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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 3.

Simulation Study C Two Error-Prone Covariates and One Error-Free Covariate Sample Size n=500

β1 β3
Scenario C1: X1, X2, Z ~ N(0, 1) and ε1, ε2 ~ N(0, 1)
M MD Emp-SD IQ-SD 95% CI M MD Emp-SD IQ-SD 95% CI F
Naive 0.4296 0.4242 0.0804 0.0781 0.000 0.8626 0.8599 0.1201 0.1223 0.769 0
RECS 1.0817 1.0341 0.3116 0.2595 0.972 1.0525 1.0286 0.2079 0.1907 0.979 0
N&S 0.8286 0.8288 0.1316 0.1319 0.826 0.9483 0.9448 0.1382 0.1412 0.951 52
SIMEX - Q 0.8113 0.8038 0.1377 0.1333 0.571 0.9587 0.9524 0.1452 0.1519 0.920 0
H&W 0.6678 0.6675 0.5038 0.3360 0.800 1.0277 0.9679 0.4669 0.3039 0.918 14
MCMC η =100 1.0608 1.0335 0.2765 0.2508 0.870 1.0445 1.0418 0.1622 0.1834 0.970 0
Scenario C2: X1, X2, Z ~ N (0, 1) and ε1, ε2 ~ N (0, 0.4 + 0.25(|X1| + |X2| + |Z|))
Naive 0.4386 0.4334 0.0824 0.0792 0.001 0.8712 0.8694 0.1223 0.1223 0.791 0
RECS 1.1884 1.1122 0.3800 0.3126 0.986 1.0828 1.0482 0.2405 0.2007 0.983 1
N&S 0.8606 0.8619 0.1329 0.1312 0.842 0.9668 0.9655 0.1439 0.1465 0.966 46
SIMEX - Q 0.8345 0.8242 0.1431 0.1394 0.819 0.9793 0.9746 0.1516 0.1562 0.933 0
H&W 0.6165 0.6176 0.4809 0.3277 0.733 0.9627 0.9279 0.4248 0.2837 0.905 9
MCMC η =100 1.0338 1.0084 0.2709 0.2637 0.890 1.0358 1.0339 0.1626 0.1701 0.950 0
Scenario C3: X1, X2 ~ MODCHI(1), Z ~ N (0, 1), and ε1, ε2 ~ MODCHI(1)
Naive 0.3853 0.3814 0.0887 0.0915 0.000 0.8883 0.8893 0.1206 0.1207 0.809 0
RECS 1.0430 0.9841 0.3726 0.3328 0.942 1.0413 1.0232 0.1856 0.1667 0.971 0
N&S 0.8656 0.8664 0.2576 0.2880 0.782 0.9261 0.9201 0.1396 0.1415 0.946 34
SIMEX - Q 0.7463 0.7315 0.1586 0.1598 0.445 0.9626 0.9588 0.1402 0.1399 0.915 0
H&W 0.4723 0.4276 0.2733 0.2108 0.654 0.9155 0.9023 0.1798 0.1638 0.971 1
MCMC η =100 1.1462 1.1199 0.3153 0.3259 0.910 1.0167 0.9887 0.1713 0.1519 0.910 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