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Table 1 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

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

Methods

ρ

% R b i a s

S E cal

S E emp

RMSE

Cover

Before

0

0.7

0.108

0.109

0.109

94.9

deletion

0.3

1.1

0.109

0.109

0.110

95.9

 

0.6

0.9

0.109

0.109

0.109

95.2

CCA

0

1.2

0.137

0.137

0.137

95.4

 

0.3

-6.1

0.135

0.135

0.148

92.0

 

0.6

-11.9

0.135

0.134

0.179

83.5

HEml

0

-0.3

0.161

0.163

0.163

95.0

 

0.3

-0.1

0.148

0.151

0.150

94.8

 

0.6

-0.1

0.134

0.132

0.132

96.1

MIHEml

0

-1.0

0.159

0.161

0.162

94.2

 

0.3

-1.0

0.148

0.150

0.150

95.5

 

0.6

-0.9

0.135

0.132

0.133

95.4

  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