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Table 2 Simulation comparison of the IPW estimator β ̂ I 1 , the AIPW estimator β ̂ A 2 and the complete-case (CC) estimator β ̂ C under various sample sizes and selection probabilities

From: Missing data approaches for probability regression models with missing outcomes with applications

 

b 0

 

b 1

 

θ

n

 

Bias

SSE

ESE

CP

 

Bias

SSE

ESE

CP

 

Bias

SSE

ESE

CP

Model 3

50

IPW

.0081

.1609

.1502

.949

 

-.0034

.5535

.2790

.954

 

-.0116

.2592

.2400

.963

 

AIPW

-.0070

.1543

.1486

.950

 

-.0134

.2715

.2690

.958

 

-.0185

.2364

.2330

.955

 

CC

.0230

.1529

.1504

.938

 

.0798

.5441

.2835

.940

 

.0648

.2367

.2414

.952

100

IPW

-.0052

.1145

.1077

.948

 

-.0001

.2073

.2014

.959

 

.0030

.1789

.1724

.948

 

AIPW

-.0124

.1077

.1041

.947

 

-.0085

.1869

.1840

.957

 

.0050

.1636

.1606

.948

 

CC

.0221

.1074

.1054

.939

 

.1023

.1830

.1937

.924

 

.0828

.1625

.1664

.915

300

IPW

-.0011

.0617

.0614

.951

 

-.0044

.1176

.1157

.952

 

.0019

.1009

.0993

.953

 

AIPW

-.0023

.0582

.0588

.956

 

-.0051

.1056

.1036

.954

 

.0022

.0936

.0910

.944

 

CC

.0295

.0577

.0596

.924

 

.1051

.1070

.1095

.824

 

.0823

.0925

.0946

.861

500

IPW

.0018

.0451

.0473

.958

 

-.0037

.0853

.0895

.958

 

-.0069

.0765

.0767

.945

 

AIPW

.0009

.0430

.0452

.957

 

-.0032

.0793

.0798

.947

 

-.0066

.0689

.0702

.951

 

CC

.0317

.0429

.0459

.903

 

.1077

.0788

.0844

.763

 

.0737

.0704

.0730

.839

800

IPW

-.0006

.0374

.0375

.951

 

-.0030

.0671

.0708

.962

 

.0004

.0617

.0605

.946

 

AIPW

-.0003

.0362

.0358

.949

 

-.0031

.0623

.0631

.954

 

-.0012

.0577

.0554

.935

 

CC

.0315

.0353

.0364

.863

 

.1065

.0630

.0667

.633

 

.0786

.0568

.0576

.721

Model 4

50

IPW

.0053

.1627

.1504

.948

 

.0825

.3531

.2832

.913

 

-.0057

.2736

.2405

.948

 

AIPW

-.0085

.1549

.1489

.950

 

-.0122

.2746

.2752

.966

 

-.0138

.2395

.2340

.961

 

CC

.2295

.2640

.0855

.531

 

.4513

.3805

.1760

.517

 

.2954

.3285

.1409

.536

100

IPW

-.0050

.1168

.1085

.939

 

.0481

.2350

.2130

.922

 

.0016

.1884

.1761

.940

 

AIPW

-.0130

.1083

.1043

.943

 

-.0067

.1920

.1885

.950

 

.0066

.1648

.1613

.949

 

CC

.0196

.1077

.1063

.943

 

.2010

.1946

.2087

.820

 

.0900

.1645

.1702

.910

300

IPW

-.0001

.0630

.0624

.945

 

-.0001

.1323

.1311

.955

 

-.0011

.1043

.1038

.946

 

AIPW

-.0020

.0588

.0588

.951

 

-.0052

.1095

.1059

.952

 

.0012

.0950

.0913

.931

 

CC

.0271

.0582

.0601

.930

 

.2020

.1060

.1173

.576

 

.0894

.0939

.0965

.863

500

IPW

.0012

.0457

.0480

.951

 

-.0007

.0966

.1010

.966

 

-.0054

.0801

.0799

.948

 

AIPW

.0006

.0433

.0453

.956

 

-.0010

.0821

.0813

.941

 

-.0059

.0697

.0704

.950

 

CC

.0291

.0434

.0463

.912

 

.2047

.0817

.0903

.364

 

.0815

.0711

.0745

.820

800

IPW

-.0006

.0381

.0380

.949

 

.0004

.0761

.0794

.967

 

.0000

.0636

.0630

.947

 

AIPW

-.0002

.0362

.0359

.949

 

-.0016

.0640

.0641

.955

 

-.0014

.0574

.0555

.942

 

CC

.0288

.0356

.0367

.885

 

.2039

.0644

.0714

.166

 

.0864

.0570

.0588

.673