In this study, the unscaled GGE biplot was first constructed for the set of 18 environments. The unscaled GGE biplot is equivalent to the pairwise SE- or SEM-scaled GGE biplots in which SE or SEM is estimated by least squares minimization of Eq. 3. Since Eq. 3 is a nonlinear function of the data, singular vectors were not computed. Amended nonparametric bootstrapping, which is appropriate when only a few singular vectors are computed and meaningful interpretation is desired, was used to assess confidence in the calculated singular vectors. Re-computing the bootstrapped singular vectors (re-sampling with replacement of the original data) after randomly re-permuting the environment ID was used to test for spurious vectors from errors in data and from local environments having no connection to the global means (in the sense of Eq. 3). Averaging the singular vectors across the 50 replicates of data produced a stable result, but single replicate singular vectors should be viewed with caution.
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