Table 1.

Simulation results for the high accuracy scenario

Random-effects	ρ	$\overline{\eta }$	$\overline{\xi }$	${\sigma }_{\eta }^2$	${\sigma }_{\xi }^2$	ρ	Failure
distribution		bias (s.e.)	bias (s.e.)	bias (s.e.)	bias (s.e.)	bias (s.e.)	rate %
		Normal-Normal
Normal	0.2	-0.19 (0.33)	0.06 (0.23)	-0.47 (0.46)	-0.13 (0.23)	-0.04 (0.27)	2.5
	0.6	-0.16 (0.33)	0.03 (0.23)	-0.42 (0.47)	-0.12 (0.23)	-0.15 (0.22)	1.8
	0.8	-0.17 (0.34)	0.02 (0.23)	-0.38 (0.48)	-0.10 (0.24)	-0.19 (0.18)	1.8
		Binomial-Normal
	0.2	0.02 (0.37)	-0.01 (0.24)	-0.10 (0.67)	-0.03 (0.28)	0.02 (0.36)	6.2
	0.6	0.02 (0.38)	-0.01 (0.24)	-0.03 (0.71)	-0.02 (0.28)	-0.01 (0.28)	11.1
	0.8	0.01 (0.37)	-0.00 (0.24)	-0.03 (0.69)	-0.01 (0.29)	-0.02 (0.20)	19.5
		SIMEX
	0.2	0.08 (0.35)	-0.07 (0.25)	0.05 (0.59)	0.14 (0.30)	-0.03 (0.28)	0.0
	0.6	0.08 (0.35)	-0.07 (0.25)	0.08 (0.59)	0.13 (0.29)	-0.13 (0.23)	0.0
	0.8	0.05 (0.35)	-0.06 (0.25)	0.07 (0.59)	0.14 (0.30)	-0.18 (0.19)	0.0
		Normal-Normal
t	0.2	-0.22 (0.39)	0.09 (0.28)	0.07 (0.72)	0.16 (0.38)	-0.06 (0.26)	1.6
	0.6	-0.23 (0.41)	0.04 (0.28)	0.23 (0.80)	0.18 (0.38)	-0.13 (0.22)	0.7
	0.8	-0.20 (0.41)	0.03 (0.29)	0.21 (0.78)	0.22 (0.41)	-0.17 (0.17)	0.8
		Binomial-Normal
	0.2	0.02 (0.46)	0.01 (0.30)	0.74 (1.13)	0.34 (0.47)	-0.01 (0.33)	3.6
	0.6	-0.02 (0.48)	-0.01 (0.30)	0.89 (1.20)	0.36 (0.48)	-0.01 (0.24)	7.9
	0.8	0.00 (0.47)	0.00 (0.31)	0.82 (1.20)	0.40 (0.53)	-0.03 (0.18)	14.0
		SIMEX
	0.2	0.05 (0.42)	-0.05 (0.31)	0.64 (0.85)	0.52 (0.47)	-0.05 (0.28)	0.0
	0.6	-0.01 (0.43)	-0.07 (0.31)	0.77 (0.90)	0.51 (0.47)	-0.10 (0.22)	0.0
	0.8	0.00 (0.42)	-0.05 (0.31)	0.66 (0.86)	0.52 (0.47)	-0.15 (0.17)	0.0
		Normal-Normal
Skew-normal	0.2	-0.64 (0.29)	0.17 (0.22)	-0.54 (0.38)	-0.13 (0.22)	0.03 (0.26)	1.4
(low skewness)	0.6	-0.57 (0.30)	0.00 (0.23)	-0.49 (0.40)	-0.13 (0.23)	-0.11 (0.21)	1.8
	0.8	-0.52 (0.31)	-0.10 (0.23)	-0.44 (0.43)	-0.13 (0.22)	-0.17 (0.17)	2.1
		Binomial-Normal
	0.2	-0.54 (0.32)	0.12 (0.23)	-0.35 (0.48)	-0.05 (0.26)	0.10 (0.33)	5.4
	0.6	-0.49 (0.32)	-0.05 (0.24)	-0.28 (0.53)	-0.03 (0.28)	0.03 (0.26)	10.6
	0.8	-0.44 (0.34)	-0.16 (0.24)	-0.18 (0.59)	-0.02 (0.29)	0.00 (0.19)	20.0
		SIMEX
	0.2	-0.48 (0.32)	0.06 (0.24)	-0.16 (0.48)	0.11 (0.28)	0.05 (0.27)	0.0
	0.6	-0.42 (0.33)	-0.11 (0.25)	-0.10 (0.51)	0.13 (0.29)	-0.09 (0.22)	0.0
	0.8	-0.38 (0.33)	-0.22 (0.25)	-0.04 (0.54)	0.13 (0.30)	-0.16 (0.18)	0.0
		Normal-Normal
Skew-normal	0.2	-0.59 (0.30)	0.37 (0.20)	-0.52 (0.40)	-0.19 (0.18)	0.20 (0.23)	1.2
(high skewness)	0.6	-0.44 (0.31)	0.24 (0.22)	-0.44 (0.43)	-0.15 (0.21)	0.01 (0.18)	1.8
	0.8	-0.32 (0.32)	0.15 (0.22)	-0.43 (0.44)	-0.13 (0.21)	-0.11 (0.15)	1.2
		Binomial-Normal
	0.2	-0.49 (0.32)	0.35 (0.21)	-0.30 (0.51)	-0.13 (0.21)	0.30 (0.29)	7.6
	0.6	-0.33 (0.35)	0.22 (0.23)	-0.14 (0.62)	-0.06 (0.26)	0.16 (0.20)	15.1
	0.8	-0.19 (0.37)	0.13 (0.24)	-0.08 (0.66)	-0.04 (0.27)	0.05 (0.16)	25.6
		SIMEX
	0.2	-0.43 (0.32)	0.31 (0.21)	-0.13 (0.50)	-0.02 (0.22)	0.22 (0.24)	0.0
	0.6	-0.26 (0.34)	0.17 (0.23)	0.00 (0.55)	0.06 (0.26)	0.03 (0.19)	0.0
	0.8	-0.14 (0.35)	0.08 (0.24)	0.02 (0.57)	0.09 (0.27)	-0.10 (0.16)	0.0

Bias and average of the estimated standard errors (s.e.) for the estimators of $\overline{\eta },\overline{\xi },{\sigma }_{\eta }^2,{\sigma }_{\xi }^2,\rho$, on the basis of 1, 000 replicates with n=10. Failure rates larger than 5% in bold