TABLE 4.

Simulation results under additive errors in Y* and X* when residual-dependent sampling is used in the second phase

		MBE				CCE				SMLE
r	p	Bias	SE	SEE	CP	Bias	SE	SEE	CP	Bias	SE	SEE	CP	RE
−0.5	0.1	0.083	0.045	0.042	0.499	0.102	0.045	0.055	0.568	−0.002	0.032	0.032	0.951	1.089
	0.3	0.170	0.057	0.050	0.089	0.205	0.050	0.055	0.026	−0.007	0.035	0.035	0.946	1.096
	0.6	0.198	0.065	0.055	0.065	0.242	0.050	0.052	0.003	−0.012	0.040	0.040	0.938	1.039
	1.0	0.170	0.071	0.058	0.202	0.222	0.049	0.049	0.007	−0.014	0.046	0.046	0.939	0.977
−0.3	0.1	0.063	0.043	0.040	0.660	0.080	0.044	0.055	0.746	−0.001	0.032	0.032	0.952	1.089
	0.3	0.136	0.055	0.049	0.216	0.166	0.051	0.057	0.138	−0.006	0.035	0.035	0.948	1.117
	0.6	0.174	0.065	0.055	0.142	0.200	0.051	0.054	0.033	−0.010	0.039	0.040	0.943	1.071
	1.0	0.166	0.073	0.060	0.241	0.180	0.051	0.052	0.062	−0.011	0.046	0.046	0.945	0.994
0.0	0.1	0.033	0.040	0.038	0.859	0.047	0.043	0.054	0.923	−0.001	0.032	0.032	0.949	1.091
	0.3	0.077	0.052	0.047	0.616	0.099	0.051	0.057	0.614	−0.003	0.034	0.034	0.949	1.135
	0.6	0.107	0.062	0.054	0.503	0.124	0.053	0.057	0.408	−0.006	0.038	0.038	0.949	1.129
	1.0	0.112	0.073	0.061	0.542	0.111	0.053	0.054	0.466	−0.007	0.046	0.046	0.950	1.010
0.3	0.1	0.006	0.038	0.037	0.939	0.012	0.041	0.053	0.986	0.000	0.032	0.032	0.952	1.084
	0.3	0.017	0.048	0.044	0.913	0.026	0.050	0.058	0.956	0.000	0.034	0.034	0.952	1.150
	0.6	0.025	0.059	0.052	0.887	0.033	0.054	0.058	0.931	−0.002	0.037	0.037	0.950	1.142
	1.0	0.027	0.070	0.059	0.879	0.030	0.054	0.056	0.926	−0.003	0.044	0.044	0.951	1.043
0.5	0.1	−0.009	0.037	0.036	0.933	−0.011	0.041	0.052	0.986	0.001	0.032	0.032	0.952	1.077
	0.3	−0.018	0.046	0.043	0.908	−0.025	0.049	0.057	0.958	0.002	0.033	0.034	0.952	1.142
	0.6	−0.025	0.056	0.050	0.888	−0.034	0.053	0.058	0.928	0.002	0.037	0.037	0.952	1.145
	1.0	−0.028	0.066	0.055	0.875	−0.034	0.054	0.057	0.919	0.001	0.042	0.043	0.953	1.068

Notes: Bias and SE are, respectively, the empirical bias and standard error of the parameter estimator; SEE is the empirical mean of the standard error estimator; CP is the coverage probability of the 95% confidence interval; RE is the empirical variance of the SMLE under simple random sampling over that under residual-dependent sampling. Each entry is based on 10 000 replicates.