One Step at a Time: Stage‐Wise Analysis of a Series of Experiments

Core Ideas Single‐stage and two‐stage analysis of multienvironment trials yield very similar results. Single‐stage and two‐stage analysis are identical when the same set of variance values is used. Modeling genotypes as random helps to exploit correlations between agro‐ecological zones. In stage‐wise analysis, genotypes need to be taken as fixed through all stages except the last. Fully efficient two‐stage analysis is similar in spirit to meta‐analysis. Multienvironment trials can be analyzed using single‐stage or stage‐wise analysis. Single‐stage analysis is fully efficient, meaning that the estimators can be expected to be as close as possible to the corresponding true genotypic values, and so is often deemed preferable to two‐stage analysis. However, two‐stage analysis is often favored in practice over single‐stage analysis in the case of large datasets because of the larger computational burden of the latter and because the former allows separate analyses of individual trials in the first stage, accounting for any specifics of each trial. In this study we demonstrate the similarities of results of single‐stage and two‐stage analysis when information on mean estimates and the associated variance–covariance matrix is forwarded from the first stage to the second stage using four examples with maize ( Zea mays L.) trial data from Ethiopia. A new fully efficient and an approximate two‐stage method with diagonal weighting matrix are used for weighting in the second stage. We extend the method to three‐stage analysis for multienvironment trials when sites are stratified by agro‐ecological zones and demonstrate how to obtain best linear unbiased predictions of genotype effects per zone using the information from neighboring zones. Two macros that compute weights for use in the fully efficient and diagonal weighting approaches are provided.