Table 4 Spatial and non-spatial models used for the first stage

M1

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

ID

M2

Y _{h i j k o q v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k}

ID

+W _{i j o} +V _{i j q} +e _{h i j k o q v}

M3

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

AR(1) within B

M4

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

LV within B + nugget

M5

Y _{h i j k o q v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k}

AR(1) × AR(1) within R

+W _{i j o} +V _{i j q} +e _{h i j k o q v}

M6

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

AR(1) × AR(1) within R

M7

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

Model 3 + nugget

M8

Y _{h i j k v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k} +e _{h i j k v}

Model 5 + nugget

M9

Y _{h i j k o q v} =(G T) _{h v} +S _i +R _{i j} +B _{i j k}

Model 6 + nugget

+W _{i j o} +V _{i j q} +e _{h i j k o q v}