Table I.

Results from 1000 simulations under the three-level mixed-effects location scale model - three continuous covariates and small random scale effect and positive covariance.

		Three-level Random Intercept Model							Three-level Mixed-effects Location Scale Model
Parameters	True Value	EST	SE*	Bias	SB	RMSE	95% COV	AW	EST	SE*	Bias	SB	RMSE	95% COV	AW
β0 : (Intercept)	6.90	6.899	0.06	-0.0012	-2.16	0.06	95.9	0.23	6.899	0.06	-0.0011	-1.99	0.06	95.8	0.23
β1 : (X1)	-0.40	-0.400	0.03	0.0002	0.80	0.03	95.4	0.11	-0.400	0.02	0.0003	1.13	0.02	94.5	0.10
β2 : (X2)	0.20	0.200	0.01	0.0001	0.50	0.01	95.5	0.06	0.200	0.01	0.0001	0.84	0.01	95.8	0.06
β3 : (X3)	0.60	0.603	0.08	0.0031	3.66	0.08	94.8	0.32	0.604	0.08	0.0037	4.41	0.08	94.3	0.32
λ0 : (Intercept)	0.20	0.194	0.08	-0.0056	-7.34	0.08	96.2	0.30	0.186	0.08	-0.0136	-17.90	0.08	96.1	0.30
λ1 : (X3)	-0.10								-0.100	0.11	0.0002	0.19	0.11	94.4	0.42
α0 : (Intercept)	-1.20	-1.136	0.08	0.0641	77.06	0.10	82.3	0.29	-1.199	0.07	0.0011	1.62	0.07	95.2	0.28
α1 : (X2)	-0.10								-0.102	0.06	-0.0019	-3.11	0.06	94.2	0.24
α2 : (X3)	-0.40								-0.404	0.10	-0.0037	-3.68	0.10	94.4	0.38
τ0 : (Intercept)	0.40	0.635	0.04	0.2351	644.84	0.24	0.0	0.06	0.398	0.04	-0.0015	-4.26	0.04	94.8	0.14
τ1 : (X1)	0.10								0.099	0.03	-0.0007	-2.44	0.03	96.4	0.13
τ2 : (X2)	-0.10								-0.100	0.01	-0.0002	-1.32	0.01	94.7	0.05
τ3 : (X3)	-0.20								-0.200	0.04	-0.0004	-0.89	0.04	95.6	0.18
${\sigma }_{\omega }^2$	0.30								0.289	0.03	-0.0106	-38.36	0.03	91.0	0.11
σ ν ω	0.15								0.151	0.04	0.0011	2.88	0.04	94.2	0.14
-2LogL				41338.5							40326.8
# of converged solutions				999							975

^*Estimated standard errors are based on the distribution of the 999 or 975 parameter estimates from the random-intercept model or mixed-effects location scale model, respectively.