Variance Models

CHOLk, CHOLkC, ANTE, US

In CHOLk models S = LDL' where L is lower triangular with ones on the diagonal, D is diagonal and k is the number of non-zero off diagonals in L.

In CHOLkC models S = LDL' where L is lower triangular with ones on the diagonal, D is diagonal and k is the number of non-zero sub diagonal columns in L. This is somewhat similar to the factor analytic model.

In ANTEk models inverse(S) = UDU' where U is upper triangular with ones on the diagonal, D is diagonal and k is the number of non-zero off diagonals in U

The CHOLk and ANTEk models are equivalent to the US structure, that is, the full variance structure, when k is w - 1,

Initial values for US, CHOL and ANTE structures are given in the form of a US matrix which is specified lower triangle row-wise, viz
  V11
  C21   V22
  C31   C32   V22
that is, initial values are given in the order, V11 C21 V22 C31 C32 V33

The US model is associated with several special features of ASReml.
  • When used in the R structure for multivariate data, ASReml automatically recognises patterns of missing values in the responses.
  • When the !GP qualifier is set, ASReml checks the matrix after every AI update and of the matrix is not Positive Definite, backs up and does an EM update instead.

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