Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Table 2 Averages of kernel elements and their predictive correlations for the Holstein data

Kernel	θ	k(x_i,x_i)	k(x_i,x_j)	Cor (ŷ^test,y^PTA)	MSE
Diffusion	10	0.369 (0.369)	0.138 (0.134)	0.727 (0.726)	215.93 (216.61)
	11	0.693 (0.693)	0.483 (0.477)	0.745 (0.741)	204.36 (208.68)
	11.5	0.801 (0.801)	0.644 (0.639)	0.739 (0.732)	207.93 (212.97)
	12	0.874 (0.874)	0.765 (0.762)	0.739 (0.728)	210.54 (215.08)
	13	0.952 (0.952)	0.907 (0.906)	0.734 (0.725)	211.50 (217.61)
	14	0.982 (0.982)	0.966 (0.965)	0.729 (0.723)	214.29 (218.70)
Gaussian	5×10⁻⁵	1 (1)	0.237 (0.225)	0.721 (0.702)	220.675 (233.21)
	2×10⁻⁵	1 (1)	0.551 (0.542)	0.736 (0.733)	213.41 (213.95)
	1×10⁻⁵	1 (1)	0.749 (0.742)	0.742 (0.736)	210.14 (211.24)
	5×10⁻⁶	1 (1)	0.866 (0.861)	0.736 (0.729)	210.24 (214.47)
	3×10⁻⁶	1 (1)	0.917 (0.914)	0.734 (0.726)	211.51 (216.42)
	1×10⁻⁶	1 (1)	0.971 (0.971)	0.729 (0.724)	214.37 (217.93)
G 1 ^∗	NA	0.992 (1.009)	-0.000126 (-0.000128)	0.729 (0.722)	214.36 (219.27)
G 2 ^∗	NA	0.894 (0.909)	-0.000113 (-0.00012)	0.730 (0.723)	213.64 (218.31)

Averages of diagonal k(x_i,x_i) and off-diagonal k(x_i,x_j) kernel elements, predictive correlation, and mean-squared error of prediction (MSE) for the diffusion, Gaussian, and two additive genomic relationship kernels (G 1^∗ and G 2^∗) with different values of the bandwidth parameter θ for the Holstein data. Values in parentheses were obtained by combining the SNP grid and the hypercube kernels by applying a same bandwidth parameter. G 1^∗ and G 2^∗ do not involve bandwidth parameters. The best prediction within the same kernel is underlined.

ISSN: 1297-9686