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Research article2020Peer reviewedOpen access

Cross-validation of stagewise mixed-model analysis of Swedish variety trials with winter wheat and spring barley

Buntaran, Harimurti; Piepho, Hans-Peter; Schmidt, Paul; Rydén, Jesper; Halling, Magnus; Forkman, Johannes


In cultivar testing, linear mixed models have been used routinely to analyze multienvironment trials. A single‐stage analysis is considered as the gold standard, whereas two‐stage analysis produces similar results when a fully efficient weighting method is used, namely when the full variance–covariance matrix of the estimated means from Stage 1 is forwarded to Stage 2. However, in practice, this may be hard to do and a diagonal approximation is often used. We conducted a cross‐validation with data from Swedish cultivar trials on winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.) to assess the performance of single‐stage and two‐stage analyses. The fully efficient method and two diagonal approximation methods were used for weighting in the two‐stage analyses. In Sweden, cultivar recommendation is delineated by zones (regions), not individual locations. We demonstrate the use of best linear unbiased prediction (BLUP) for cultivar effects per zone, which exploits correlations between zones and thus allows information to be borrowed across zones. Complex variance–covariance structures were applied to allow for heterogeneity of cultivar × zone variance. The single‐stage analysis and the three weighted two‐stage analyses all performed similarly. Loss of information caused by a diagonal approximation of the variance–covariance matrix of adjusted means from Stage 1 was negligible. As expected, BLUP outperformed best linear unbiased estimation. Complex variance–covariance structures were dispensable. To our knowledge, this study is the first to use cross‐validation for comparing single‐stage analyses with stagewise analyses.

Published in

Crop Science
2020, Volume: 60, number: 5, pages: 2221-2240