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Description
The transformation of both sides of a regression model is a method for modeling heteroskedastic errors. A flexible approach to this method uses a nonparametric maximized penalized likelihood function. In this dissertation, we combine and implement the use of a transform both sides (TBS) methodology with the LatticeKrig spatial model. After a brief review of spline theory, we explain the transform both sides methodology, including the theory and an exploration of the parameter settings needed to implement it. We use two examples of very different sized data sets to demonstrate the strengths and parameterization of TBS. Next, we discuss the LatticeKrig spatial model, which uses a multiresolution basis function representation of the spatial process. Then, we describe the algorithm used for the combined TBS LatticeKrig methodology, which requires some modifications and extensions to the original implementation and theory of each component. Finally, the combined TBS LatticeKrig model is demonstrated with an example from climatology. Prediction of snowfall and snow pack is important, as snow affects water resources, ecosystems, and the economy. However, accurately modeling and predicting snow presents a scientific challenge, in part because it is difficult to measure both directly and indirectly. As such, there is no single, standard gridded snow data set that can be used for climate model evaluation. In this project, a blended product is created from multiple snow data sets that can be used for predictions and uncertainty quantification. To combine the data sets, the LatticeKrig model is implemented and combined with the nonparametric transform both sides method. Monthly snow predictions from the blended product are presented along with the standard errors of the predictions. Explorations of the effects of parameterization on the current spatial model are also presented. We conclude that using the TBS LatticeKrig methodology with reasonable parameterization of both components is an effective approach to modeling spatial data that otherwise exhibits heteroskedasticity. The TBS approach provides a justifiable and more objective method than transformation of only the dependent variable. Transforming both sides of the model maintains the relationship between the independent and dependent variables and provides easily interpretable results.
