Weighted Analysis

!WT

Weighted analyses are achieved by using !WT weight as a qualifier to the response variable. An example of this is
y !WT wt ~ mu A X
where y is the name of the response variable and wt is the name of a variate in the data containing weights. If these are relative weights (to be scaled by the units variance) then this is all that is required. If they are absolute weights, that is, the reciprocal of known variances, use the !DISPERSION 1 qualifier to fix the unit variance. When a structure is present in the residuals the weights are applied as a matrix product. If S is the structure and W is the diagonal matrix constructed from the square root of the values of the variate weight, then R inverse = W ( S inverse) W. Negative weights are treated as zeros.

In the case of multivariate analysis, specifying a single !WT variable applies the weights to the set of response variables. In this case, the R structure may be written algebraicly as W^-1 cross Σ although the syntax might be

 TrA TrB !WT wt ~ Trait ...
 residual units.us(Trait)

If you wanted trait speciic weights, you would need to write

  !ASUV
 TrA TrB !WT wtA !WT wtB ~ Trait ... mv !r ...
 residual units.us(Trait)

Example

 Analysing means with known absolute weights
  Trial !A
  Genotype !A
  meanyld
  weight
 Summary.asd !skip 1
 meanyld !WT weight !DISP 1 ~ mu Trial !r xfa1(Trial).Genotype
 predict Genotype

More examples

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