Eigenvalue
correction and isotonic regression methods in AMMI models

Lúcio Borges de ARAÚJO^{[1]}

Carlos Tadeu dos Santos DIAS^{1}

§ ABSTRACT: In agricultural research
it is common to analyze groups of experiments. There are several methods of
analysis and interpretation for the genotype x environment interaction from a
group of genotypes tested in several environments. These methods include AMMI
models, which an ANOVA for the main effects and assume multiplicative effects
for interaction using DVS. The overestimation and underestimation problem with
eigenvalues estimated in the conventional way is found in the specialized literature.
To correct these problems three methods are presented, but it is observed that
they do not always maintain the order of values. The authors then suggest the
use of isotonic regression. The results indicated that: isotonic regression was
sufficient to order the values corrected by the methods; there was a reduction
in the number of significant components to be kept in the AMMI models; method 2
and method 3 had, respectively, the smallest and the largest rates of
correction to the sum of squares of the genotype x environment interaction; measure RMSPD_{PRESS}
was smallest when method of correction
2 was used. Method of correction 3 had the largest values for RMSPD_{PRESS};
method 2 was also better when the interest was to verify the gain in number of replicates
that lack for the full AMMI model to present a similar performance to that of
the AMMI model selected. This benefit was always close to three replicates.

§ KEYWORDS: Correction of eigenvalues;
isotonic regression; AMMI models; genotype x environment interaction; efficiency
replicates.

[1]Departamento de Ciências Exatas, Universidade de São Paulo, campus de Piracicaba - ESALQ/USP, CEP

13418-900 Piracicaba, SP, Brasil. E-mail: *araujolb@gmail.com*
/ *ctsdias@esalq.usp.br*