The use of linear mixed models for analysis of repeated measurements applied to water-soluble carbohydrates in perennial ryegrass for seed production

Abstract

Repeated measurements of a response variable in crops or plants receiving different treatments are widely used in agricultural science. In this paper we analyse repeated measurements of the concentration of water-soluble carbohydrates in stem and ear of perennial ryegrass (Lolium perenne L.) receiving different doses of growth regulators at different times. The objectives were to examine and compare three covariance structures and illustrate their effect on significance levels, the estimates, and standard error of estimates. The three covariance structures tested were unstructured, compound symmetry, and first-order antedependence. The Akaike Information Criterion and the Bayesian Information Criterion were used to find the best covariance structure. The choice of covariance structure had an effect on the significance levels for the stem data, whereas no effect was observed for the ear data. The estimates of the water-soluble carbohydrates concentrations within the stem and ear datasets were similar for all three covariance structures, while the smallest standard errors were obtained using the compound symmetry covariance structure. As it was the goal to do parsimonious modelling more weight was given to the Bayesian information criteria than to the Akaike information criteria. Accordingly, the compound symmetry structure was chosen for the stem data and the unstructured structure was found to be the best structure for the ear data. A model check of the residuals showed that there was no pattern in the residuals.