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Parametric Bootstrap Methods for Testing Multiplicative Terms in GGE and AMMI Models

Forkman, Johannes and Piepho, Hans-Peter (2014). Parametric Bootstrap Methods for Testing Multiplicative Terms in GGE and AMMI Models. Biometrics. 70:3, 639-647
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Official URL: http://onlinelibrary.wiley.com/doi/10.1111/biom.12...

Abstract

The genotype main effects and genotype-by-environment interaction effects (GGE) model and the additive main effects and multiplicative interaction (AMMI) model are two common models for analysis of genotype-by-environment data. These models are frequently used by agronomists, plant breeders, geneticists and statisticians for analysis of multi-environment trials. In such trials, a set of genotypes, e.g. crop cultivars, are compared across a range of environments, e.g. locations. The GGE and AMMI models use singular value decomposition to partition genotype-by-environment interaction into an ordered sum of multiplicative terms. This article deals with the problem of testing the significance of these multiplicative terms in order to decide how many terms to retain in the final model. We propose parametric bootstrap methods for this problem. Models with fixed main effects, fixed multiplicative terms and random normally distributed errors are considered. Two methods are derived: a full and a simple parametric bootstrap method. These are compared with the alternatives of using approximate F-tests and cross-validation. In a simulation study based on four multi-environment trials, both bootstrap methods performed well with regard to Type I error rate and power. The simple parametric bootstrap method is particularly easy to use, since it only involves repeated sampling of standard normally distributed values. This method is recommended for selecting the number of multiplicative terms in GGE and AMMI models. The proposed methods can also be used for testing components in principal component analysis.

Authors/Creators:Forkman, Johannes and Piepho, Hans-Peter
Title:Parametric Bootstrap Methods for Testing Multiplicative Terms in GGE and AMMI Models
Series/Journal:Biometrics (0006-341X)
Year of publishing :2014
Volume:70
Number:3
Page range:639-647
Publisher:Wiley
ISSN:0006-341X
Language:English
Additional Information:The definite version is available at onlinelibrary.wiley.com
Publication Type:Journal article
Refereed:Yes
Article category:Scientific peer reviewed
Version:Accepted version
Full Text Status:Public
Agris subject categories.:C Education, extension, and advisory work > C20 Extension
Subjects:(A) Swedish standard research categories 2011 > 1 Natural sciences > 101 Mathematics > 10106 Probability Theory and Statistics
Keywords:AMMI, Genotype-environment interaction, GGE, Multi-environment trials, Principal component analysis, Singular value decomposition
URN:NBN:urn:nbn:se:slu:epsilon-e-2192
Permanent URL:
http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilon-e-2192
Additional ID:
Type of IDID
DOI10.1111/biom.12162
ID Code:11041
Faculty:NJ - Fakulteten för naturresurser och jordbruksvetenskap
Department:(NL, NJ) > Dept. of Crop Production Ecology
Deposited By: Johannes Forkman
Deposited On:31 Oct 2014 06:53
Metadata Last Modified:04 Mar 2015 00:15

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