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Table 2 Performance measures for the estimation of the marginal mean, GHQ scores on raw scale

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 10.2319 0.0008 0.1862 0.0179 0.0174 0.943
Post-imputation rounding 10.2445 0.0134 0.1851 0.0180 0.0167 0.941
Truncated regression 10.2206 -0.0105 0.1846 0.0172 0.0172 0.959
Predictive mean matching 10.1805 -0.0506 0.1832 0.0176 0.0138 0.894
MAR       
Regression, non-rounded 10.2243 -0.0068 0.1838 0.0220 0.0191 0.939
Post-imputation rounding 10.2353 0.0042 0.1828 0.0221 0.0185 0.928
Truncated regression 10.2183 -0.0128 0.1825 0.0219 0.0191 0.936
Predictive mean matching 10.1378 -0.0933 0.1818 0.0213 0.0158 0.852
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 3.3178 -0.0002 0.1058 0.0055 0.0054 0.956
Post-imputation rounding 3.3741 0.0561 0.1023 0.0053 0.0044 0.846
Truncated regression 3.5582 0.2402 0.1025 0.0054 0.0077 0.233
Predictive mean matching 3.2931 -0.0248 0.1048 0.0058 0.0050 0.925
MAR       
Regression, non-rounded 3.3150 -0.0029 0.1055 0.0065 0.0061 0.946
Post-imputation rounding 3.3687 0.0508 0.1021 0.0061 0.0050 0.880
Truncated regression 3.5505 0.2326 0.1024 0.0060 0.0086 0.318
Predictive mean matching 3.2664 -0.0515 0.1045 0.0067 0.0059 0.880
Standard Q ^ = 1.8081 U = 0.094    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage for Q ^
Regression, non-rounded 1.8085 0.0004 0.0951 0.0045 0.0045 0.950
Post-imputation rounding 1.9276 0.1195 0.0894 0.0046 0.0029 0.436
Truncated regression 2.2988 0.4907 0.0982 0.0078 0.0434 0.293
Predictive mean matching 1.7791 -0.0290 0.0934 0.0044 0.0035 0.894
MAR       
Regression, non-rounded 1.8057 -0.0024 0.0941 0.0056 0.0051 0.933
Post-imputation rounding 1.9198 0.1117 0.0887 0.0054 0.0033 0.552
Truncated regression 2.3043 0.4962 0.0984 0.0082 0.0445 0.291
Predictive mean matching 1.7624 -0.0457 0.0930 0.0053 0.0040 0.848
  1. 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.