Biplot Analysis of Incomplete Two-Way Data.
As a graphical data analysis tool, biplot analysis has increasingly been used in analyzing genotype × environment data and other types of two-way data. One limitation of biplot analysis is that it requires a complete two-way table. This paper reports on a procedure for estimating missing values in a two-way table so that incomplete data can be effectively analyzed using biplots. This procedure involves iteration of missing values based on singular value decomposition (SVD), which is the basic technique for biplot analysis. Simulation indicates that the proposed procedure successfully predicts missing values and recovers patterns for two sample datasets. On a smaller wheat (Triticum aestivum L.) dataset, the estimation was successful only when the proportion of missing data was less than 40%; for a larger oat (Avena sativa L.) dataset, the estimation was successful even when 60% of the data were treated as missing. The use of the SVD-based missing-value-estimation procedure enabled incomplete multiple-year data to be effectively analyzed in a single biplot. As a result, genotypes not tested in the same environments can be reasonably compared, and genotypes that have not been fully tested can be critically evaluated.
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