. Author manuscript; available in PMC: 2017 Mar 15.

Published in final edited form as: Biometrics. 2016 Mar 21;72(4):1017–1025. doi: 10.1111/biom.12511

Table 1.

Empirical size and power for different methods, under various sample size, number of predictors, and correlation among predictors, with continuous outcome.

			size		nonlinear		linear

		method	n=500	n=1000	n=500	n=1000	n=500	n=1000
℘=0.2	p=5	Wald	0.050	0.050	0.317	0.519	0.543	0.791
		k_L	0.048	0.052	0.361	0.588	0.530	0.778
		k_Q	0.037	0.044	0.801	0.987	0.493	0.745
		k_G	0.033	0.039	0.994	1.000	0.611	0.909
		Omnibus	0.035	0.043	0.990	1.000	0.572	0.881
		Crump	0.069	0.063	0.361	0.559	0.582	0.795

	p=20	Wald	0.051	0.046	0.275	0.401	0.458	0.693
		k_L	0.044	0.047	0.318	0.541	0.498	0.745
		k_Q	0.028	0.031	0.653	0.933	0.425	0.679
		k_G	0.043	0.046	0.386	0.779	0.511	0.774
		Omnibus	0.032	0.037	0.603	0.921	0.461	0.736
		Crump	0.099	0.062	0.388	0.459	0.561	0.733

℘=0.5	p=5	Wald	0.044	0.042	0.275	0.414	0.429	0.665
		k_L	0.054	0.051	0.316	0.480	0.466	0.709
		k_Q	0.041	0.051	0.893	0.985	0.371	0.613
		k_G	0.041	0.045	0.998	1.000	0.604	0.910
		Omnibus	0.046	0.048	0.995	1.000	0.530	0.866
		Crump	0.077	0.075	0.302	0.434	0.447	0.671

	p=20	Wald	0.039	0.041	0.215	0.319	0.357	0.562
		k_L	0.049	0.046	0.297	0.470	0.474	0.706
		k_Q	0.045	0.039	0.818	0.969	0.390	0.623
		k_G	0.047	0.046	0.706	0.990	0.517	0.808
		Omnibus	0.040	0.040	0.816	0.987	0.469	0.763
		Crump	0.080	0.064	0.325	0.361	0.455	0.625