Table 3.

Results of simulation study under MNAR: comparison of ${\hat{θ}}_{0}$ , ${\hat{θ}}_{I W}$ , ${\hat{θ}}_{D R}$ , ${\hat{θ}}_{D R - N}$ , ${\hat{θ}}_{I W - S}$ , ${\hat{θ}}_{D R - S}$ , and ${\hat{θ}}_{D R - N - S}$ using modified weights, when ε ~ N(0, 1) and Z₁ and Z₂ are identical. True θ is 0.722. The details of true models and misspecified working models are provided in Section 3.2.

	RB (%)	SE	SD	SMSE	CR (%)
${\hat{θ}}_{G S}$	−0.2	0.036	0.037	0.037	94.0
${\hat{θ}}_{0}$	−8.1	0.053	0.055	0.080	78.2
Correct subset of Z₁ and D included in $(M 1)$
${\hat{θ}}_{I W}$	−5.8	0.052	0.055	0.069	85.4
${\hat{θ}}_{I W - S}$	−1.0	0.049	0.052	0.053	93.0
Correct subset of Z and D included in both models
${\hat{θ}}_{D R}$	−0.5	0.039	0.040	0.041	95.0
${\hat{θ}}_{D R - N}$	−0.5	0.039	0.040	0.040	94.4
${\hat{θ}}_{D R - S}$	−0.2	0.038	0.039	0.039	93.8
${\hat{θ}}_{D R - N - S}$	−0.2	0.038	0.039	0.039	93.6
Incorrect subset of Z₁ and D included in $(M 1)$
${\hat{θ}}_{D R}$	−0.6	0.039	0.040	0.041	94.6
${\hat{θ}}_{D R - N}$	−0.5	0.039	0.040	0.040	93.2
${\hat{θ}}_{D R - S}$	−0.2	0.038	0.039	0.039	94.0
${\hat{θ}}_{D R - N - S}$	−0.2	0.038	0.039	0.039	93.4
Incorrect subset of Z₂ and D included in $(M 2)$
${\hat{θ}}_{D R}$	−5.3	0.049	0.053	0.065	85.0
${\hat{θ}}_{D R - N}$	−5.3	0.050	0.053	0.065	86.2
${\hat{θ}}_{D R - S}$	−0.8	0.047	0.049	0.049	92.8
${\hat{θ}}_{D R - N - S}$	−0.8	0.048	0.049	0.049	93.8