Diagnostics for the evaluation of spatial linear models

Graduation date: 1996Geostatistical linear interpolation procedures such as kriging require knowledge of the\ud covariance structure of the spatial process under investigation. In practice, the covariance of the\ud process is unknown, and must be estimated from the available data. As the quality of the\ud resulting predictions, and associated mean square prediction errors, depends on adequate\ud specification of the covariance structure, it is important that the analyst be able to detect\ud inadequacies in the specified covariance model. Case-deletion diagnostics are currently used by\ud geostatisticians to evaluate spatial models.\ud The second chapter of the thesis describes a particular case-deletion diagnostic based on\ud standardized PRESS residuals, and its use in assessing the predictive capacity of spatial\ud covariance models. Distributional properties of this statistic, denoted T [subscript PR], are discussed, and\ud a saddlepoint approximation to its distribution is derived. Guidelines for calculating\ud approximate p-values for the statistic under an hypothesized covariance model are also given. A\ud simulation study demonstrates that the distributional and p-value approximations are accurate.\ud The proposed method is illustrated through an example, and recommendations for calculation of\ud T [subscript PR], and associated approximate p-values on a regional basis are given.\ud The third chapter investigates the behavior of the standardized PRESS residuals under\ud various misspecifications of the covariance matrix, V. A series of simulation studies show\ud consistent patterns in the standardized PRESS residuals under particular types of\ud misspecifications of V. It is observed that misspecification of V may lead to variability among\ud the standardized PRESS residuals greater or less than would be expected if V was correctly specified, depending on the nature of the misspecification. Based on this observation, an adjustment to normal probability plots of the standardized PRESS residuals is proposed. The adjusted normal probability plots may be used to identify potential improvements to covariance models, without requiring extensive further calculations