Multi-environment trials generally have highly unbalanced data structures in which a particular cultivar is only observed in a subset of all environments for which data are available. A very common approach to reporting data from such unbalanced data is to subset the data into balanced sets and restrict comparisons within balanced sets. Such an approach results in much information being ignored. In an attempt to make use of all available information, a likelihood-based mixed linear model approach can be chosen since unbalanced data can be analyzed in a straightforward manner. Two studies were undertaken to determine the complexity of heterogeneity of genotype variance, correlation and error variance and to investigate predictive ability of multivariate mixed linear models with varying levels of heterogeneity of those variance components for hybrid performance in unobserved environment in the data sets of the Iowa Crop Performance Tests-Corn. In the first study, a likelihood-based model selection approach identified evidence of heterogeneity of error variances among 58 of 65 singe-year and single-district balanced data sets for two model selection criteria, AIC and BIC. Heterogeneity of genotypic variances and correlations between pairs of environments was found in about half of the data sets analyzed. In the second study where two years of data within a district formed 51 highly unbalanced data sets, there was no substantial difference between the best and worst prediction models among all 24 models considered using cross validation, although the best models were generally simpler and parsimonious models. When there was a relatively large difference between the best and worst prediction model, the magnitude of the difference appeared to be highly positively associated with the difference in pooled GE interaction variance among models and to be negatively associated with number of common hybrids between two years in the data sets. There seemed to be a negative association between the difference in pooled GE interaction variance among models and the number of common hybrids in the data sets. A simulation study indicated that the cause of the deviation of pooled GE interaction variance that was obtained from heterogeneous models from that obtained from the homogeneous genotype variance covariance model was due mainly to poor estimation of some of the variance components by very small number of common hybrids across two years. Because the prediction ability based on an average BLUPs across environments are about the same for models with varying degrees of heterogeneity in genotype variance, correlation and error variance, we may still need to find a statistical model with the best fit of the observed data which would give the most appropriate shrinkage estimator for each environment.