Single-group structural model analyses
Like CFA, the structural relationships among the proposed constructs were investigated using SEM technique. Single-group SEM was conducted to test three alternative models (Figure 3.1), in order to choose the best model to explain the structural relationships among the proposed latent variables. A causal relationship is expected among goals, processes, and the three patterns of bureaucracy. To investigate these causal relationships, three models were proposed (see Figure 1). In models A and B, the relationship between the importance athletic departments place on certain goals and bureaucracy is expected to be mediated by how frequent athletic departments engage in certain processes. Model A is the fully mediated model. Model B is the partially mediated model. In model C, the direct-effects model, goals and processes directly affect the patterns of bureaucracy of athletic departments, without any mediation.
Model A has more degrees of freedom and is nested in model B. Therefore, between models A and B, a formal test of difference can be performed to test which of these two models fit the data better. C is the direct-effects model, which represents an alternative model that is not nested either in B or in A. Model C is apparently nested in B.
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But, this is this is not a fact, because when one adds a path from goals to process (to transform C in B), one changes the nature of the variables. In B, there are two endogenous variables and one exogenous variable. In C, there is one endogenous variable and two exogenous variables. Model C has fewer degrees of freedom than B and, therefore, can not be considered to be nested in this model. But C is still a valid model for comparison. To compare C to A or B, since no formal test can be conducted, I compared fit indices (CFI, RMSEA confidence intervals, and RMS) between these three models.