Table 2.

Simulations results for the power and relative efficiency.^†

		β 1		β2 = −0.5		β 1		β2 = −0.5
β 1	Method	RE	Size/Power	RE	Power	RE	Size/Power	RE	Power
		(n0, n1, n3) = (100, 50, 50), σ2 = 4				(n0, n1, n3) = (150, 25, 25), σ2 = 4
0.0	${\widehat{\beta }}_X$	1.000	0.055	1.000	0.284	1.000	0.051	1.000	0.245
	${\widehat{\beta }}_{{\mathit{PDS}}_1}$	0.983	0.056	1.011	0.312	1.001	0.048	1.016	0.296
	${\widehat{\beta }}_{{\mathit{PDS}}_2}$	1.002	0.058	0.780	0.436	1.013	0.044	0.806	0.354
	${\widehat{\beta }}_{\mathit{ODS}}$	1.011	0.059	0.934	0.331	1.019	0.044	1.036	0.308
	${\widehat{\beta }}_{\mathit{IPW}}$	1.188	0.071	1.085	0.278	1.106	0.055	1.042	0.267
	${\widehat{\beta }}_{\mathit{SRS}}$	1.332	0.058	1.227	0.229	1.238	0.058	1.187	0.229
0.1	${\widehat{\beta }}_X$	1.000	0.167	1.000	0.286	1.000	0.134	1.000	0.240
	${\widehat{\beta }}_{{\mathit{PDS}}_1}$	1.005	0.172	0.980	0.322	1.000	0.128	0.981	0.252
	${\widehat{\beta }}_{{\mathit{PDS}}_2}$	1.010	0.176	0.795	0.446	1.005	0.148	0.823	0.380
	${\widehat{\beta }}_{\mathit{ODS}}$	1.016	0.159	0.940	0.350	1.042	0.131	1.015	0.287
	${\widehat{\beta }}_{\mathit{IPW}}$	1.189	0.144	1.099	0.264	1.093	0.129	1.053	0.293
	${\widehat{\beta }}_{\mathit{SRS}}$	1.336	0.110	1.234	0.236	1.225	0.110	1.178	0.236
0.5	${\widehat{\beta }}_X$	1.000	0.997	1.000	0.291	1.000	0.990	1.000	0.259
	${\widehat{\beta }}_{{\mathit{PDS}}_1}$	1.031	0.999	0.942	0.315	1.000	0.976	0.837	0.316
	${\widehat{\beta }}_{{\mathit{PDS}}_2}$	1.042	0.997	0.812	0.443	1.001	0.980	0.829	0.334
	${\widehat{\beta }}_{\mathit{ODS}}$	1.068	0.996	0.962	0.324	1.027	0.985	0.991	0.282
	${\widehat{\beta }}_{\mathit{IPW}}$	1.191	0.981	1.117	0.274	1.068	0.978	1.036	0.254
	${\widehat{\beta }}_{\mathit{SRS}}$	1.338	0.930	1.237	0.207	1.202	0.930	1.114	0.207

^†Results are based on the model Y = β₀ + β₁X + β₂l_log(|x|)+e>1 +∊, where e ~ N(0, 1), ∊ ~ N(0, σ²), and X ~ N(0, 1).