Design and analysis of experiments in the presence of spatial correlation

This dissertation consists of three papers written on the design and analysis of experiments in the presence of spatial correlation. The first paper discusses the use of optimality criteria in the design of experiments. In the context of linear models, an optimality criterion is developed for models that include random effects. This criterion also allows for the inclusion of fixed and/or random nuisance parameters in the model and for the presence of a general covariance structure. Also, a general formula is presented for which all previously published optimality criteria are special cases. The second paper presents a simulation study on changing the support of a spatial covariate. Researchers are increasingly able to capture spatially referenced data on both a response and a covariate more frequently and in more detail. A combination of geostatisical models and analysis of covariance methods is used to analyze such data. However, basic questions regarding the effects of using a covariate whose support differs from that of the response variable must be addressed to utilize these methods more efficiently. A simulation study was conducted to assess the effects of including a covariate whose support differs from that of the response variable in the analysis. This study suggests that the support of the covariate should be as close as possible to the support of the response variable. The third paper presents a new method for analysis of covariance with a spatial covariate. Data sets which contain measurements on a spatially referenced response and covariate are analyzed using either cokriging or spatial analysis of covariance. While cokriging accounts for the correlation structure of the covariate, it is purely a predictive tool. Alternatively, spatial analysis of covariance allows for parameter estimation yet disregards the correlation structure of the covariate. A method is proposed which both accounts for the correlation in and between the response and covariate and allows for the estimation of model parameters; also, this method allows for analysis of covariance when the response and covariate are not colocated