TABLE 4.

Simulation study 1: bias and RMSE for unconstrained maximum likelihood (ML) estimation and constrained maximum likelihood (CML) estimation of the latent correlation as a function of the true correlation (ρ), the sample size (N), and different sets of replications.

		Bias					RMSE
		Conv+Adm.		Conv.		All	Conv+Adm.		Conv.		All
ρ	N	ML	CML	ML	CML	CML	ML	CML	ML	CML	CML
0.3	30	0.022	0.055	0.043	0.068	–0.016	0.352	0.358	0.395	0.395	0.411
	50	0.025	0.035	0.040	0.049	–0.003	0.284	0.288	0.310	0.309	0.328
	100	0.003	0.006	0.004	0.006	–0.004	0.202	0.201	0.203	0.203	0.210
0.5	30	–0.037	–0.003	0.019	0.048	–0.025	0.299	0.295	0.332	0.322	0.360
	50	–0.042	–0.032	–0.015	–0.005	–0.049	0.266	0.262	0.299	0.285	0.316
	100	0.000	0.002	0.006	0.008	0.003	0.196	0.194	0.202	0.201	0.206
0.7	30	−0.124	−0.088	–0.034	–0.008	−0.068	0.299	0.269	0.299	0.274	0.344
	50	−0.071	−0.063	–0.012	–0.005	–0.035	0.242	0.234	0.252	0.245	0.275
	100	–0.026	–0.025	–0.004	–0.003	–0.004	0.172	0.171	0.184	0.183	0.185

RMSE = root mean square error; ρ = true latent correlation; N = sample size; ML = unconstrained ML estimation; CML = constrained ML estimation. Conv+Adm = all replications in which unconstrained ML converged with admissible values, that is, estimated correlation was within the interval [−1, 1]; Conv = all replications in which unconstrained ML estimation converged and estimated correlations outside [−1, 1] are truncated to −1 or 1; All = all replications (only constrained ML produced estimates for all replications). Biases smaller than −0.05 or larger than.05 are printed in bold.