Genotype by environment variance heterogeneity in a two-stage analysis

The analysis of a series of crop variety trials often proceeds using a mixed model in which the data are the combined means from individual trials. The residual variation for this model consists of genotype by environment (G.E) interactions and within-trial error variation. The latter is regarded as known from the analyses of individual trials, and any associated heterogeneity can be accounted for in the overall mixed model by the use of weights. The G.E interactions may also have nonconstant variance and, since the variances themselves are often of interest, we propose that heterogeneity arising from these sources be accommodated by modelling the G.E variances as a log-linear function of explanatory variables. We present a residual maximum likelihood estimation method and develop a diagnostic technique for detecting dependence. The approach is demonstrated using a large unbalanced set of crop variety testing data. The methodology is easily generalized to residual variance modelling in any mixed model application.