Table 2.

Results of simulation study under MAR: comparison of ${\widehat{\theta }}_0$, ${\widehat{\theta }}_{IW}$, ${\widehat{\theta }}_{DR}$ and ${\widehat{\theta }}_{DR-N}$ using modified weights, when Z₁ and Z₂ are independent. ε is Gaussian (i.e., ε ~ N(0, 1)) or non-Gaussian (i.e., ε = 20{η ~ E(η)} with η ~ Beta(5, 1)). True θ is 0.722 for Gaussian ε and 0.675 for non-Gaussian ε. The details of true models and misspecified working models are provided in Section 3.1.

	Gaussian ε					non-Gaussian ε
	RB (%)	SE	SD	SMSE	CR (%)	RB (%)	SE	SD	SMSE	CR (%)
${\widehat{\theta }}_{GS}$	0.2	0.036	0.035	0.035	96.0	0.2	0.038	0.036	0.036	96.0
${\widehat{\theta }}_0$	−0.1	0.059	0.057	0.057	95.8	0.4	0.063	0.061	0.061	96.4
	Both mean models correctly specified
${\widehat{\theta }}_{IMP}$	0.1	0.039	0.040	0.040	94.2	−0.6	0.051	0.050	0.050	95.8
${\widehat{\theta }}_{IW}$	−0.1	0.059	0.060	0.059	94.8	0.3	0.062	0.065	0.065	94.6
${\widehat{\theta }}_{DR}$	0.2	0.044	0.040	0.040	96.4	0.1	0.056	0.053	0.053	95.8
${\widehat{\theta }}_{DR-N}$	0.2	0.041	0.041	0.041	95.4	0.1	0.056	0.053	0.053	95.2
	Mean model for $\left(\mathcal{M}1\right)$ misspecified
${\widehat{\theta }}_{IW}$	−0.2	0.058	0.059	0.059	95.0	0.3	0.062	0.062	0.062	95.2
${\widehat{\theta }}_{DR}$	0.2	0.041	0.040	0.040	95.0	0.2	0.053	0.051	0.051	95.8
${\widehat{\theta }}_{DR-N}$	0.2	0.041	0.040	0.040	94.8	0.1	0.054	0.051	0.051	96.2
	Mean model for $\left(\mathcal{M}2\right)$ misspecified
${\widehat{\theta }}_{DR}$	−0.2	0.059	0.055	0.055	96.0	0.4	0.063	0.062	0.062	95.4
${\widehat{\theta }}_{DR-N}$	−0.2	0.057	0.055	0.055	96.4	0.4	0.063	0.062	0.062	95.2
	th Mean Models misspecified
${\widehat{\theta }}_{DR}$.	−0.2	0.054	0.054	0.054	95.0	0.4	0.059	0.059	0.059	95.2
${\widehat{\theta }}_{DR-N}$	−0.2	0.055	0.054	0.054	95.8	0.4	0.061	0.059	0.059	95.8