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Improved Statistical Inference for Graphical Description and Interpretation of Genotype × Environment Interaction
Author(s) -
Hu Zhiqiu,
Yang RongCai
Publication year - 2013
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci2013.04.0218
Subject(s) - biplot , bootstrapping (finance) , procrustes analysis , statistics , varimax rotation , principal component analysis , nonparametric statistics , mathematics , resampling , hordeum vulgare , pattern recognition (psychology) , artificial intelligence , biology , computer science , econometrics , genotype , botany , poaceae , biochemistry , cronbach's alpha , descriptive statistics , gene
Nonparametric resampling bootstrapping approach to constructing confidence regions (CR) for genotypic and environmental principal component (PC) scores recently has been used to statistically assess the biplot analysis of genotype × environment interaction (GE). However, it is possible to generate “greater‐than‐expected” CR due to nonunique singular value decomposition (SVD) of two‐way GE data from bootstrap samples. The objective of this study is to improve the current bootstrapping procedure to correct for the “systematic bias” due to the nonuniqueness of SVD through the use of Procrustes rotation. The Procrustes rotation is to compare the genotypic and environmental PC scores from bootstrap samples and original (target) data, with the comparison being done by rotating and then stretching and/or shrinking the PC scores from bootstrap samples such that the sum of squared distances between the corresponding elements of bootstrap and target scores is minimized. The bootstrapping and Procrustes rotation are implemented in an R package, bbplot/R. The analysis of two data sets from wheat ( Triticum aestivum L.) and barley ( Hordeum vulgare L.) cultivar trials shows that the CR for rotated genotypic and environmental scores are up to 10 times smaller than the CR for the corresponding unrotated scores. The shrunk CR constructed using the rotated scores for the biplot analysis reveal more definite delineations of mega‐environments than the assessment based on mere visual inspection of biplots. Thus, the improved bootstrapping approach will construct the more precise CR for the genotypic and environmental PC scores, thereby facilitating the correct use of biplot analysis for critical decisions on genotype selection or mega‐environment delineation.