Table 1.

Simulation results for the MLE of within-subject measurement error covariance parameters ρ and σ² in a random effects model obtained under the normal random effects X_i assumption. True σ² = 0.50 and four underlying X_i distributions are considered. Reported values are Mean, Monte Carlo average of estimate; RB, estimated relative bias (presented as percentages), as the difference between the Monte Carlo average of estimates and the true parameter, divided by the true parameter; SD, Monte Carlo standard deviation; SE, average of estimated standard errors; CP, Monte Carlo coverage probability of 95% Wald confidence interval.

True ρ		Mean	RB (%)	SD	SE	CP	Mean	RB	SD	SE	CP
Xi Normal							Xi Bimodal mixture
0.25	$\widehat{\rho }$	0.25	0.6	0.02	0.02	0.96	0.25	−0.2	0.02	0.02	0.96
	${\widehat{\sigma }}^2$	0.50	0.1	0.02	0.02	0.95	0.50	0.1	0.02	0.02	0.95
0.50	$\widehat{\rho }$	0.50	0.3	0.02	0.02	0.95	0.50	−0.2	0.03	0.02	0.94
	${\widehat{\sigma }}^2$	0.50	0.4	0.03	0.03	0.95	0.50	0.1	0.03	0.03	0.95
−0.25	$\widehat{\rho }$	−0.25	−0.5	0.02	0.02	0.95	−0.25	0.0	0.02	0.02	0.96
	${\widehat{\sigma }}^2$	0.50	−0.1	0.01	0.01	0.95	0.50	0.1	0.01	0.01	0.93
−0.50	$\widehat{\rho }$	−0.50	−0.2	0.01	0.01	0.94	−0.50	0.0	0.01	0.01	0.96
	${\widehat{\sigma }}^2$	0.50	−0.2	0.01	0.01	0.94	0.50	0.1	0.01	0.01	0.94
Xi Skew-normal							Xi Bivariate t5
0.25	$\widehat{\rho }$	0.25	0.1	0.02	0.02	0.97	0.25	0.0	0.02	0.02	0.96
	${\widehat{\sigma }}^2$	0.50	0.0	0.02	0.02	0.96	0.50	0.1	0.02	0.02	0.96
0.50	$\widehat{\rho }$	0.50	0.0	0.02	0.02	0.97	0.50	0.0	0.03	0.03	0.95
	${\widehat{\sigma }}^2$	0.50	0.2	0.03	0.03	0.96	0.50	0.3	0.03	0.03	0.96
−0.25	$\widehat{\rho }$	−0.25	0.0	0.02	0.02	0.96	−0.25	−0.2	0.02	0.02	0.96
	${\widehat{\sigma }}^2$	0.50	0.0	0.01	0.01	0.95	0.50	0.1	0.01	0.01	0.96
−0.50	$\widehat{\rho }$	−0.50	0.0	0.01	0.01	0.95	−0.50	−0.1	0.01	0.01	0.95
	${\widehat{\sigma }}^2$	0.50	0.0	0.01	0.01	0.95	0.50	0.0	0.01	0.01	0.95