Trait index calculation

!GINDEX t i

The qualifier !GINDEX ModelTerm index is motivated by the concept of a selection index, wishing to predict effects indices that are linear combinations of objective traits that are not measured. In principle these objective traits could be included directly in a mixed model but it is sometimes more computationally feasible to calculate the predicted values by using the idea of a selection index and form the index from the predictions of the measured traits. If the i-th index for an individual is αiuowith linear combination αi of objective traits effects uo, then this index can be predicted with βiumwith βi= αiGom Gmm-1 where Gom is the covariance between objective and measured trait effects and Gmm is the variance of measured trait effects and uo is the prediction of the effects for the measured traits. Note that this qualifier is envisaged to be used to provide predictions of effects using one round of iteration and using known values of the variance parameters. For example 
 harvey.dat !MAXIT 1
 !GINDEX us(Trait).nrm(animal) 0.25 0.75, 0.70 0.30
 !ASSIGN INITS 19.96 8.985 117.2
 !ASSIGN INITR 134.8 -66.45 655.2
 ADG WT ~ Trait Tr.line at(Tr,2).Age !r +
  us(Trait $INITS).nrm(animal)
 residual units.us(Trait $INITR)
generates predicted values for 2 indices using animal effect predicted values for traits ADG and Y3. The term us(Trait) identifies Gmm . Forty coefficients can be supplied and the number is a multiple of the number of traits. The computed selection and prediction error standard errors are written to the .sli file. Note that the prediction error standard errors are calculated from the prediction of βium. The prediction error of βium also includes an extra term dependent on βium- αiuo, the extra variation from predicting the indices using measured traits instead of objective traits. This variation depends on Goo - Gom Gmm-1 Gmo' but at present this is not calculated by ASReml. This qualifier should be placed after the datafile line and before the model line.

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