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An advanced and widely used method of analysis for multi-environment trial data involves a linear mixed model with factor analytic (FA) variance structures for the variety by environment effects. This model can accommodate unbalanced data, that is, not all varieties in all environments, it allows the use of pedigree information and appropriate accommodation of individual trial experimental designs, and most importantly the FA structure for the variety by environment effects is parsimonious and regularly results in a good fit to the data. The model provides accurate predictions of the variety effects for every environment in the data-set but this constitutes a large and unwieldly amount of information to process for the purpose of variety selection. We address this issue in the current paper by proposing factor analytic selection tools to summarise the predictions in a concise yet informative manner. The tools, which are natural derivatives of the FA structure, result in measures of overall performance and stability across the environments in the data-set. All measures are expressed on the same scale as the trait under consideration and can easily be combined to form an index for selection.

Plant breeding selection tools built on factor analytic mixed models for multi-environment trial data