Spatially varying coefficient models

What is it about?

In spatial data analysis, a common problem is to identify the nature of the relationship that exists between variables. In many situations, a simple "global" model often cannot explain the relationships between some sets of variables, which is referred to as "spatial nonstationarity". To handle such nonstationarity, the model needs to reflect the spatially varying structure within the data. In this paper, we investigate a class of spatially varying coefficient models to explore the spatial nonstationarity of a regression relationship. The data in our study need not be evenly distributed; instead, we assume that the observations are randomly distributed over a two-dimensional domain of arbitrary shape, for example, a polygonal domain with interior holes.

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Why is it important?

In summary, the proposed method has the following advantages in analyzing the spatial nonstationarity of a regression relationship for spatial data. First, compared with GWR, the proposed method is much more computationally efficient to deal with large data sets. In addition, as a global estimation with an explicit model expression, the proposed spline approach enables easy-to-implement prediction compared with the local approaches. Second, our method can overcome the problem of "leakage" across the complex domains that many conventional tools suffer. Third, it can alleviate the adverse effect of the collinearity problem in GWR and provide more accurate estimators of the coefficient functions. By assigning different penalty parameters, our method also easily allows different smoothness for different functional coefficients. Finally, with increasing volumes of data being collected on the environment through remote sensing platforms, complex sensor networks, and Global Positioning System (GPS) movement, this work provides one feasible approach to study large-scale environmental spatial data.