ASReml-S reference manual - VSN International

8.8 Paired Case-Control Study 106The multivariate data frame> riceMV names(riceMV)[1] "Pair" "Run" "Variety" "yc" "ye" "syc" "sye"contains factors Variety and Run and variates for root weight and square root of rootweight for both the control and exposed treatments (yc, ye, syc, sye respectively).A plot of the treated vs the control root area (on the square root scale) for each variety isshown in Figure 8.8. There is a strong dependence between the treated and control rootarea, which is not surprising. The aim of the experiment was to determine the toleranceof varieties to bloodworms and identify the most tolerant varieties. The definition oftolerance should allow for the fact that varieties differ in their inherent seedling vigour(Figure 8.8). The initial approach was to regress the treated root area against the controlroot area and define the index of vigour as the residual from this regression. This is clearlyinefficient since there is error in both variables. We seek to determine an index of tolerancefrom the joint analysis of treated and control root area.141210sye864210 15 20sycFig. 8.8. Rice bloodworm data: Plot of square root of root weight for treated versus controlStandard analysisPreliminary analyses indicated variance heterogeneity so that subsequent analyses wereconducted on the square root scale. The allocation of bloodworm treatments withinvarieties and varieties within runs defines a nested block structure of the formRun/Variety/Tmt = Run + Run:Variety + Run:Variety:Tmt( = Run + Pair + Pair:Tmt )( = Run + Run:Variety + units )There is an additional blocking term, however, due to the fact that the bloodworms withina run are derived from the same batch of larvae whereas between runs the bloodwormscome from different sources. This defines a block structure of the form