TABLE 8.

Simulation study 2: bias and RMSE for the latent correlation as a function of the distribution of the observed variables (skewness and kurtosis) and the sample size.

		Bias							RMSE Gain
skew/kurt	N	PML	PMLR	ULS	ULSR	MAP	Med	EAP	PML	PMLR	ULS	ULSR	MAP	Med	EAP
0/0	30	−0.065	−0.067	−0.010	−0.011	−0.003	−0.131	−0.154	100	101	99	101	116	80	77
	50	–0.019	–0.020	0.016	0.017	–0.018	−0.085	−0.092	100	101	96	98	114	85	82
	100	–0.014	–0.016	0.008	0.008	−0.051	−0.063	−0.061	100	101	94	95	116	95	92
	500	–0.002	–0.002	0.002	0.001	–0.011	–0.012	–0.013	100	101	99	100	102	101	101
0/3	30	–0.038	–0.033	0.000	0.007	0.027	−0.106	−0.130	100	100	101	98	119	80	77
	50	–0.042	–0.036	0.002	0.001	–0.037	−0.102	−0.109	100	98	97	94	108	84	81
	100	–0.007	–0.004	0.015	0.016	–0.041	−0.058	−0.056	100	94	96	91	117	95	92
	500	–0.003	–0.005	0.001	–0.002	–0.011	–0.013	–0.014	100	97	99	95	104	101	101
0/7	30	–0.043	–0.024	0.007	0.016	0.024	−0.108	−0.133	100	95	101	98	116	82	79
	50	–0.021	–0.011	0.019	0.021	–0.021	−0.085	−0.092	100	96	97	93	115	87	84
	100	–0.004	–0.004	0.018	0.013	–0.037	−0.054	−0.052	100	92	98	89	117	94	91
	500	–0.003	–0.002	0.001	0.002	–0.012	–0.013	–0.014	100	92	99	91	101	100	101
1/3	30	–0.048	–0.046	0.003	0.004	0.026	−0.110	−0.136	100	99	103	99	119	81	79
	50	–0.023	–0.018	0.016	0.019	–0.019	−0.086	−0.093	100	98	95	94	111	82	79
	100	–0.006	–0.012	0.013	0.008	–0.042	−0.055	−0.054	100	99	94	93	116	96	92
	500	0.002	–0.002	0.005	0.001	–0.006	–0.008	–0.009	100	97	99	96	103	101	101
2/7	30	–0.015	–0.009	0.033	0.029	0.064	−0.078	−0.105	100	95	99	93	114	77	74
	50	–0.017	–0.017	0.017	0.001	–0.014	−0.079	−0.086	100	94	97	94	113	87	84
	100	–0.003	–0.015	0.015	0.001	–0.035	−0.051	–0.049	100	93	98	89	117	96	93
	500	0.003	–0.014	0.007	–0.011	–0.006	–0.007	–0.008	100	95	99	94	103	100	100

RMSE = root mean square error. PML = penalized maximum likelihood; PMLR = penalized maximum likelihood with robustly estimated covariance matrix; ULS = unweighted least squares; ULSR = unweighted least squares with robustly estimated covariance; MAP = mode of marginal posterior; Med = median of marginal posterior; EAP = mean of marginal posterior; μ_ρ = prior guess for latent correlation; ν_ρ = prior sample size for latent correlation; skew = skewness; kurt = kurtosis; Biases smaller than –0.05 or larger than 0.05 are printed in bold. For the RMSE gain, the RMSE of PML estimation is used as a reference method; values smaller than 100 indicate that the RMSE of the respective method is lower than the RMSE of the reference method. The true correlation and loadings were set to ρ = 0.50 and λ = 0.50, respectively.