Measuring Spatial Dependence to Understand the Three Inseparable Issues in Geography—Scale, Spatial Dependence, and Spatial Heterogeneity

Authors: Liem Tran*, University of Tennessee at Knoxville, Nicholas Nagle, Geography Department, University of Tennessee at Knoxville, Qiusheng Wu, Geography Department, University of Tennessee at Knoxville, Lam Tran, Biostatistics, University of Michigan
Topics: Spatial Analysis & Modeling, Quantitative Methods, Geographic Information Science and Systems
Keywords: spatial dependence, spatial heterogeneity, scale, spatial autocorrelation
Session Type: Paper
Presentation File: No File Uploaded


The issue of spatial dependence was aptly captured by Tobler in what has become known as the First Law of Geography. Spatial dependence underlies many aspects of the Geographic Information System design (e.g., spatial interpolation, resampling, contour mapping), as well as the discipline known as geostatistics in which models and methods focus on statistically interpolating continuous spatial phenomena based on data observed at a discrete set of locations. While the random (i.e., stochastic) behavior of spatial dependence can be in any type or form (e.g., continuous or discrete, symmetrical or skewed distribution), current approaches in geospatial analyses is dominated by Gaussian thinking. For instance, most of the measures of spatial dependence are based on the calculations of moments of a normal distribution, consequently they are prone to even minor but common data issues, such as outliers, and not robust to other distributions (e.g., Pareto, binomial, Poisson, negative binomial, Gamma distributions) common in geographical studies. We introduce in this talk a new measure of spatial dependence which is robust to various distributions commonly seen in geographical studies (e.g., Pareto, binomial, Poisson, negative binomial, Gamma distributions) as well as to common data issues (e.g., outliers). We show how the newly-developed measure of spatial dependence can be used in multiple-scale analyses to understand how spatial dependence and spatial heterogeneity change across scales.

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