Selecting the number of multiplicative terms in AMMI and GGE models
Final Report Abstract
Additive Main Effects and Multiplicative Interaction (AMMI) and Genotype and Genotype-Environment (GGE) models play an important role in the analysis of plant breeding and variety trials. Such multiplicative models can be used to graphically represent genotypes and environments in bi-plots, which greatly facilitates the study of interaction and adaptation patterns. A further important application is the delineation of mega-environments, where environments in a mega-environment share the 'winning genotype' based on predictions obtained from the fitted GGE or AMMI model. Another pertinent application is the pre-processing of phenotypic data for association studies and mapping of quantitative trait loci. AMMI and GGE models have several multiplicative terms. A key step in the analysis using these models therefore is the selection of terms to be included. The purpose of this project therefore was to develop new methods for selecting the number of multiplicative terms in AMMI and GGE models and to compare these new methods to other existing methods, including significance tests. The main focus was on computer-intensive methods such as cross-validation and bootstrapping. The methods were compared both using real datasets and simulations parameterized using these real datasets. We developed parametric and non-parametric tests of significance for the number of significant terms in AMMI and GGE models when replicate data are available, including procedures accounting for heterogeneity of variance between environments. Further, we developed non-parametric tests for unreplicated data, extending on a parametric test previously published that assumes normality. The ideas developed for these tests, such as a parametric bootstrap method, was also applied to principal component analysis when variates are standardized. This is an application equivalent to GGE analysis when data are standardized by environment. A further approach that does not require normality is cross-validation. Among the nine variants of cross-validation for replicated data we examined, the one sampling one of the replications per genotype-environment combinations for validation, using data corrected for effects of replicates and blocks, performed best in terms of the probability of selecting the correct model. In a separate study, we also considers a scenario that differs from the ones considered in the papers reported so far in two respects: (i) The data can be unbalanced with some genotype-environments missing entirely. (ii) Environments are modeled as a random factor, meaning that AMMI and GGE models correspond to factor-analytic variance-covariance structures. A cross-validation scheme was proposed that is based on pairwise differences among genotypes within environments. The method effectively deals with incomplete data. We also developed an estimation procedure that can accounting for heterogeneity of variance and correlation among adjusted means when replicate data are analyzed by a two-stage procedure. The adjusted genotype means computed from the individual environments may be homoscedastic and correlated on account of the experimental design and analysis model used. Such heterogeneity calls for a weighted analysis, and the paper proposes three novel methods for this purpose. The three methods were shown to produce comparable methods, and the method requiring the least computing time can therefore be recommended.
Publications
- (2015) Multiplicative interaction in network meta-analysis. Statistics in Medicine, 34, 582-594
Piepho, H.P., Madden, L.V., Williams, E.R.
(See online at https://doi.org/10.1002/sim.6372) - (2017) Cross validation in AMMI and GGE model: A comparison of methods. Crop Science, 57, 264-274
Hadasch, S., Forkman, J., Piepho, H.P.
(See online at https://doi.org/10.2135/cropsci2016.07.0613) - (2017) Prediction of the accuracy and consistency in cultivars ranking for factor-analytic linear mixed models for winter wheat multi-environmental trials. Crop Science, 57, 2506-2516
Studnicki, M., Paderewski, J., Piepho, H.P., Wójcik-Gront, E.
(See online at https://doi.org/10.2135/cropsci2017.01.0004) - (2018) Biplots: Do not stretch them! Crop Science, 58, 1061-1069
Malik, W.A., Piepho, H.P.
(See online at https://doi.org/10.2135/cropsci2017.12.0747) - (2018) Non-parametric bootstrap methods for testing multiplicative terms in AMMI and GGE models for multienvironment trials. Crop Science, 58, 752-761
Malik, W.A., Hadasch, S., Forkman, J., Piepho, H.P.
(See online at https://doi.org/10.2135/cropsci2017.10.0615) - (2018) Weighted estimation of AMMI and GGE models. Journal of Agricultural, Biological and Environmental Statistics, 23(2), 255-275
Hadasch, S., Forkman, J., Malik, W.A., Piepho, H.P.
(See online at https://doi.org/10.1007/s13253-018-0323-z) - (2019) Hypothesis tests for principal component analysis when datasets are small and columns are standardized. Journal of Agricultural Biological and Environmental Statistics, 24
Forkman, J., Josse, J., Piepho, H.P.
(See online at https://doi.org/10.1007/s13253-019-00355-5) - (2019) Testing multiplicative terms in AMMI and GGE models for Multienvironment trials with replicates. Theoretical and Applied Genetics
Malik, W.A., Forkman, J., Piepho, H.P.
(See online at https://doi.org/10.1007/s00122-019-03339-8)
