IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v22y2017i1d10.1007_s13253-016-0267-0.html
   My bibliography  Save this article

Residual Variance–Covariance Modelling in Analysis of Multivariate Data from Variety Selection Trials

Author

Listed:
  • Joanne De Faveri

    (Department of Agriculture and Fisheries)

  • Arūnas P. Verbyla

    (Data61, CSIRO
    The University of Adelaide)

  • Brian R. Cullis

    (NIASRA, University of Wollongong)

  • Wayne S. Pitchford

    (The University of Adelaide)

  • Robin Thompson

    (Rothamsted Research)

Abstract

Field trials for variety selection often exhibit spatial correlation between plots. When multivariate data are analysed from these field trials, there is the added complication in having to simultaneously account for correlation between the traits at both the residual and genetic levels. This may be temporal correlation in the case of multi-harvest data from perennial crop field trials, or between-trait correlation in multi-trait data sets. Use of parsimonious yet plausible models for the variance–covariance structure of the residuals for such data is a key element to achieving an efficient and inferentially sound analysis. In this paper, a model is developed for the residual variance–covariance structure firstly by considering a multivariate autoregressive model in one spatial direction and then extending this to two spatial directions. Conditions for ensuring that the processes are directionally invariant are presented. Using a canonical decomposition, these directionally invariant processes can be transformed into a set of independent separable processes. This simplifies the estimation process. The new model allows for flexible modelling of the spatial and multivariate interaction and allows for different spatial correlation parameters for each harvest or trait. The methods are illustrated using data from lucerne breeding trials at several environments.

Suggested Citation

  • Joanne De Faveri & Arūnas P. Verbyla & Brian R. Cullis & Wayne S. Pitchford & Robin Thompson, 2017. "Residual Variance–Covariance Modelling in Analysis of Multivariate Data from Variety Selection Trials," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 1-22, March.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:1:d:10.1007_s13253-016-0267-0
    DOI: 10.1007/s13253-016-0267-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-016-0267-0
    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/s13253-016-0267-0?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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arūnas P. Verbyla & Joanne Faveri & John D. Wilkie & Tom Lewis, 2018. "Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 478-508, December.

    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. Brian R. Cullis & Alison B. Smith & Nicole A. Cocks & David G. Butler, 2020. "The Design of Early-Stage Plant Breeding Trials Using Genetic Relatedness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 553-578, December.
    2. T. Caliński & S. Czajka & Z. Kaczmarek & P. Krajewski & W. Pilarczyk, 2005. "Analyzing Multi-environment Variety Trials Using Randomization-Derived Mixed Models," Biometrics, The International Biometric Society, vol. 61(2), pages 448-455, June.
    3. Joel Jorge Nuvunga & Carlos Pereira da Silva & Luciano Antonio de Oliveira & Renato Ribeiro de Lima & Marcio Balestre, 2019. "Bayesian factor analytic model: An approach in multiple environment trials," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-26, August.
    4. Sudipto Banerjee & Gregg A. Johnson, 2006. "Coregionalized Single- and Multiresolution Spatially Varying Growth Curve Modeling with Application to Weed Growth," Biometrics, The International Biometric Society, vol. 62(3), pages 864-876, September.
    5. Boby Mathew & Jens Léon & Mikko J Sillanpää, 2018. "Impact of residual covariance structures on genomic prediction ability in multi-environment trials," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-11, July.
    6. Alison B. Smith & Lauren M. Borg & Beverley J. Gogel & Brian R. Cullis, 2019. "Estimation of Factor Analytic Mixed Models for the Analysis of Multi-treatment Multi-environment Trial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 573-588, December.
    7. Gambin, Brenda L. & Coyos, Tomás & Di Mauro, Guido & Borrás, Lucas & Garibaldi, Lucas A., 2016. "Exploring genotype, management, and environmental variables influencing grain yield of late-sown maize in central Argentina," Agricultural Systems, Elsevier, vol. 146(C), pages 11-19.
    8. Emi Tanaka, 2020. "Simple outlier detection for a multi‐environmental field trial," Biometrics, The International Biometric Society, vol. 76(4), pages 1374-1382, December.
    9. 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.
    10. 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.
    11. Johannes Forkman, 2013. "The use of a reference variety for comparisons in incomplete series of crop variety trials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2681-2698, 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:22:y:2017:i:1:d:10.1007_s13253-016-0267-0. 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.