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Table 4 Performance measures for the estimation of the regression coefficient with GHQ scores on raw scale

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

Scenario Validation statistics
Likert Q ^ = 0.03227 U = 0.02143    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage of Q ^
Regression, non-rounded 0.03181 -0.00046 0.02211 0.00027 0.00022 0.922
Post-imputation rounding 0.03192 -0.00035 0.02219 0.00027 0.00022 0.920
Truncated regression 0.03247 0.00020 0.02217 0.00028 0.00022 0.914
Predictive mean matching 0.02551 -0.00676 0.02223 0.00019 0.00016 0.918
MAR       
Regression, non-rounded 0.02888 -0.00340 0.02270 0.00080 0.00067 0.927
Post-imputation rounding 0.02926 -0.00301 0.02279 0.00079 0.00066 0.924
Truncated regression 0.03010 -0.00217 0.02278 0.00084 0.00066 0.926
Predictive mean matching 0.01727 -0.01500 0.02298 0.00036 0.00036 0.911
C-GHQ Q ^ = 0.04794 U = 0.03967    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage of Q ^
Regression, non-rounded 0.04694 -0.00100 0.04014 0.00077 0.00076 0.946
Post-imputation rounding 0.04805 0.00012 0.04123 0.00080 0.00069 0.932
Truncated regression 0.04360 -0.00433 0.04130 0.00086 0.00073 0.925
Predictive mean matching 0.03738 -0.01055 0.04033 0.00053 0.00056 0.939
MAR       
Regression, non-rounded 0.04283 -0.00511 0.04056 0.00232 0.00219 0.939
Post-imputation rounding 0.04932 0.00138 0.04158 0.00224 0.00195 0.928
Truncated regression 0.06470 0.01676 0.04133 0.00243 0.00210 0.906
Predictive mean matching 0.02442 -0.02352 0.04087 0.00109 0.00121 0.929
Standard Q ^ = 0.05236 U = 0.04202    
MCAR E Q ¯ m bias E U ¯ m Var Q ¯ m (1 + m - 1)E[B m ] coverage of Q ^
Regression, non-rounded 0.05066 -0.00170 0.04336 0.00101 0.00085 0.938
Post-imputation rounding 0.05252 0.00016 0.04550 0.00106 0.00067 0.889
Truncated regression 0.04613 -0.00623 0.04218 0.00101 0.00096 0.930
Predictive mean matching 0.04069 -0.01167 0.04368 0.00065 0.00061 0.929
MAR       
Regression, non-rounded 0.04557 -0.00679 0.04441 0.00278 0.00261 0.942
Post-imputation rounding 0.06226 0.00990 0.04590 0.00238 0.00187 0.911
Truncated regression 0.09485 0.04249 0.04092 0.00233 0.00259 0.857
Predictive mean matching 0.02669 -0.02567 0.04517 0.00122 0.00139 0.939
  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.