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Table 3 Performance measures for the estimation of the marginal mean with transformed GHQ scores

From: Comparison of methods for imputing limited-range variables: a simulation study

Scenario Validation statistics
Likert Q ^ = 10.2311 U = 0.1855    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage for Q ^
Regression, non-rounded 10.2366 0.0055 0.1861 0.0181 0.0174 0.947
Post-imputation rounding 10.1446 -0.0865 0.1857 0.0416 0.0170 0.820
Truncated regression 10.2227 -0.0084 0.1840 0.0181 0.0163 0.935
Predictive mean matching 10.1926 -0.0385 0.1837 0.0174 0.0148 0.916
MAR       
Regression, non-rounded 10.2119 -0.0192 0.1846 0.0223 0.0197 0.928
Post-imputation rounding 10.0985 -0.1326 0.1842 0.0628 0.0193 0.758
Truncated regression 10.2010 -0.0301 0.1825 0.0217 0.0180 0.915
Predictive mean matching 10.1401 -0.0910 0.1819 0.0216 0.0164 0.858
C-GHQ Q ^ = 3.3179 U = 0.1055    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage for Q ^
Regression, non-rounded 3.3268 0.0088 0.1087 0.0057 0.0063 0.960
Post-imputation rounding 3.3231 0.0051 0.1053 0.0058 0.0052 0.931
Truncated regression 3.5563 0.2384 0.1028 0.0053 0.0048 0.096
Predictive mean matching 3.3009 -0.0170 0.1049 0.0057 0.0053 0.941
MAR       
Regression, non-rounded 3.3265 0.0086 0.1094 0.0065 0.0077 0.969
Post-imputation rounding 3.3185 0.0005 0.1055 0.0065 0.0063 0.954
Truncated regression 3.5452 0.2273 0.1027 0.0060 0.0055 0.160
Predictive mean matching 3.2722 -0.0457 0.1045 0.0069 0.0059 0.886
Standard Q ^ = 1.8081 U = 0.0947    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage for Q ^
Regression, non-rounded 263.63 261.82 30917 53900000 998000000 0.992
Post-imputation rounding 1.7996 -0.0086 0.1055 0.0037 0.0074 0.992
Truncated regression 2.2661 0.4580 0.0953 0.0056 0.0047 0.000
Predictive mean matching 1.8052 -0.0029 0.0943 0.0043 0.0041 0.940
MAR       
Regression, non-roundedƗ       
Post-imputation rounding 1.8035 -0.0046 0.1074 0.0043 0.0095 0.989
Truncated regression 2.2603 0.4522 0.0951 0.0061 0.0054 0.000
Predictive mean matching 1.7829 -0.0252 0.0937 0.0053 0.0045 0.909
  1. ƗValues larger than those obtained under the MCAR condition Key: Q ^ = complete data estimate; U = estimated variance of Q ^ from complete data; E Q ¯ m = average of MI-based point estimates across 1000 simulated datasets; bias = difference between E Q ¯ m and Q ^ ; E U ¯ m = average of estimated within-imputation variance across simulated datasets; Var Q ¯ m = variance of the MI point estimates across simulated datasets; (1 + m- 1)E[Bm] = average of estimated between-imputation variance (with adjustment for number of imputations) across simulated datasets; coverage = proportion of (nominally) 95% confidence intervals that contain the complete data estimate.