Modelling spatial trends and local competition effects using semiparametric additive models

Abstract

The aim of this project was to develop a joint approach to the estimation of spatial trends and competition effects in agricultural field trials. We chose to model the trend by means of a semi parametric model and to extend this class of models to include any number of smooth terms. Explicit expressions for the linear and smooth parts of the model are derived. Two approximations to the standard errors of the linear part are presented and compared. We discuss graphical methods for the initial identification of spatial structure in the data and propose more formal procedures to select the degree of smoothing and to test for the significance of treatment effects. We review the methodology already developed for competition models and improve the fitting procedure by calculating exact adjustments of the profile likelihood for a class of normal regression models. Classical competition models are extended to allow for the estimation of spatial trends via one or more linear smoothers. Methods to estimate the smoothing parameter in the presence of competition were derived. However, we have established that this approach needs to be extended to include correlated errors before it is complete. A mixed model approach to competition was also investigated. The analysis of the data from two agricultural trials grown at SCRI indicated that SAMs provide a flexible framework for identifying underlying trends in field trials. They generally improve precision of the treatment estimates and they enable spatial trends to be easily visualised. Competition between neighbouring plots was also identified.