IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v23y2018i2d10.1007_s13253-018-0323-z.html
   My bibliography  Save this article

Weighted Estimation of AMMI and GGE Models

Author

Listed:
  • S. Hadasch

    (University of Hohenheim)

  • J. Forkman

    (Swedish University of Agricultural Sciences)

  • W. A. Malik

    (University of Hohenheim)

  • H. P. Piepho

    (University of Hohenheim)

Abstract

The AMMI/GGE model can be used to describe a two-way table of genotype–environment means. When the genotype–environment means are independent and homoscedastic, ordinary least squares (OLS) gives optimal estimates of the model. In plant breeding, the assumption of independence and homoscedasticity of the genotype–environment means is frequently violated, however, such that generalized least squares (GLS) estimation is more appropriate. This paper introduces three different GLS algorithms that use a weighting matrix to take the correlation between the genotype–environment means as well as heteroscedasticity into account. To investigate the effectiveness of the GLS estimation, the proposed algorithms were implemented using three different weighting matrices, including (i) an identity matrix (OLS estimation), (ii) an approximation of the complete inverse covariance matrix of the genotype–environment means, and (iii) the complete inverse covariance matrix of the genotype–environment means. Using simulated data modeled on real experiments, the different weighting methods were compared in terms of the mean-squared error of the genotype–environment means, interaction effects, and singular vectors. The results show that weighted estimation generally outperformed unweighted estimation in terms of the mean-squared error. Furthermore, the effectiveness of the weighted estimation increased when the heterogeneity of the variances of the genotype–environment means increased.

Suggested Citation

  • S. Hadasch & J. Forkman & W. A. Malik & H. P. Piepho, 2018. "Weighted Estimation of AMMI and GGE Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 255-275, June.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:2:d:10.1007_s13253-018-0323-z
    DOI: 10.1007/s13253-018-0323-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-018-0323-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-018-0323-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alison Smith & Brian Cullis & Robin Thompson, 2001. "Analyzing Variety by Environment Data Using Multiplicative Mixed Models and Adjustments for Spatial Field Trend," Biometrics, The International Biometric Society, vol. 57(4), pages 1138-1147, December.
    2. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    3. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    4. Bert Green, 1952. "The orthogonal approximation of an oblique structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 429-440, December.
    5. J. Besag & D. Higdon, 1999. "Bayesian analysis of agricultural field experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 691-746.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Griffin, Maryclare & Hoff, Peter D., 2019. "Lasso ANOVA decompositions for matrix and tensor data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 181-194.
    2. Jan Schepers & Hans-Hermann Bock & Iven Mechelen, 2017. "Maximal Interaction Two-Mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 49-75, April.
    3. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    4. Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    5. Michael Browne & Walter Kristof, 1969. "On the oblique rotation of a factor matrix to a specified pattern," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 237-248, June.
    6. W. Gibson, 1962. "On the least-squares orthogonalization of an oblique transformation," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 193-195, June.
    7. Ahakpaz, Farhad & Abdi, Hossein & Neyestani, Elyas & Hesami, Ali & Mohammadi, Behrouz & Mahmoudi, Kourosh Nader & Abedi-Asl, Gholamreza & Noshabadi, Mohammad Reza Jazayeri & Ahakpaz, Farzad & Alipour,, 2021. "Genotype-by-environment interaction analysis for grain yield of barley genotypes under dryland conditions and the role of monthly rainfall," Agricultural Water Management, Elsevier, vol. 245(C).
    8. Franck, Christopher T. & Nielsen, Dahlia M. & Osborne, Jason A., 2013. "A method for detecting hidden additivity in two-factor unreplicated experiments," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 95-104.
    9. Fernanda De Bastiani & Robert A. Rigby & Dimitrios M. Stasinopoulous & Audrey H.M.A. Cysneiros & Miguel A. Uribe-Opazo, 2018. "Gaussian Markov random field spatial models in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 168-186, January.
    10. Peter Schönemann, 1968. "On two-sided orthogonal procrustes problems," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 19-33, March.
    11. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    12. Martin P. Boer & Hans-Peter Piepho & Emlyn R. Williams, 2020. "Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 676-698, December.
    13. Angela Andreella & Livio Finos, 2022. "Procrustes Analysis for High-Dimensional Data," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1422-1438, December.
    14. Maria Victoria Ibañez & Marina Martínez-Garcia & Amelia Simó, 2021. "A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data," Mathematics, MDPI, vol. 9(13), pages 1-23, July.
    15. Odette D. Weedon & Maria R. Finckh, 2019. "Heterogeneous Winter Wheat Populations Differ in Yield Stability Depending on their Genetic Background and Management System," Sustainability, MDPI, vol. 11(21), pages 1-20, November.
    16. Nicholas George & Kim Tungate & Cameron Beeck & Michael Stamm, 2012. "Exploring Genotype by Environment Interaction in Winter Canola in North Carolina," Journal of Agricultural Science, Canadian Center of Science and Education, vol. 4(2), pages 237-237, February.
    17. repec:jss:jstsof:34:i10 is not listed on IDEAS
    18. Bert Green, 1969. "Best linear composites with a specified structure," Psychometrika, Springer;The Psychometric Society, vol. 34(3), pages 301-318, September.
    19. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    20. Demba Fofana & E. O. George & Dale Bowman, 2021. "Combining assumptions and graphical network into gene expression data analysis," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-17, December.
    21. Richard Sherin, 1966. "A matrix formulation of Kaiser's varimax criterion," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 535-538, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jagbes:v:23:y:2018:i:2:d:10.1007_s13253-018-0323-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.