Transformations in mixed models: Application to risk analysis for a multienvironment trial

An important trait in crop cultivar evaluation is stability of performance across environments. There are many different measures of stability, most of which are related to variance components of a mixed model. We believe that stability measures assessing yield risk are of particular relevance, because they integrate location and scale parameters in a meaningful way. A prerequisite for obtaining valid risk estimates is an appropriate model for the distribution of yield across environments. Multienvironment trials (MET) are often analyzed by mixed linear models, assuming that environments are a random sample from a target population, and that random terms in the model are normally distributed. The normality assumption may not always be tenable, and consequently, risk estimates may be biased. In this article, we suggest a transformation approach based on the Johnson system to cope with nonnormality in mixed models. The methods are exemplified using an international wheat yield trial. The importance of accounting for nonnormality in risk analyses based on MET is emphasized. We suggest that transformations should be routinely considered in analyses to assess risk.