. Author manuscript; available in PMC: 2016 Sep 7.

Published in final edited form as: Biometrics. 2016 Jan 20;72(3):678–686. doi: 10.1111/biom.12474

Table 1.

Simulation results using different combinations of range parameters and measurement error variance. Reported numbers are averaged over 1000 simulations with 500 observations per simulation.

Range* ( $τ_{G_{1}}$ )	No measurement error				Measurement error variance, $σ_{u}^{2} = 0.25$				Measurement error variance, $σ_{u}^{2} = 0.5$
Range* ( $τ_{G_{1}}$ )	OLS	LME	GAM	Proposed	OLS	LME	GAM	Proposed	OLS	LME	GAM	Proposed
Estimated coefficient
0.1	2.001	2.001	2.002	1.991	1.928	1.439	1.332	2.066	1.858	1.274	0.986	2.034
0.3	1.999	1.999	1.999	1.988	1.927	1.574	1.327	2.096	1.858	1.343	0.987	2.036
0.5	2.001	2.001	2.001	1.991	1.926	1.599	1.312	2.064	1.857	1.389	0.999	2.035

Empirical standard error
0.1	0.029	0.028	0.040	0.029	0.032	0.609	0.216	0.056	0.035	0.751	0.216	0.069
0.3	0.035	0.030	0.030	0.032	0.036	0.554	0.211	0.045	0.038	0.730	0.219	0.058
0.5	0.031	0.027	0.026	0.029	0.035	0.543	0.223	0.051	0.039	0.712	0.210	0.052

Average of estimated standard errors
0.1	0.014	0.021	0.030	0.015	0.022	0.040	0.058	0.051	0.027	0.037	0.057	0.053
0.3	0.014	0.020	0.026	0.014	0.022	0.035	0.057	0.041	0.027	0.035	0.056	0.052
0.5	0.014	0.018	0.023	0.014	0.022	0.034	0.057	0.049	0.026	0.034	0.056	0.051

Average of simulated standard errors
0.1	—	—	—	0.015	—	—	—	0.050	—	—	—	0.068
0.3	—	—	—	0.014	—	—	—	0.041	—	—	—	0.052
0.5	—	—	—	0.014	—	—	—	0.049	—	—	—	0.051

$τ_{G_{1}}$ : values of the range parameter following exponential correlation in G₁(s_i).