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Table 6 Continuous 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

0.2

0.063

0.063

94.6

-0.1

0.063

0.064

95.8

 

0.3

0.1

0.064

0.065

94.8

0.0

0.063

0.064

94.7

 

0.6

-0.3

0.064

0.065

94.0

0.2

0.063

0.063

95.2

CCA

0

0.1

0.095

0.092

94.8

-28.9

0.097

0.307

15.9

 

0.3

-6.3

0.093

0.118

87.4

-33.8

0.094

0.351

4.7

 

0.6

-13.3

0.090

0.162

69.7

-37.7

0.090

0.388

1.6

HEml

0

0.1

0.113

0.112

94.3

-27.7

0.118

0.306

34.6

 

0.3

-0.3

0.110

0.121

92.7

-26.9

0.110

0.294

34.4

 

0.6

-0.6

0.103

0.106

93.3

-27.5

0.099

0.293

20.9

MIHEml

0

-0.1

0.107

0.103

95.0

1.2

0.111

0.107

95.8

 

0.3

-0.9

0.105

0.109

94.1

-0.1

0.108

0.107

93.7

 

0.6

-2.2

0.101

0.099

94.9

-1.7

0.103

0.097

94.2

HE2steps

0

0.2

0.114

0.111

94.8

-28.1

0.117

0.306

30.8

 

0.3

0.0

0.114

0.123

92.7

-27.7

0.111

0.300

29.2

 

0.6

-0.3

0.113

0.114

93.9

-28.0

0.104

0.299

23.7

MIHE2steps

0

-0.1

0.107

0.101

95.5

1.1

0.110

0.107

96.1

 

0.3

-0.6

0.106

0.112

93.1

0.0

0.108

0.110

94.7

 

0.6

-1.5

0.105

0.105

94.8

-1.3

0.105

0.102

94.5

  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