Table 5.

Performances of methods using instrument pr

		Instrument strength
		Weak				Mod				Strong
Level	Method	rB	sd	rMSE	pval	rB	sd	rMSE	pval	rB	sd	rMSE	pval
High	Tr	1.62	0.23	0.24	0.06	0.52	0.26	0.24	0.04	1.93	0.40	0.32	0.06
	Conv	46.14	0.23	1.40	1.00	42.40	0.26	1.29	1.00	39.62	0.39	1.23	1.00
	2SRI	14.98	0.66	0.85	0.13	9.41	0.47	0.53	0.09	8.49	0.44	0.53	0.10
	GMM	72.01	315.65	5.06	0.27	75.50	109.91	4.70	0.32	71.32	60.00	4.25	0.40
Med	Tr	0.58	0.25	0.23	0.05	1.25	0.31	0.30	0.07	1.61	0.48	0.32	0.04
	Conv	25.40	0.25	0.80	0.96	23.98	0.31	0.78	0.85	21.37	0.48	0.72	0.63
	2SRI	9.93	0.66	0.70	0.07	6.90	0.54	0.61	0.08	5.45	0.54	0.54	0.09
	GMM	36.76	47.90	43.89	0.40	32.85	32.04	2.17	0.51	44.82	41.87	3.36	0.35
Low	Tr	0.66	0.26	0.26	0.07	1.51	0.33	0.28	0.04	2.20	0.55	0.35	0.05
	Conv	7.86	0.26	0.35	0.15	7.96	0.33	0.37	0.11	7.72	0.55	0.41	0.10
	2SRI	6.43	0.71	0.74	0.07	5.76	0.64	0.62	0.06	5.91	0.66	0.67	0.10
	GMM	22.04	31.69	2.42	0.49	26.15	31.68	3.49	0.64	43.12	25.42	4.14	0.46

Legend: Tr = True model, Conv = Conventional model, 2SRI = Two-Stage Residual Inclusion, GMM = Generalized Method of Moment. Low, Med (Medium), High denote the level of confounding whereas Weak, Mod (Moderate), Strong stand for instrument strength. For the criteria, rB= relative bias (%),sd= standard deviation, rMSE= root Mean Squares error and pval= non-coverage probabilities