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952Table 5. Proportion of interaction variation ( ˆR ) explained when Self,Complement and average Complement index vectors are usedin AMMI model for the analysis of data set consisting of 40genotypes by 9 environments (subset of the CIMMYT ISWYNdata for 1967-1968).Set Self Index Complement Index Average Complement Index1243.6441.4228.0528.6432.8233.41Performance of the average Complement index vectorThe question of the suitability of the average Complement indexvector as an effective index vector is an important one. To investigatethe performance of the average Complement index vector ( θa) weanalysed the CIMMYT dataset of 40 genotypes in 9 environments with3 replications. Again, the data matrix was randomly split into 2 subsets(each subset of size 20 genotypes x 9 environments x 3 replicationsdata matrix) and the Self index vector was estimated from each subset.For each subset of 20 x 9 x 3 data matrix, the Complement indexvector was estimated from the corresponding Complement set of20 x 9 x 3 data matrix. The average Complement index vector wasthen estimated as the average of the two Complement index vectors.2Table 5 shows ˆR values from regressing the genotype vectors ofthe residual interaction matrix on the Self index vector, Complementindex vector and average Complement index vector.2It can be seen that ˆR values from using the average Complementindex vector and Complement index vector are relatively close2compared to the ˆR values from the Self index vector. This suggeststhat the average Complement index vector and Complement indexvector are closely related. Essentially, the pattern of response for thetwo Complement vectors appear to be similar across the two targetsets suggesting that average Complement index has a useful predictive2value. The differences in the ˆR values indicate the amount of biasintroduced into the estimation of the average Complement indexvector. Future work will need to use an appropriate scaling factor to2scale down ˆR values arising from the use of average Complementindex vectors in order to achieve the same level of accuracy as theComplement index vector.ConclusionAMMI model is a powerful tool for partitioning GEI data. However,the structure of the residual interaction matrix after fi tting the additiveterms exhibit high correlations between the genotype vectors overthe environments. Ignoring the correlations between the terms of the