Chapter 2: Factor Analysis

Path diagrams

Factor analysis models and other latent variable models are often depicted with path diagrams where most elements of the model equations are presented graphically. In a path diagram all observed variables are denoted by rectangles, and latent variables by circles. Arrows depict relationships among the variables. A double-headed arrow between two variables denotes a correlation between them, and a single-headed arrow denotes a conditional distribution (regression model) between two variables, with the arrow pointing to the dependent variable. Single-headed arrows which point to a variable without another variable at the other end of the arrow denote measurement errors (residuals); these may also be omitted from the diagram. In addition, labels and/or estimated values for some variables and/or parameters may also be included in the diagram, but these are also often omitted.

Figure 2.1 illustrates these conventions. It shows the path diagram for the two-factor confirmatory factor analysis model defined by the last set of equations on the previous page.

Figure 2.1: Theoretical model for the relationships of the constructs in the example.

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