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Document Type

Dissertation - University Access Only

Award Date


Degree Name

Doctor of Philosophy (PhD)

Department / School

Mathematics and Statistics

First Advisor

Gary D. Hatfield


This dissertation research consists of five chapters with a focus on modeling spatial and temporal data. In chapter 1, we explained different terminology and principles that appear frequently in the analysis of spatial and temporal data. These concepts were explained in detail to form a basis and motivation for the research work. In particular, the measures of spatial autocorrelation were discussed in detail and various methods of the computing these measures were discussed. In chapter 2, Spatial Modeling Techniques for Lattice Data were discussed. In addition to Ordinary least squares, a conventional method of modeling spatial data; various types of spatial regression techniques, such as Simultaneous Autoregressive (SAR), Conditional Autoregressive (CAR), Generalized Least Squares (GLS), Linear Mixed Effects (LME), and Geographically Weighted Regression (GWR) were discussed. Comparative studies of these modeling techniques were carried out using a real world dataset and an artificially generated spatial dataset. In chapter 3, a recently developed spatial analytical tool, Geographically Weighted Regression (GWR) was used to deal with spatial non stationarity in modeling the crop residue yield potential for North Central region of the USA. The explanatory power of the Ordinary Least Squares and Geographically Weighted Regression models were assessed by approximate likelihood ratio test. Furthermore, the effect of sample size on the spatial heterogeneity of the GWR parameters was investigated by using data sets with small and large samples. In chapter 4, Statistical Analysis of Land Cover of South Dakota was carried out. In particular, the research work focused on how land cover of 66 counties of South Dakota State changed over the years 2001-2006. In addition, it studied the existing relationships between population density and agricultural land cover for 66 counties of South Dakota for these years. In chapter 5, we conclude this study with a summary of the results and directions for future research.

Library of Congress Subject Headings

Spatial analysis(Statistics) -- Data processing
Regression analysis
Land use -- South Dakota


Includes bibliographical references



Number of Pages



South Dakota State University


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