Crossover (i.e., rank-change) interactions (COIs) are of particular in
terest in the interpretation of cultivar yield trial data. The shifted
multiplicative model (SHMM) was used to search for subsets of cultiva
rs in which cultivar COIs could be regarded as insignificant or small
in a 1985 Kentucky wheat (Triticum aestivum L.) trial with 41 cultivar
s and seven locations. The first step was to obtain a dendrogram by co
mplete linkage (farthest neighbor) cluster analysis with the ''distanc
e'' between a pair of cultivars defined as the residual sum of squares
when SHMM with one multiplicative term (SHMM(1)) is fitted subject to
a constraint that the fitted model be free of COIs. Statistical tests
were computed on subsets of cultivars suggested by branching of the d
endrogram to identify subsets in which a constrained SHMM, would accou
nt for the variation. Five clusters of five cultivars each and four sm
aller clusters were found satisfactory. Six cultivars did not cluster
with any other cultivar. Analysis of all 2x2 interactions indicated th
at the method effectively assigned cultivars involved in large COIs to
different clusters. Only 6% of COIs within clusters were significant
as compared to 29% among clusters. Clustering would allow breeders and
growers to restrict selection of cultivars to the better ones in each
cluster.