Eigenvalue correction and isotonic regression methods in AMMI models

Lúcio Borges de ARAÚJO[1]

Carlos Tadeu dos Santos DIAS1

§    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 RMSPDPRESS  was smallest when method of correction 2 was used. Method of correction 3 had the largest values for RMSPDPRESS; 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