Prediction

Complicated weighting

Generally, when forming a prediction table, it is necessary to average over (or ignore) some potential dimensions of the prediction table. By default, ASReml uses equal weights (1/f for a factor with f levels). More complicated weighting is achieved by using the !AVERAGE qualifier to set specific (unequal) weights for each level of a factor. However, sometimes the weights to be used need to be defined with respect to two or more factors. The simplest case is when there are missing cells and weighting is equal for those cells in a multiway table that are present; achieved by using the !PRESENT qualifier. This is now further generalised by allowing the user to fill in the weights for use by the !PRESENT machinery via the !PRWTS qualifier.

The user specifies the factors in the table of weights with the !PRESENT statement and then gives the table of weights using the !PRWTS qualifier. There may only be one !PRESENT qualifier on the predict line when !PRWTS is specified. The order of factors in the tables of weights must correspond to the order in the !PRESENT list with later factors nested within preceding factors. Check the output to ensure that the values in the tables of weights are applied in the correct order. ASReml may transpose the table of weights to match the order it needs for processing.

Consider a rather complicated example from a rotation experiment conducted over several years. This particular analysis followed the analysis of the daily live weight gain per hectare of the sheep grazing the plots. There were periods when no sheep grazed. Different flocks grazed in the different years. Daily liveweight gain was assessed between 5 and 8 times in the various years. To obtain a measure of total productivity in terms of sheep liveweight, we need to weight the daily per sheep figures by the number of sheep grazing days per month. To obtain treatment effects for each year, the experimenter used 
 predict year 1 crop 1 pasture lime !AVE month 56 55 56 53 57 63 6*0
 predict year 2 crop 1 pasture lime !AVE month 36 0 0 53 23 24 54 54 43 35 0 0
 predict year 3 crop 1 pasture lime !AVE month 70 0 21 17 0 0 0 70 0 0 53 0
 predict year 4 crop 1 pasture lime !AVE month 53 56 22 92 19 44 0 0 36 0 0 49
 predict year 5 crop 1 pasture lime !AVE month 0 22 0 53 70 22 0 51 16 51 0 0
but then wanted to average over years as well. Both of the following predict statements produce the required values. 
 predict crop 1 pasture lime !PRES year month !PRWTS { 56 55 56 53 57 63 0 0 0,
 0 0 0 36 0 0 53 23 24 54 54 43 35 0  0 70 0  21 17 0  0  0  70 0  0  53 0 53,
 56 22 92 19 44 0  0  36 0  0  49 0  22 0  53 70 22 0  51 16 51 0  0}/5
 predict crop 1 pasture lime !PRES month year !PRWTS { 56 36 70 53 0,
 55 0 0 56 22  56 0 21 22 0  53 53 17 92 53  57 23 0 19 70  63 24 0 44 22,
 0 54 0  0 0   0 54 70 0 51   0 43  0 36 16   0 35 0  0 51  0 0 53 5*0 49 0}/5
We have presented both sets of predict statements to show how the weights were derived and presented. Notice that the order in !PRESENT year month implies that the weight coefficients are presented with values for months nested within years. There is a check which reports if non zero weights are associated with cells that have no data. The weights are reported in the .pvs file. !PRESENT counts are reported in the .res file.
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