Does the ADF fit function decrease when the kurtosis increases?

In this study we demonstrate how the asymptotically distribution-free (ADF) fit function is affected by (excessive) kurtosis in the observed data. More specifically, we address how different levels of univariate kurtosis affect fit values (and therefore fit indices) for misspecified factor models. By using numerical calculation, we show (for 13 factor models) that the probability limit F(0) of F empty set for the ADF fit function decreases considerably as the kurtosis increases. We also give a formal proof that the value of F(0) decreases monotonically with the kurtosis for a whole class of structural equation models.