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2.5 Inference: Fixed effects define U c = Dc U where D c is a diagonal matrix whose elements are given by the inverse elements of the last column of U ie dcii = 1/uir , i = 1, . . . , r. The matrix U c is therefore upper triangular with the elements in the last column equal to one. If the vector σ is ordered in the “natural” way, with σ 2 being the last element, then we can define the vector of so called “pseudo” stratum variance components by ξ = U cσ Thence var (ξ) = D 2c The diagonal elements can be manipulated to produce effective stratum degrees of freedom Thompson (1980) viz νi = 2ξi2 /d2cii In this way the closeness to an orthogonal block structure can be assessed. 24
