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. Author manuscript; available in PMC: 2013 Apr 10.
Published in final edited form as: Biometrics. 2013 Feb 4;69(1):80–90. doi: 10.1111/j.1541-0420.2012.01833.x

Table 1.

Simulation Study A X ~ N(0, 1) and ε ~ N(0, γ1 + γ2|X| + γ3Y) Results for Slope Parameter β1 – Sample Size n=200, Validation Sample Size m=70

M MD Emp-SD IQ-SD 95% CI F M MD Emp-SD IQ-SD 95% CI F
γ1 = 0.5, γ2 = 0, γ3 = 0
γ1 = 1.0, γ2 = 0, γ3 = 0
Naive 0.6469 0.6379 0.1512 0.1520 0.360 0 0.4713 0.4660 0.1262 0.1264 0.027 0
RECS 1.0782 1.0314 0.3373 0.3013 0.958 0 1.1567 1.0231 0.5421 0.4266 0.933 2
N&S 1.0368 1.0257 0.2740 0.2867 0.907 0 0.9487 0.9859 0.2283 0.2365 0.897 8
SIMEX - Q 0.8940 0.8737 0.2245 0.2157 0.877 0 0.7182 0.6989 0.2048 0.2039 0.626 0
H&W 1.0600 0.9514 0.5264 0.3818 0.951 4 0.8840 0.7851 0.5249 0.3751 0.917 4
MCMC η =100 1.2797 1.2364 0.4072 0.4324 0.950 0 1.2304 1.1671 0.4350 0.4848 0.970 0
γ1 = 0.3, γ2 = 0.25, γ3 = 0
γ1 = 0.7, γ2 = 0.35, γ3 = 0
Naive 0.6573 0.6494 0.1553 0.1573 0.390 0 0.4812 0.4749 0.1284 0.1279 0.036 0
RECS 1.0429 1.0054 0.3102 0.2784 0.949 0 1.0658 0.9797 0.4673 0.3663 0.912 1
N&S 1.0929 1.0881 0.3001 0.3208 0.899 1 0.9926 1.0305 0.2402 0.2348 0.890 7
SIMEX - Q 0.9169 0.8926 0.2368 0.2313 0.891 0 0.7358 0.7167 0.2115 0.2053 0.660 0
H&W 1.0370 0.9679 0.4451 0.2980 0.949 1 1.0310 0.9134 0.5109 0.3566 0.941 4
MCMC η =100 1.2539 1.2292 0.3691 0.3750 0.950 0 1.2866 1.2396 0.4414 0.4678 0.940 0
γ1 = 0.15, γ2 = 0.25, γ3 = 0.25
γ1 = 0.35, γ2 = 0.25, γ3 = 0.50
Naive 0.6512 0.6437 0.1513 0.1488 0.373 0 0.5091 0.5029 0.1282 0.1285 0.060 0
RECS 1.0782 1.0316 0.3477 0.2921 0.950 0 1.1123 0.9989 0.4765 0.3793 0.929 0
N&S 1.1099 1.1037 0.2987 0.3215 0.896 2 1.0293 1.0674 0.2451 0.2514 0.858 12
SIMEX - Q 0.8718 0.8545 0.2241 0.2194 0.840 0 0.7259 0.7125 0.1986 0.1868 0.605 0
H&W 1.0410 0.9682 0.4373 0.3121 0.957 2 1.0600 0.9600 0.5004 0.3425 0.942 3
MCMC η =100 1.0950 1.0748 0.3028 0.3490 0.990 0 1.1408 1.0934 0.3828 0.3606 0.980 0

SIMEX results are based on B = 100, λ = (0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9) and the simex R library

L - linear extrapolation; Q - quadratic extrapolation; NL - non-linear extrapolation of Cook and Stefanski (1994)

M - empirical mean; MD - empirical median; Emp-SD - empirical standard deviation; IQ-SD - inter-quartile dispersion; 95% CI - empirical coverage rate of 95% Wald confidence interval (or HPD interval, for MCMC); F - number of samples with no solution