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Brian Cullis

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Separability<br />

Direct products in G-structures<br />

Simple illustration (continued):<br />

• If u = vec ( U 20×2) = [u ′ 1 ,u′ 2 ]′ then a reasonable and<br />

commonly used variance model is<br />

• Collectively we have<br />

var(u 1 ) = g 11 I 20<br />

var(u 2 ) = g 22 I 20<br />

cov(u 1 , u 2 ) = g 12 I 20<br />

say where G 2×2<br />

e<br />

matrix.<br />

var(u) = G e ⊗I 20<br />

= {g ij } is a symmetric positive definite<br />

VSN Applied Statistics Conference 2011<br />

Modelling variance structures of multi-term effects

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