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1. Aspects of Spatial Autocorrelation 2. Measuring Spatial Autocorrelation Topics: Lecture 10: Spatial Autocorrelation I References: Goodchild, Michael F., 1986. Spatial Autocorrelation, CATMOG 47, Geo Books, Norwich, UK, 56 pp. Griffith, Daniel A., 1987. Spatial Autocorrelation: A Primer, Resource Publications in Geography, AAG, Washington, 82 pp. Odland, John, 1987. Spatial Autocorrelation, SAGE Pulications, Inc., Beverly Hills, CA, 85 pp.

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Outlines Aspects of Spatial Autocorrelation First law of geography: everything is related to everything else, but near things are more related than distant things' (Tobler, 1970). 1.1 Definition of spatial autocorrelation (continuity) Definition Types (positive and negative) (Figure) 1.2 The causes (why are things autocorrelated over space?) 1.2.1 spatial homogeneity over area 1.2.2 spatial diffusion within objects 1.2.3 spatial interaction between objects

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1. Aspects of Spatial Autocorrelation: (continued…) 1.3 The Nature of spatial autocorrelation 1) Scale and resolution dependence 2) Area specific 3) Attribute specific 4) Direction dependence Isotropic Anisotropic

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1. Aspects of Spatial Autocorrelation: (continued…) 1.4 The need to understand spatial autocorrelation 1) For regression models Y = X β + e e is uncorrelated between locations, otherwise inference based on this model is invalid. Y = X β + ρWea + er ea is the autoregressive portion of the error and er is the random portion of the error. W is the weight for two locations. 2) For spatial interpolation

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2. Measures of Spatial Autocorrelation: 2.1 Feature types, spatial adjacency, and attribute types 2.1.1 Feature types: (1) area features: (2) linear features (3) point features 2.1.2 Spatial neighborhood stationarity – spatial adjacency: (1) absolute adjacency (1, 0) (2) adjacency defined as distance between objects (3) length of shared edges 2.1.3 Attribute types (1) Interval/Ratio (2) Nominal/Ordinal

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2. Measures of Spatial Autocorrelation: (continued…) 2.2 Common framework: 2.2.1 Common notations: 2.2.2 The basic idea: 2.2.3 The logic of statistical testing: 1) A null hypothesis about the map of values 2) A probability distribution of the statistics 3) Comparison of the observed with the expected

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1. What is spatial autocorrelation? Why does it exist? 2. Why do we need to study spatial autocorrelation? 3. What is similarity in attribute and what is similarity in location? 4. What is absolute adjacency? 5. What are the step in testing spatial autocorrelation? What is the null hypothesis for testing spatial autocorrelation? Questions