A First Course in Structural Equation Modeling by Tenko Raykov

By Tenko Raykov

This publication is designed to introduce scholars to the fundamentals of structural equation modeling via a conceptual, nonmathematical process. The few mathematical formulation incorporated are utilized in a conceptual or illustrative nature, instead of a computational one. The booklet beneficial properties examples from LISREL and EQS. consequently, the ebook can be used as a starting consultant to studying the right way to manage enter documents to slot the main usual kinds of structural equation versions with those courses. meant as an advent for graduate scholars or researchers in psychology, schooling, company, and different utilized social and health and wellbeing sciences. the one prerequisite is a easy records path.

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Example text

The first corresponds to the number (index) of the dependent variable, and the second corresponds to the number of the independent variable in the pertinent equation. For example, in the fifth equation of Equations 9, Y5 = λ52η2 + ε5, the factor loading λ has two subscripts; the first corresponds to the dependent variable (Y5), and second is the index of the latent variable (η2). Independent variable variances and covariances have as subscripts the indices of the variables they are related to. Therefore, every variance has the index of the variable it belongs to as page_55 Page 56 Figure 8.

Conveying inforpage_46 Page 47 mation about the model begins with a listing of each observed and unobserved variable as well as the way they relate to one another. It is just as important that the program be informed about the parameters of the model. As discussed in the previous chapter, each program has in its memory the formal way the model reproduced matrix Σ can be obtained, once it is informed about the model and its parameters. Thus, as illustrated in chapter 1, one must first draw the path diagram of the model and then define all the necessary parameters using Rules 1 to 6 before proceeding with the computer analysis.

Thus, all that is provided by overall measures of model fit is a summary picture of how well the proposed model fits the whole analyzed matrix, but no information is provided about how well the model reproduces the individual elements of that matrix. To counteract this possibility, two types of residuals can be examined in most SEM models. The unstandardized residuals index the amount of unexplained covariance and variance in terms of the original metric of the raw data. However, if the original metric of the raw data is quite different across measured variables, it is impossible to examine residuals and deterpage_42 Page 43 mine which are large and which are small.

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