Comparison of a one- and two-stage mixed model analysis of Australia’s National Variety Trial Southern Region wheat data

A one-stage analysis of a series of variety trials involves a combined analysis of the individual plot data across trials. Together with prudent modelling of the genetic effects across trials, this is considered to be the gold standard analysis of multi-environment field trial data. An alternative is a two-stage approach in which the variety means from an analysis of the individual trials in stage one are combined into a weighted mixed model analysis in stage two to give the full set of predicted variety by environment effects and an estimate of their associated variance structure. The two-stage analysis will exactly reproduce the one-stage analysis if the full variance-covariance matrix of the means from stage one is known and is utilised in stage two. Typically the full matrix is not stored and a diagonal approximation is used. This introduces a compromise to the full analysis. The impacts of a diagonal approximation are greater in the presence of sophisticated models for the genetic effects. A second compromise is through a loss of information in estimating the non-genetic variance parameters using the two-stage approach. In this paper we draw a direct link between the one and two-stage analysis approaches for crop variety evaluation data in Australia. We now have the computing power to analyse large and complex multi-environment variety trial data sets using the one-stage approach without the need for a two-stage approximation. This should motivate a move away from the two-stage approach in a range of contexts.