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

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1.1 Model Formulation

In SEM, researchers begin with the specification of a model to be estimated. There are different approaches to specify a model of interest. The most intuitive way of doing this is to describe one's model by path diagrams first suggested by Wright (1934). Path diagrams are fundamental to SEM since it allows researchers to formulate the model of interest in a direct and appealing fashion. The diagram provides a useful guide for clarifying a researcher's ideas about the relationships among variables and they can be directly translated into corresponding equations for modeling. Several conventions are used in developing a SEM model path diagram, in which the observed variables (also known as measured variables, manifest variables, or indicators) are presented in boxes, and latent variables or factors are in circles or ovals. Relationships between variables are indicated by lines; lack of line connecting variables implies that no direct relationship has been hypothesized between the corresponding variables. A line with a single arrow represents a hypothesized direct relationship between two variables, with the head of the arrow pointing toward the variable being influenced by another variable. The bidirectional arrows refer to relationships or associations, instead of effects, between variables.

An example of a hypothesized general structural equation model is specified in the path diagram shown in Figure 1.1. As mentioned above, the latent variables are enclosed ...

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