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

Table 2 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

Methods	ρ	% R b i a s	S E _cal	S E _emp	RMSE	Cover
Before	0	0.0	0.064	0.064	0.064	95.1
deletion	0.3	0.0	0.063	0.065	0.065	95.0
	0.6	-0.2	0.064	0.064	0.064	94.3
CCA	0	0.1	0.083	0.084	0.084	95.1
	0.3	-9.1	0.082	0.081	0.122	80.3
	0.6	-17.8	0.078	0.079	0.194	38.2
HEml	0	0.0	0.103	0.103	0.103	95.2
	0.3	-0.4	0.101	0.101	0.101	94.6
	0.6	-0.4	0.092	0.092	0.092	94.2
MIHEml	0	0.0	0.105	0.103	0.103	94.7
	0.3	-0.3	0.103	0.102	0.102	95.3
	0.6	-0.3	0.096	0.094	0.094	94.8
HE2steps	0	0.0	0.103	0.102	0.102	95.4
	0.3	-0.4	0.103	0.103	0.103	94.6
	0.6	-0.2	0.100	0.099	0.099	95.4
MIHE2steps	0	0.0	0.105	0.103	0.103	95.2
	0.3	-0.4	0.104	0.104	0.104	94.0
	0.6	-0.2	0.103	0.100	0.099	95.2

%Rbias: % relative bias; SE_cal: Root mean square of the estimated standard error; SE_emp: 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

ISSN: 1471-2288