Brian Cullis

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Separability Direct products in G-structures Simple illustration: • Analysis of a multi-environment trial with p = 2 sites and m = 20 varieties • If u represents (only) the effects for a first-order interaction between Site and Variety then q = 1 and, • if the effects are ordered varieties within sites, then Site is the outer factor and Variety is the inner factor. VSN Applied Statistics Conference 2011 Modelling variance structures of multi-term effects
Separability Direct products in G-structures Simple illustration (continued): • If u = vec ( U 20×2) = [u ′ 1 ,u′ 2 ]′ then a reasonable and commonly used variance model is • Collectively we have var(u 1 ) = g 11 I 20 var(u 2 ) = g 22 I 20 cov(u 1 , u 2 ) = g 12 I 20 say where G 2×2 e matrix. var(u) = G e ⊗I 20 = {g ij } is a symmetric positive definite VSN Applied Statistics Conference 2011 Modelling variance structures of multi-term effects
Page 1 and 2: Modelling variance structures of mu
Page 3 and 4: Linear mixed model The model Let y
Page 5 and 6: R-structures General Framework •
Page 7: Separability Direct products in R-s
Page 11 and 12: Syntax for multi-term variance mode
Page 13 and 14: Multi-site toy example Recall: mult
Page 15 and 16: Salinity tolerance in bread wheat A
Page 17 and 18: Salinity tolerance in bread wheat P
Page 19 and 20: Salinity tolerance in bread wheat M
Page 21 and 22: Salinity tolerance in bread wheat M
Page 23 and 24: Competition modelling in sorghum pl
Page 37 and 38: Partial compositing example from Sm

Brian Cullis

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