TABLE 2.
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 | ||
|
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 | |
|
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 | ||
|
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.