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

Clayton R. Forknall (), Arūnas P. Verbyla, Yoni Nazarathy, Adel Yousif, Sarah Osama, Shirley H. Jones, Edward Kerr, Benjamin L. Schulz, Glen P. Fox and Alison M. Kelly
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Clayton R. Forknall: The University of Queensland
Arūnas P. Verbyla: The University of Queensland
Yoni Nazarathy: The University of Queensland
Adel Yousif: University of Tasmania
Sarah Osama: Department of Regional New South Wales
Shirley H. Jones: University of Southern Queensland
Edward Kerr: The University of Queensland
Benjamin L. Schulz: The University of Queensland
Glen P. Fox: University of California
Alison M. Kelly: The University of Queensland

Journal of Agricultural, Biological and Environmental Statistics, 2024, vol. 29, issue 2, No 3, 232-256

Abstract: Abstract The 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.

Keywords: Barley; k-Means clustering; Linear mixed model; Mass spectrometry; Multi-phase design; Proteomics (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13253-023-00574-x

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