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

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.