Skip to main content

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.