TABLE 2.

Univariate Skewness and Kurtosis of Observed Exogenous Variables of Previous Studies

Coenders et al. (2008)		Theoretical Values		Simulation Values
		Median |Skewness|	Median Kurtosis	Median |Skewness|	Median Kurtosis
ξ1 and ξ2 ~ Normal		0	0	0.000	0.005
${\xi }_1:{\chi }_9^2$	Low correlation	0.898	1.560	0.892	1.546
ξ2: Skew.=1.1,	High correlation	0.864	1.441	0.864	1.437
Kurt.=1.9
Marsh et al. (2004)
ξ and δ ~ Normal	rξ1, ξ2 = 0.3	0	0	−0.001	0.002
	rξ1, ξ2 = 0.7	0	0	0.002	−0.001
ξ: Skew.=0, Kurt.= −0.69	rξ1, ξ2 = 0.3	0	−0.479	0.001	−0.481
δ ~ Uniform	rξ1, ξ2 = 0.7	0	−0.478	0.001	−0.479
ξ: Skew.=0.86, Kurt.=1.12	rξ1, ξ2 = 0.3	0.713	0.790	0.717	0.801
$\mathbf{\delta }~{\chi }_6^2$	rξ1, ξ2 = 0.7	0.715	0.791	0.716	0.801
Wall & Amemiya (2001)
ξ and δ ~ Normal		0	0	−0.001	0.003
ξ and δ ~ Uniform		0	−0.750	−0.001	−0.751
$\mathbf{\delta }~{\chi }_9^2$		0.730	0.833	0.727	0.813
Klein & Moosbrugger (2000), Klein & Muthén (2007), and Klein et al. (2009)
ξ and δ ~ Normal		0	0	−0.000	−0.002
ξ1: Skew.= −2, Kurt.=6,		0.519	1.083	0.515	1.070
ξ2: Skew.=1.5, Kurt.=5, δ ~ Normal
ξ1: Skew.= 2, Kurt.=6,		0.519	1.083	0.524	1.057
ξ2: Skew. = 1.5, Kurt. =5, δ ~ Normal

Note. |Skewness| means skewness taking absolute values. Skew. means skewness. Kurt. means excess kurtosis. Theoretical values were calculated based on Mattson (1997). Simulation values were calculated using one randomly generated dataset of size 1,000,000.