Table 3.

The percent (%) bias, average bootstrap standard error (ASE) for SIMEX, average model standard error (ASE) for naive, empirical standard error (ESE), mean squared error (MSE), and coverage probabilities (CP) are given for 2000 simulated data sets for the SIMEX and naive methods with exponential time and a shifted gamma distribution (mean 0) for the error term. Type 1 error is shown instead of % bias for β = 0.

β	${\sigma }_{\upsilon }^2$	n	Method	% Bias	ASE	ESE	MSE	CP
log(1.5)	0.25	300	SIMEX	−7.270	0.077	0.076	0.082	0.929
			Naive	−17.65	0.061	0.064	0.096	0.766
		1000	SIMEX	−8.025	0.041	0.041	0.053	0.864
			Naive	−18.33	0.033	0.034	0.082	0.379
	0.5	300	SIMEX	−16.98	0.081	0.082	0.107	0.841
			Naive	−30.01	0.060	0.063	0.137	0.483
		1000	SIMEX	−17.87	0.043	0.043	0.084	0.594
			Naive	−29.74	0.033	0.035	0.126	0.055
	1	300	SIMEX	−27.54	0.084	0.083	0.139	0.706
			Naive	−41.07	0.060	0.062	0.178	0.207
		1000	SIMEX	−28.37	0.044	0.045	0.124	0.278
			Naive	−42.45	0.032	0.034	0.176	0.003
log(3)	0.25	300	SIMEX	−5.578	0.105	0.106	0.122	0.898
			Naive	−15.94	0.074	0.084	0.194	0.360
		1000	SIMEX	−6.380	0.057	0.059	0.091	0.758
			Naive	−16.55	0.040	0.047	0.188	0.017
	0.5	300	SIMEX	−15.96	0.113	0.122	0.214	0.636
			Naive	−27.45	0.070	0.089	0.314	0.042
		1000	SIMEX	−17.19	0.062	0.066	0.200	0.146
			Naive	−28.71	0.038	0.049	0.319	0.000
	1	300	SIMEX	−29.28	0.117	0.124	0.345	0.232
			Naive	−41.6	0.066	0.095	0.467	0.000
		1000	SIMEX	−30.91	0.065	0.068	0.346	0.001
			Naive	−42.43	0.035	0.049	0.469	0.000
β	${\sigma }_{\upsilon }^2$	n	Method	Type 1 Error	ASE	ESE	MSE
0	0.25	300	SIMEX	0.049	0.071	0.069	0.069
		1000	SIMEX	0.057	0.037	0.037	0.037
	0.5	300	SIMEX	0.052	0.074	0.074	0.074
		1000	SIMEX	0.049	0.039	0.039	0.039
	1	300	SIMEX	0.037	0.077	0.075	0.075
		1000	SIMEX	0.056	0.040	0.041	0.041