ASReml-S reference manual - VSN International

8.3 Unbalanced nested design 84[4,] 7.682954 7.682954 7.682954 NA 9.715025 9.715025 9.715025 9.715025[5,] 9.715025 9.715025 9.715025 9.715025 NA 7.682954 7.682954 7.682954[6,] 9.715025 9.715025 9.715025 9.715025 7.682954 NA 7.682954 7.682954[7,] 9.715025 9.715025 9.715025 9.715025 7.682954 7.682954 NA 7.682954[8,] 9.715025 9.715025 9.715025 9.715025 7.682954 7.682954 7.682954 NA[9,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[10,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[11,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[12,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[,9] [,10] [,11] [,12][1,] 9.715025 9.715025 9.715025 9.715025[2,] 9.715025 9.715025 9.715025 9.715025[3,] 9.715025 9.715025 9.715025 9.715025[4,] 9.715025 9.715025 9.715025 9.715025[5,] 9.715025 9.715025 9.715025 9.715025[6,] 9.715025 9.715025 9.715025 9.715025[7,] 9.715025 9.715025 9.715025 9.715025[8,] 9.715025 9.715025 9.715025 9.715025[9,] NA 7.682954 7.682954 7.682954[10,] 7.682954 NA 7.682954 7.682954[11,] 7.682954 7.682954 NA 7.682954[12,] 7.682954 7.682954 7.682954 NA$‘Variety:Nitrogen‘$avsedmin mean max7.682954 9.160824 9.715025For the first two predictions, the average SED is calculated from the average variance ofdifferences.8.3 Unbalanced nested designThis example illustrates some further aspects of testing fixed effects in linear mixedmodels. It differs from the previous split plot example in that it is unbalanced, so morecare is required in assessing the significance of fixed effects.The experiment was reported by Dempster et al. [1984] and was designed to comparethe effect of three doses of an experimental compound (control, low and high) on thematernal performance of rats. Thirty female rats (Dams) were randomly split into threegroups of 10 and each group randomly assigned to the three different doses. All pups ineach litter were weighed. The litters differed both in total size and composition of malesand females. Thus the additional covariate littersize was included in the analysis. Thedifferential effect of the compound on male and female pups was also of interest.Three litters had to be dropped from the experiment, which meant that one dose had only7 dams. The analysis must account for the presence of between dam variation, but mustalso recognise the stratification of the experimental units (pups within litters) and therestricted randomisation of the doses to the dams. An indicative ANOVA decompositionfor this experiment is given in Table 8.2.The Dose and littersize effects are implicitly tested against the residual dam variation,while the remaining effects are tested against the residual within litter variation. Theasreml call is:> rats.asr