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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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Chapter 2

Confirmatory Factor Analysis

As discussed in Chapter 1, the key difference between path analysis and SEM is that the former analyzes relationships among observed variables, while the latter focuses on relationships among latent variables (latent constructs or factors). In order to conduct SEM, latent variables/factors must be defined appropriately using a measurement model before they are incorporated into a SEM model. Latent variables are unobservable and must be indirectly estimated from observed indicators/items. Traditionally, the exploratory factor analysis (EFA) technique is applied to assess factorial structure of a measuring instrument (Mulaik, 1972; Gorsuch, 1983; Comrey and Lee, 1992). EFA extracts unobserved factors from data without specifying the number of factors or without determining how the measurement items or the observed indicators are loaded onto which specific factors, instead, factors are defined after they are extracted. In other words, EFA is applied in situations where the factorial structure or the dimensionality of an instrument for a given population is unknown, usually in the situation of developing new instruments. In contrast, confirmatory factor analysis (CFA) (Bollen, 1989a; Brown, 2006) is used in situations where one has some knowledge of the dimensionality of the variables under study either based on a theory or empirical findings. The factors are theoretically defined, and how specific indicators or measurement items are loaded onto ...

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