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Table 5 Binary Y: Simulation results for β1=1 with ρ=0, representing a MAR mechanism, and ρ=0.3 and 0.6, representing an MNAR mechanism, in the presence of missing data on X2

From: Heckman imputation models for binary or continuous MNAR outcomes and MAR predictors

  

R2 depends on X1 and X3

R2 depends on X1 and Y

Methods

ρ

% R b i a s

S E cal

RMSE

Cover

% R b i a s

S E cal

RMSE

Cover

Before deletion

0

0.7

0.109

0.113

95.0

0.8

0.109

0.111

94.9

 

0.3

0.5

0.108

0.108

95.7

0.9

0.109

0.109

95.0

 

0.6

0.5

0.108

0.106

95.8

1.1

0.109

0.106

95.5

CCA

0

1.0

0.158

0.159

95.3

-20.3

0.165

0.262

73.9

 

0.3

-3.8

0.158

0.166

93.4

-26.9

0.164

0.313

60.9

 

0.6

-8.4

0.158

0.178

90.9

-33.2

0.165

0.369

47.6

HEml

0

-1.3

0.182

0.182

94.8

-21.1

0.190

0.287

78.5

 

0.3

-0.5

0.169

0.175

94.3

-21.2

0.178

0.274

76.3

 

0.6

-1.1

0.158

0.158

95.0

-22.5

0.165

0.277

73.8

MIHEml

0

-2.1

0.167

0.167

95.2

-1.4

0.166

0.168

94.5

 

0.3

-1.8

0.155

0.153

95.6

-1.7

0.155

0.151

95.7

 

0.6

-2.5

0.146

0.140

96.6

-2.5

0.145

0.140

96.0

  1. %Rbias: % relative bias; SEcal: Root mean square of the estimated standard error; SEemp: Empirical Monte Carlo standard error; RMSE: Root mean square error; Cover: % coverage of the nominal 95% confidence interval; CCA: Complete case analysis; HEml: Heckman’s one-step ML estimation; MIHEml: Multiple imputation using Heckman’s one-step ML estimation