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. 2017 Jan 3;104(1):31–50. doi: 10.1093/biomet/asw054

Table 1.

Empirical bias, empirical and estimated variances, coverages and mean squared errors for the settings with one mismeasured covariate, when Inline graphic

      Ma & Yin method Naive method Simex method
Inline graphic Inline graphic Estimate Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
200 0.1 Bias -1.0 3.2 -0.2 4.3 -9.2 0.2 -0.4 1.5 -0.1
    Emp. var. 5.3 13.2 4.1 4.7 9.9 4.0 5.2 12.8 4.1
    Est. var. 5.3 13.0 3.6 4.6 9.8 3.6 5.2 12.4 3.6
    95% cv 94.6 94.8 93.6 93.6 93.4 93.8 94.2 94.2 93.8
    MSE 5.3 13.3 4.1 4.8 10.8 4.0 5.2 12.8 4.1
200 0.2 Bias -3.0 8.5 -0.5 14.2 -31.5 .7 3.6 -7.6 0.1
    Emp. var. 6.9 22.6 4.4 4.1 7.5 4.0 5.4 14.3 4.2
    Est. var. 7.4 22.7 3.9 4.0 7.4 3.6 5.2 12.7 3.7
    95% cv 96.0 96.8 93.2 88.4 78.8 93.4 93.8 92.4 93.0
    MSE 7.0 23.4 4.4 6.1 17.5 4.0 5.5 14.8 4.2
300 0.1 Bias -1.1 3.7 -1.4 4.2 -8.4 -1.1 -0.5 2.3 -1.4
    Emp. var. 3.9 9.4 2.6 3.4 7.1 2.5 3.8 9.0 2.6
    Est. var. 3.5 8.7 2.4 3.1 6.5 2.4 3.4 8.3 2.4
    95% cv 95.6 94.4 96.6 93.4 93.2 96.6 95.4 94.2 96.6
    MSE 3.9 9.5 2.6 3.6 7.8 2.5 3.8 9.1 2.6
300 0.2 Bias -2.1 6.8 -1.8 14.2 -31.0 -0.6 3.6 -6.9 -1.3
    Emp. var. 4.9 14.5 2.7 3.0 5.1 2.5 3.9 9.7 2.6
    Est. var. 4.6 13.9 2.6 2.7 4.9 2.4 3.4 8.4 2.5
    95% cv 96.6 95.8 95.8 85.2 71.6 95.4 93.8 93.4 95.8
    MSE 5.0 14.9 2.7 5.0 14.7 2.5 4.1 10.2 2.6

Emp. var., empirical variance; Est. var., estimated variance; 95% cv, coverage probabilities of 95% confidence intervals computed based on the asymptotic normal distribution; MSE, mean squared error. All numbers were multiplied by 100.