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 !S2==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.

Example

 Analysing means with known absolute weights
  Trial !A
  Genotype !A
  meanyld
  weight
 Summary.asd !skip 1
 meanyld !WT weight ~ mu Trial !r Trial.Genotype
 predict Genotype
 1 1 1
 0 !S2==1
 Trial.Genotype 2
 Trial 0 CORUH .8
 10 * 3.5    # assuming 10 trials
 Genotype

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