A comparison was made between the alternative models of analysis in a mixed model approach to partially balanced incomplete block designs, namely: (a) fixed model; (b) analysis with recovery of interblock information (lattice); (c) BLUP analysis of treatment's effects; and (d) random model. Two alternatives for construct the ANOVA table was also considered: (e) to take the mean squares of treatments adjusted to blocks and lattice effective errors; (f) to take the replications as random complete blocks. An Eucalyptus grandis (Hill) Maiden progeny trial illustrates the implications of model choice in selection and variability studies. It was found that, in general, the ranking of treatment means was more affected by the type of model chosen than the estimation of genetic progress expected from selection. This was particularly true under higher selection intensities. The analysis forms that consider the restriction of the randomization (incomplete blocks) were the most precise and among them, the analysis BLUP of treatments is conceptually the best (because the treatments were open pollination progenies), being the one that differs most of the usual analysis of the lattice. This indicates to be possible to lessen the selection mistakes in the analyses of incomplete blocks in plant breeding.
linear models; experimental designs; partially balanced incomplete block designs; mixed model methods; BLUP
