A SHIFTED MULTIPLICATIVE MODEL CLUSTER-ANALYSIS FOR GROUPING ENVIRONMENTS WITHOUT GENOTYPIC RANK CHANGE

The shifted multiplicative model (SHMM) is used with a cluster method to identify subsets of sites in an international maize (Zea mays L.) trial without genotypic rank-change. For cluster analysis, distance between two sites is defined as the residual sum of squares after fitting SHMM with one multiplicative term (SHMM1) if SHMM1 does not show genotypic rank-change. However, if SHMM1 does show genotypic rank-change, the distance between two sites is defined as the smaller of the sums of squares owing to genotypes within each of the two sites. Calculation of distance between two sites is facilitated by using the site regression model with one multiplicative term (SREG1), which can be reparameterized as SHMM1 when only two sites are considered. The dichotomous splitting procedure, used on the dendrogram obtained from cluster analysis, will first perform SHMM analyses on each of the last two cluster groups to join (end of the dendrogram). If SHMM1 does not give an adequate fit, the next step is to move down the branches of the tree until groups of sites (clusters) are found to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign. Five final groups of sites to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign were obtained. The procedure appears to be useful in identifying subsets of sites in which genotypic rank-change interactions are negligible.