Spatial statistics using quasi-likelihood methods with applications

Abstract

<p>Spatial Statistics have been applied to many types of problems in the environmental sciences, mostly dealing with continuously distributed data from Gaussian or near-Gaussian processes. There is a need for methods capable of handling discrete, non-Gaussian data, such as species counts from biological processes. This thesis applies the method of quasi-likelihood from general linear models to the problem of spatial prediction of benthic invertebrate counts. These organisms are important elements of the aquatic food chain and are indicators of pollutant impacts. Predictions of their abundance are needed as clean up targets in areas where remedial actions are being considered. The proposed method is illustrated using an example data set from Great Lakes reference sites. The applicability of the method is first illustrated by re-analysis of examples from the literature. Variogram models are fitted to quasi-likelihood residuals with two alternative distance metrics. The models are compared using cross-validation and predictions are made using the classical estimator of the variogram and distance determined from a Geographic Information System (GIS). Asymptotic normality of quasi-likelihood parameter estimates is shown to hold when spatial dependence is accounted for by an exponential variogram model. A brief simulation study is included that verifies the applicability of asymptotic results to the estimation of model parameters.</p>