Download pdf guide - VSN International

104 8 REML analysis of unbalanced designsThe REML facilities thus produce the same information as that given by the Analysis ofVariance menu where this is possible in their more general context, but they are not ableto match its more specialized output. The advantage of the REML menus, however, liesin the fact that they can also analyse unbalanced designs.8.2 PracticalUse the Linear Mixed Models menu to reanalyse the experiment on meat-tenderizingchemicals (spreadsheet file Meat.gsh), but without fitting the polynomials totemperature. Compare the analysis with the split-plot analysis, originally performed inSection 5.2, using the Analysis of Variance menu.8.3 Linear mixed models: a non-orthogonal designWe now consider the analysis of a rather more complicated field experiment (at SlateHall Farm in 1976), previously analysed by Gilmour et al. (1995). The design was set upto study 25 varieties of wheat, and contained six replicates (each with one plot for everyvariety) laid out in a two by three array. The variety grown on each plot is shown in theplan below.Each replicate has a block structure of rows crossed with columns, so the randommodel isreplicates / (rows * columns)(rows crossed with columns, nested within replicates), which expands to givereplicates + replicates.rows + replicates.columns +replicates.rows.columnsSo we have random terms for replicates, rows within replicates, columns within replicatesand, finally, replicates.rows.columns represents the residual variation. The fixedmodel contains just the main effect of the factor variety.1 2 4 3 5 19 23 2 6 15 18 25 9 11 26 7 9 8 10 8 12 16 25 4 5 7 16 23 1421 22 24 23 25 11 20 24 3 7 6 13 22 4 2011 12 14 13 15 22 1 10 14 18 24 1 15 17 816 17 19 18 20 5 9 13 17 21 12 19 3 10 213 18 8 13 23 16 24 10 13 2 10 4 17 11 231 16 6 11 21 12 20 1 9 23 12 6 24 18 55 20 10 15 25 4 7 18 21 15 19 13 1 25 72 17 7 12 22 25 3 14 17 6 21 20 8 2 144 19 9 14 24 8 11 22 5 19 3 22 15 9 16