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Table 4 Results when IQ simulated as MAR (factor 3 in scenarios)

From: Multiple imputation using linked proxy outcome data resulted in important bias reduction and efficiency gains: a simulation study

Scenario (factors 1 and 2) Complete records MI including linked attainment score (KS4)
Estimate (empirical SE) % bias MSE Estimate (empirical SE) % bias MSE Gain in precisiona (%) FMI (%)
IQ 20% missing Correlation(IQ:KS4) = 0.7 0.1005 (0.033) 0.5 0.001 0.1004 (0.031) 0.3 0.001 10 15
0.1990 (0.030) − 0.5 0.0009 0.1993 (0.029) − 0.3 0.0008 11 13
0.3006 (0.025) 0.2 0.0006 0.3002 (0.024) 0.1 0.0006 7 13
IQ 40% missing 0.0994 (0.038) − 0.6 0.001 0.1004 (0.034) 0.3 0.001 22 30
Correlation(IQ: KS4) = 0.7 0.1988 (0.035) − 0.6 0.001 0.1996 (0.033) − 0.2 0.001 17 28
  0.3004 (0.030) 0.1 0.0009 0.3004 (0.027) 0.1 0.0008 17 29
IQ 60% missing 0.1005 (0.049) 0.5 0.002 0.1009 (0.042) 1.1 0.002 34 50
Correlation(IQ: KS4) = 0.7 0.1975 (0.042) − 1.3 0.002 0.1980 (0.037) − 0.8 0.001 33 47
  0.2988 (0.037) − 0.4 0.001 0.3002 (0.032) 0.1 0.001 33 48
IQ 80% missing 0.1040 (0.073) 4.0 0.005 0.1050 (0.061) 4.8 0.004 41 83
Correlation(IQ: KS4) = 0.7 0.2009 (0.062) 0.4 0.004 0.2000 (0.052) 0 0.003 40 81
  0.3011 (0.056) 0.4 0.003 0.3022 (0.046) 0.8 0.002 47 81
  1. MSE mean squared error, FMI fraction of missing information
  2. aRelative to complete records analysis