Table 2.

Results from the main simulation study for conditional selection method

Parameter	Method	Mean	SD	Mean SE	Power
${\theta }_1$	Oracle	0.357	0.129	0.120	82.5
	Cond select	0.334	0.137	0.126	73.3
	MV‐IVW‐PCA	0.299	0.126	0.118	70.8
	MV‐LIML‐PCA	0.349	0.150	0.130	76.3
${\theta }_2$	Oracle	−0.012	0.133	0.121	7.2
	Cond select	−0.015	0.140	0.126	7.4
	MV‐IVW‐PCA	−0.018	0.126	0.119	5.8
	MV‐LIML‐PCA	−0.009	0.148	0.131	7.1
${\theta }_3$	Oracle	−0.543	0.130	0.121	98.7
	Cond select	−0.515	0.142	0.127	96.5
	MV‐IVW‐PCA	−0.475	0.130	0.119	95.9
	MV‐LIML‐PCA	−0.539	0.151	0.131	96.6

Note: Results from oracle, conditional selection, MV‐IVW‐PCA, and MV‐LIML‐PCA methods across 1000 simulated datasets: mean estimates, standard deviation (SD) of estimates, mean standard error (mean SE) of estimates, and empirical power of the 95% confidence interval to estimate ${\theta }_1=0.4$, ${\theta }_2=0$, and ${\theta }_3=-0.6$.