Choosing components in the additive main effect and multiplicative interaction (AMMI) models

Abstract

The additive main effect and multiplicative interaction (AMMI) models allows analysts to detect interactions between rows and columns in a two-way table. However, there are many methods proposed in the literature to determine the number of multiplicative components to include in the AMMI model. These methods typically give different results for any particular data set, so the user needs some guidance as to which methods to use. In this paper we compare four commonly used methods using simulated data based on real experiments, and provide some general recommendations. Key words: two-way table, principal components, simulation ESCOLHA DE COMPONENTES NOS MODELOS DE EFEITOS PRINCIPAIS ADITIVOS E INTERAÇÃO MULTIPLICATIVA (AMMI)RESUMO: Os modelos de efeitos principais aditivos e interação significativa (AMMI) permitem ao analista detectar interações entre linhas e colunas em uma tabela de dupla entrada. Entretanto, existem muitos métodos propostos na literatura para determinar o número de componentes multiplicativos a incluir nos modelos AMMI. Esses métodos fornecem diferentes resultados para um particular conjunto de dados. Assim, o usuário necessita de orientação sobre quais métodos usar. Nesse trabalho investigamos quatro métodos comumente utilizados em um amplo espectro de condições usando dados simulados baseados em dados de ensaios reais. O método de Eastment-Krzanowski apresentou melhor desempenho; cada um dos outros métodos exibiram baixo desempenho em alguma das situações estudadas. Palavras-chave: tabela de dupla entrada, componentes principais, simulação

Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

“…This interaction is the multiplicative part of the model. In the second phase, the interaction is analysed by singular value decomposition (SVD) of the matrix (GE (g×e) = [(ge) ij ]) or by principal component analysis (PCA) (Gauch, 1992;Dias and Krzanowski, 2003;Dias and Krzanowski, 2006;Gauch et al, 2011;Gauch, 2013).…”

“…where G (g×e) is the genotype effect and H (n×e) the location effect (Gauch, 1992;Dias and Krzanowski, 2006;Gauch, 2006).…”

“…The choice of an appropriate statistical method depends on the experimental data, the number of available environments, and the accuracy of the information. Applications of the AMMI model to yield trials have appeared frequently during the last two decades, and there have been several recent review articles (Dias and Krzanowski, 2006;Gauch, 2006;Yan et al, 2007;Gauch et al, 2008;Yan et al, 2009;Gauch, 2013;Rodrigues et al, 2014). This analysis can help in the identification of genotypes which have high productivity and are well adapted to an agronomic zone, with the aim of regionalised recommendation and selection of test sites (Gauch and Zobel, 1996;Gauch et al, 2011;Gauch, 2013).…”

Deterministic Imputation in Multienvironment Trials

“…An inherent requirement of the AMMI model is prior specification of the number of multiplicative components [49][50][51]. Rodrigues [28] made an exhaustive analysis of the related literature and concluded that usually two or three components can be used because, in general, one component is not enough to capture the entire pattern of response in the data, but with more than three components there are obvious visualization problems, and a huge quantity of noise is liable to be captured.…”

Métodos para escolha de componentes em modelo de efeito principal aditivo e interação multiplicativa (AMMI).

“…Dias e Krzanowski (2003) propuseram dois métodos baseados em um procedimento "leave-one-out" completo, que otimiza o processo de validação cruzada.…”