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Table 4 Continuous Y and logit selection model: Simulation results for β1=1 estimates

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

Methods

\(\beta _{Y}^{sl}\)

% R b i a s

S E cal

S E emp

RMSE

Cover

Before

0

0.2

0.063

0.064

0.064

95.4

deletion

1

0.0

0.064

0.066

0.066

94.2

 

2

-0.2

0.063

0.061

0.061

96.2

CCA

0

0.3

0.079

0.078

0.078

95.8

 

1

-18.9

0.079

0.080

0.205

33.5

 

2

-30.1

0.075

0.076

0.310

2.1

HEml

0

0.3

0.105

0.108

0.108

93.6

 

1

-1.3

0.117

0.131

0.131

92.7

 

2

-1.5

0.098

0.111

0.112

94.3

MIHEml

0

0.3

0.107

0.110

0.110

94.0

 

1

-1.2

0.121

0.133

0.134

92.6

 

2

-1.3

0.105

0.113

0.114

94.7

HE2steps

0

0.3

0.107

0.105

0.105

95.4

 

1

0.9

0.149

0.158

0.158

95.0

 

2

0.0

0.162

0.165

0.165

95.6

MIHE2steps

0

0.3

0.110

0.106

0.106

95.5

 

1

0.9

0.151

0.159

0.159

94.6

 

2

0.0

0.163

0.166

0.166

94.8

  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 one-step ML estimation; MIHEml: Multiple imputation using Heckman’s one-step ML estimation; HE2steps: Heckman’s two-step estimation; MIHE2steps: Multiple imputation using Heckman’s two-step estimation