# A First Course in Structural Equation Modeling, 2nd edition by Tenko Raykov, George A. Marcoulides

By Tenko Raykov, George A. Marcoulides

During this ebook, authors Tenko Raykov and George A. Marcoulides introduce scholars to the fundamentals of structural equation modeling (SEM) via a conceptual, nonmathematical technique. For ease of knowing, the few mathematical formulation provided are utilized in a conceptual or illustrative nature, instead of a computational one. that includes examples from EQS, LISREL, and Mplus, a primary path in Structural Equation Modeling is a wonderful beginner’s advisor to studying how one can arrange enter records to slot the main primary kinds of structural equation types with those courses. the elemental principles and strategies for accomplishing SEM are self sustaining of any specific software program. Highlights of the second one variation comprise: • evaluate of latent switch (growth) research versions at an introductory point • insurance of the preferred Mplus software • up-to-date examples of LISREL and EQS • A CD that includes all the text’s LISREL, EQS, and Mplus examples. a primary path in Structural Equation Modeling is meant as an introductory e-book for college kids and researchers in psychology, schooling, enterprise, drugs, and different utilized social, behavioral, and wellbeing and fitness sciences with constrained or no past publicity to SEM. A prerequisite of simple statistics via regression research is usually recommended. The e-book usually attracts parallels among SEM and regression, making this earlier wisdom important.

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Alternative hypotheses of difference or change), SEM is pragmatically concerned with finding a model that does not contradict the data. That is, in an empirical SEM session, one is typically 40 1. FUNDAMENTALS OF STRUCTURAL EQUATION MODELING interested in retaining a proposed model whose validity is the essence of a pertinent null hypothesis. In other words, statistically speaking, when using SEM one is usually ‘interested’ in not rejecting the null hypothesis. However, recall from introductory statistics that not rejecting a null hypothesis does not mean that it is true.

The number of nonredundant elements in its matrix S(g) or S) is generated with as many unknowns as there are model parameters—that is, 21, as there are 21 asterisks in Fig. 6. Hence, one can conceive of the process of fitting a structural equation model as solving a system of possibly nonlinear equations. , the corresponding expression of model parameters at the same position in the model reproduced covariance matrix. Therefore, fitting a structural equation model is conceptually equivalent to solving this system of equations obtained according to the consequences of the model, whereby this solution is sought in an optimal way that is discussed in the next section.

This law is quite similar to the rule of disclosing brackets used in elementary algebra. Indeed, to apply Law 2 all one needs to do is simply determine each resulting product of constants and attach the covariance of their pertinent variables. Note that the right-hand side of the equation of this law simplifies markedly if some of the variables are uncorrelated, that is, one or more of the involved covariances is equal to 0. 3 Using Laws 1 and 2, and the fact that Cov(X,Y) = Cov(Y,X) (since the covariance does not depend on variable order), one obtains the next equation, which, due to its importance for the remainder of the book, is formulated as a separate law: 3 Law 2 reveals the rationale behind the rules for determining the parameters for any model once the definition equations are written down (see section “Rules for Determining Model Parameters” and Appendix to this chapter).