Covariance Clustering: Modelling Covariance in Designed Experiments When the Number of Variables is Greater than Experimental Units

Article


Forknall, Clayton R., Verbyla, Arūnas P., Nazarathy, Yoni, Yousif, Adel, Osama, Sarah, Jones, Shirley H., Kerr, Edward, Schulz, Benjamin L., Fox, Glen P. and Kelly, Alison M.. 2024. "Covariance Clustering: Modelling Covariance in Designed Experiments When the Number of Variables is Greater than Experimental Units." Journal of Agricultural, Biological, and Environmental Statistics. 29 (2), pp. 232-256. https://doi.org/10.1007/s13253-023-00574-x
Article Title

Covariance Clustering: Modelling Covariance in Designed Experiments When the Number of Variables is Greater than Experimental Units

ERA Journal ID807
Article CategoryArticle
AuthorsForknall, Clayton R., Verbyla, Arūnas P., Nazarathy, Yoni, Yousif, Adel, Osama, Sarah, Jones, Shirley H., Kerr, Edward, Schulz, Benjamin L., Fox, Glen P. and Kelly, Alison M.
Journal TitleJournal of Agricultural, Biological, and Environmental Statistics
Journal Citation29 (2), pp. 232-256
Number of Pages25
Year2024
PublisherSpringer
Place of PublicationUnited States
ISSN1085-7117
1537-2693
Digital Object Identifier (DOI)https://doi.org/10.1007/s13253-023-00574-x
Web Address (URL)https://link.springer.com/journal/13253/volumes-and-issues/29-2
AbstractThe size and complexity of datasets resulting from comparative research experiments in the agricultural domain is constantly increasing. Often the number of variables measured in an experiment exceeds the number of experimental units composing the experiment. When there is a necessity to model the covariance relationships that exist between variables in these experiments, estimation difficulties can arise due to the resulting covariance structure being of reduced rank. A statistical method, based in a linear mixed model framework, is presented for the analysis of designed experiments where datasets are characterised by a greater number of variables than experimental units, and for which the modelling of complex covariance structures between variables is desired. Aided by a clustering algorithm, the method enables the estimation of covariance through the introduction of covariance clusters as random effects into the modelling framework, providing an extension of the traditional variance components model for building covariance structures. The method was applied to a multi-phase mass spectrometry-based proteomics experiment, with the aim of exploring changes in the proteome of barley grain over time during the malting process. The modelling approach provides a new linear mixed model-based method for the estimation of covariance structures between variables measured from designed experiments, when there are a small number of experimental units, or observations, informing covariance parameter estimates.
KeywordsBarley; k-Means clustering; Linear mixed model; Mass spectro; Multi-phase design; Proteomics
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 20203099. Other agricultural, veterinary and food sciences
Byline AffiliationsUniversity of Queensland
Department of Agriculture, Food and Fisheries, Queensland
University of Tasmania
Elizabeth Macarthur Agricultural Institute, Australia
Institute for Life Sciences and the Environment
University of California Davis, United States
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