Table 4.

Spatial and non-spatial models used for the first stage

Label	Model	Variance-covariance
		structure for error
M1	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	ID
M2	Y hijkoqv=(G T)hv+S i+R ij+B ijk	ID
	+W ijo+V ijq+e hijkoqv
M3	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	AR(1) within B
M4	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	LV within B + nugget
M5	Y hijkoqv=(G T)hv+S i+R ij+B ijk	AR(1) × AR(1) within R
	+W ijo+V ijq+e hijkoqv
M6	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	AR(1) × AR(1) within R
M7	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	Model 3 + nugget
M8	Y hijkv=(G T)hv+S i+R ij+B ijk+e hijkv	Model 5 + nugget
M9	Y hijkoqv=(G T)hv+S i+R ij+B ijk	Model 6 + nugget
	+W ijo+V ijq+e hijkoqv

Y _hijkv is the observed dry matter yield of the h-th genotype testcrossed with the v-th tester in the k-th block within the j-th replicate of the i-th trial, (G T)_hv is the effect of the h-th genotype testcrossed with the v-th tester, S _i is the effect of the i-th trial , R _ij is the effect of the j-th replicate nested within the i-th trial , B _ijk is the effect of the k-th block nested within the j-th replicate of the i-th trial and e _hijkv is the plot error associated with the Y _hijkv observation . In the models including row and column effects, W _ijo is the effect of the o-th row within the j-th replicate of the i-th trial and V _ijq is the effect of the q-th column within the j-th replicate of the i-th trial . Spatial variance-covariance structure were independent (ID), autoregressive in one direction [AR(1)], one-dimension linear variance (LV) and two-dimension autoregressive [AR(1) × AR(1)].