Testing structural equation models: The effect of kurtosis

The Satorra Bentler (SB) and the Browne ADF chi-square statistics are used for testing structural equation models with non-normal data. The relationships between the SB and ADF statistics and kurtosis are developed and it is shown that the weighted deviations of the "population" true second-order moments and the fitted second-order moments for these statistics tend to decrease with increasing kurtosis if the model does not hold. The results predict that high kurtosis can lead to loss of power. The results are obtained without simulation.