This may be necess= ary for those who want to browse the index to do searches that are unreason= able requests (for example, would occupy too much time of a member of the U= SHMM
staff), generic searches or those that do not want to wait for a respo= nse from the museum.
We report here on a study of a dataset of 22 yr of multilocation regional spring wheat variety trials in Alberta, using SHMM
and SREG models.
Previously, we successfully used SHMM
and ISS classification methods to analyze the relationships among international testing sites for the Semi-Arid Wheat Yield Trial (SAWYT; targeted for dryland environments) (Trethowan et al., 2001), the Elite Spring Wheat Yield Trial (ESWYT; targeted for irrigated environments) (Trethowan et al., 2003), and the High Rainfall Wheat Yield Trial (HRWYT; targeted for high rainfall environments) (Lillemo et al., 2004).
For a given dataset, all types of biplots listed above except the SHMM
biplot can be readily generated and visualized using the GGEbiplot software.
Recently, we have used both SHMM
and ISS classification methods to analyze the relationships among international testing sites for the Semi-Arid Wheat Yield Trial (SAWYT) (Trethowan et al., 2001) and the Elite Spring Wheat Yield Trial (ESWYT) targeted to irrigated environments (Trethowan et al., 2003).
(1993, 1996) obtained shrinkage estimators of multiplicative models (AMMI, SREG, GREG, COMM, and SHMM
) for estimating the realized performance level of cultivars in the testing environments and presented evidence that predictive accuracy of shrinkage estimators was at least as good as, and often better than, the better choice of truncated multiplicative models and the best linear unbiased prediction (BLUP) of the cell means using a two-way random effects model.
Shrinkage estimation of SHMM
is more complicated than for the other multiplicative models, computation of which requires an iterative algorithm (Cornelius and Crossa, 1995, 1999).
Adjusted means were calculated and used in all subsequent SHMM
and pattern analyses to examine site clustering or grouping.
For some model forms (SHMM
and SREG), the model with smallest PRESS predicted data in a deleted cell better than they were predicted by three replicates of data with all cells present.
and SREG models with one multiplicative component (SHM[M.sub.1] and SRE[G.sub.1]) are adequate for fitting the data (second, third, and higher order multiplicative components are negligible) and primary effects of the sites, [[gamma].sub.j1], are either all non-positive or all non-negative, SHM[M.sub.1] and SRE[G.sub.1] predict non-COI.
These are the shifted multiplicative model (SHMM
) in which [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The multiplicative model forms AMMI (Additive Main effects and Multiplicative Interactions), GREG (Genotypes Regression), SREG (Sites Regression), SHMM
(Shifted Multiplicative), and COMM (Completely Multiplicative) all include a sum of multiplicative terms [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] but differ with respect to which additive components in Eq.