald, 2002; Raykov, 1997; Raykov & Marcoulides, 2001, 2007; Raykov & Penev, 1999; Williams, Bozdogan, & Aiman-Smith, 1996). Additional developments in the study of model equivalence have also arisen from graph theorists’ attempts to formulate a mathematical basis for causal inferences (Pearl, 2009). This is not surprising given the many shared characteristics of graph models and structural equation models.