Griffith, Daniel A.
Permanent URI for this collectionhttps://hdl.handle.net/10735.1/3736
Daniel Griffith is an Ashbel Smith Professor of Geospatial Information Sciences. His primary areas of research are in spatial statistics, quantitative urban and economic geography, and applied statistics.
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Browsing Griffith, Daniel A. by Subject "Autocorrelation (Statistics)"
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Item Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches(Wiley, 2018-03-25) Murakami, Daisuke; Griffith, Daniel A.; 0000-0001-5125-6450 (Griffith, DA); 14855602 (Griffith, DA); Griffith, Daniel A.Eigenvector spatial filtering (ESF) is a spatial modeling approach, which has been applied in urban and regional studies, ecological studies, and so on. However, it is computationally demanding, and may not be suitable for large data modeling. The objective of this study is developing fast ESF and random effects ESF (RE-ESF), which are capable of handling very large samples. To achieve it, we accelerate eigen-decomposition and parameter estimation, which make ESF and RE-ESF slow. The former is accelerated by utilizing the Nystrom extension, whereas the latter is by small matrix tricks. The resulting fast ESF and fast RE-ESF are compared with nonapproximated ESF and RE-ESF in Monte Carlo simulation experiments. The result shows that, while ESF and RE-ESF are slow for several thousand samples, fast ESF and RE-ESF require only several seconds for the samples. It is also suggested that the proposed approaches effectively remove positive spatial dependence in the residuals with very small approximation errors when the number of eigenvectors considered is 200 or more. Note that these approaches cannot deal with negative spatial dependence. The proposed approaches are implemented in an R package "spmoran."Item Spatially Simplified Scatterplots for Large Raster Datasets(Taylor & Francis, 2016-05-24) Bin, Li; Griffith, Daniel A.; Becker, Brian; 0000 0001 0872 2508 (Griffith, DA); Griffith, Daniel A.Scatterplots are essential tools for data exploration. However, this tool poorly scales with data-size, with overplotting and excessive delay being the main problems. Generalization methods in the attribute domain focus on visual manipulations, but do not take into account the inherent nature of information redundancy in most geographic data. These methods may also result in alterations of statistical properties of data. Recent developments in spatial statistics, particularly the formulation of effective sample size and the fast approximation of the eigenvalues of a spatial weights matrix, make it possible to assess the information content of a georeferenced data-set, which can serve as the basis for resampling such data. Experiments with both simulated data and actual remotely sensed data show that an equivalent scatterplot consisting of point clouds and fitted lines can be produced from a small subset extracted from a parent georeferenced data-set through spatial resampling. The spatially simplified data subset also maintains key statistical properties as well as the geographic coverage of the original data.Item The Importance of Scale in Spatially Varying Coefficient Modeling(Routledge Journals, Taylor & Francis Ltd, 2018-02) Murakami, Daisuke; Lu, Binbin; Harris, Paul; Brunsdon, Chris; Charlton, Martin; Nakaya, Tomoki; Griffith, Daniel A.; 0000-0001-5125-6450 (Griffith, DA); 14855602 (Griffith, DA); Griffith, Daniel A.Although spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the "spatial scale" of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa, and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are naively assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR).