In previous sections of this chapter we have discussed and demonstrated how to conduct power analysis and estimate an appropriate sample size for a SEM model in terms of the ability to detect nonzero model parameters, such as factor covariance, slope of outcome growth trajectory, and effect size of predictor variable. Some recently developed approaches of power analysis for SEM, such as MacCallum, Browne, and Sugawara's method (MacCallum, Browne, and Sugawara, 1996) and Kim's method (Kim, 2005), have been developed to calculate power of a given sample size or to estimate an appropriate sample size to achieve a desired power (e.g., 0.80) based upon testing the model's overall fit. In these approaches a noncentrality parameter is defined as a function of sample size and a specific model fit index, and the model fit index plays the role of effect size. MacCallum, Browne, and Sugawara's method computes power by defining the null hypothesis in terms of model fit index RMSEA. The method was extended later by MacCallum and Hong (1997) to use the goodness-of-fit index (GFI) and the adjusted goodness-of-fit index (AGFI) for power and sample size estimation though their results show using GFI is not trustable. Kim (2005) has developed some useful equations to calculate sample size for a given power based on model fit indices, such as CFI, RMSEA, Steiger's , and MacDonald's fit index. Kim's method allows researchers to calculate ...

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