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# 2.5 Higher Order CFA Model

In a CFA model with multiple factors, the variance/covariance structure of the factors may be further analyzed by introducing second- order factors into the model if (1) the first- order factors are substantially correlated with each other, and (2) the second- order factors may be hypothesized to account for the variation among the first- order factors. For example, the three factors (SOM, DEP, ANX) of the BSI- 18 scale in our example are highly correlated with each other, and theoretically speaking, there may exist a more generalized construct (e.g., general severity of mental health) that underlies depression, anxiety, and somatization; as such, a second- order factor (e.g., general severity) may be specified to account for the covariation among the three first- order factors. If there are multiple second- order factors and a covariance structure exists among the second- order factors, then third- order factors might be considered. This kind of model is called a higher order or hierarchical CFA model and was first introduced by Jö reskog (1971a). Though the level of hierarchical orders in higher order factor analysis is unlimited in principle, usually a second- order CFA model is applied in real research.

Let us use the BSI- 18 to demonstrate the second- order CFA model shown in Figure 2.4. This model consists of two factorial structures: (1) the observed indicators (e.g., the BSI- 18 items) are indicators of the three first- order factors (i.e., SOM, ...

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