TABLE 7.

Simulation study 1: bias and RMSE for the latent correlation as a function of different misspecified prior distributions and the sample size.

				Bias					RMSE
			μλ = 0.5			μλ = 0.8		μλ = 0.5			μλ = 0.8
Meth	μρ	νρ	νλ = 0	νλ = 1	νλ = 3	νλ = 1	νλ = 3	νλ = 0	νλ = 1	νλ = 3	νλ = 1	νλ = 3
			N = 30
PML	0	0	–0.038	0.009	0.019	−0.139	–0.022	0.391	0.393	0.379	0.361	0.367
	0.5	1	0.161	0.196	0.201	–0.008	0.119	0.388	0.396	0.397	0.325	0.344
	0.5	3	0.094	0.120	0.123	–0.019	0.089	0.281	0.281	0.278	0.261	0.263
	0.2	1	–0.027	0.021	0.026	−0.114	–0.002	0.320	0.322	0.317	0.323	0.318
	0.2	3	−0.086	–0.040	–0.039	−0.136	–0.046	0.269	0.259	0.255	0.290	0.272
	0.8	1	0.297	0.328	0.347	0.112	0.237	0.432	0.444	0.447	0.358	0.384
	0.8	3	0.337	0.360	0.392	0.153	0.271	0.427	0.436	0.453	0.329	0.373
EAP	0	0	−0.141	−0.070	–0.050	−0.180	−0.103	0.303	0.307	0.314	0.313	0.314
	0.5	1	0.131	0.151	0.161	–0.035	0.056	0.222	0.264	0.276	0.247	0.268
	0.5	3	0.004	0.038	0.048	−0.066	0.011	0.157	0.188	0.196	0.199	0.202
	0.2	1	−0.121	−0.071	−0.058	−0.163	−0.088	0.242	0.248	0.252	0.277	0.268
	0.2	3	−0.178	−0.140	−0.131	−0.192	−0.131	0.245	0.231	0.228	0.266	0.243
	0.8	1	0.360	0.340	0.330	0.145	0.222	0.387	0.377	0.375	0.282	0.319
	0.8	3	0.309	0.320	0.327	0.151	0.231	0.334	0.346	0.352	0.252	0.300
			N = 100
PML	0	0	–0.011	0.002	0.006	–0.039	–0.024	0.203	0.196	0.194	0.194	0.181
	0.5	1	0.089	0.090	0.090	0.031	0.035	0.273	0.261	0.255	0.231	0.212
	0.5	3	0.032	0.042	0.046	0.002	0.014	0.183	0.180	0.179	0.173	0.162
	0.2	1	–0.008	0.004	0.008	–0.034	–0.020	0.190	0.184	0.183	0.186	0.173
	0.2	3	–0.036	–0.024	–0.020	–0.055	–0.040	0.172	0.165	0.164	0.176	0.164
	0.8	1	0.188	0.185	0.163	0.091	0.082	0.332	0.324	0.302	0.262	0.234
	0.8	3	0.218	0.216	0.203	0.135	0.118	0.340	0.332	0.321	0.286	0.253
EAP	0	0	−0.059	–0.034	–0.024	−0.113	−0.069	0.191	0.187	0.187	0.207	0.185
	0.5	1	0.039	0.054	0.059	–0.053	–0.016	0.199	0.207	0.208	0.195	0.180
	0.5	3	–0.016	0.003	0.011	−0.069	–0.030	0.155	0.156	0.157	0.171	0.154
	0.2	1	−0.062	–0.039	–0.029	−0.109	−0.066	0.176	0.171	0.171	0.197	0.174
	0.2	3	−0.095	−0.072	−0.061	−0.128	−0.086	0.174	0.163	0.160	0.195	0.170
	0.8	1	0.191	0.182	0.178	0.038	0.059	0.278	0.270	0.266	0.213	0.204
	0.8	3	0.177	0.173	0.176	0.041	0.064	0.248	0.249	0.253	0.195	0.189

RMSE = root mean square error. PML = penalized maximum likelihood (mode of joint posterior); EAP = mean of marginal posterior; μ_ρ = prior guess for latent correlation; ν_ρ = prior sample size for latent correlation; μ_λ = prior guess for loading ν_λ = prior sample size for loading; biases smaller than –0.05 or larger than 0.05 are printed in bold. For each sample size condition, RMSE values larger than the RMSE for the PML method with uniform priors on loadings (μ_λ = 0.5, ν_λ = 0) and the correlation (μ_ρ = 0, ν_ρ = 0) are printed in bold. The true correlation and loadings were set to ρ = 0.50 and λ = 0.50, respectively.