1. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 1 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.

2. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 2 Outlines 1.Aspects of Spatial Autocorrelation First law of geography: First law of geography: everything is related to everything else, but near things everything is related to everything else, but near things are more related than distant things” (Tobler, 1970). are more related than distant things” (Tobler, 1970). 1.1 Definition of spatial autocorrelation (continuity) 1.1 Definition of spatial autocorrelation (continuity) Definition Definition Types (positive and negative) (Figure) Types (positive and negative) (Figure) 1.2 The causes (why are things autocorrelated over space?) 1.2 The causes (why are things autocorrelated over space?) 1.2.1 spatial homogeneity over area 1.2.1 spatial homogeneity over area 1.2.2 spatial diffusion within objects 1.2.2 spatial diffusion within objects 1.2.3 spatial interaction between objects 1.2.3 spatial interaction between objects

3. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 3 1. Aspects of Spatial Autocorrelation: (continued…) 1.3 The Nature of spatial autocorrelation 1.3 The Nature of spatial autocorrelation 1) Scale and resolution dependence 1) Scale and resolution dependence 2) Area specific 2) Area specific 3) Attribute specific 3) Attribute specific 4) Direction dependence 4) Direction dependence Isotropic Isotropic Anisotropic Anisotropic

4. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 4 1. Aspects of Spatial Autocorrelation: (continued…) 1.4 The need to understand spatial autocorrelation 1.4 The need to understand spatial autocorrelation 1) For regression models 1) For regression models Y = X β + e Y = X β + e e is uncorrelated between locations, otherwise e is uncorrelated between locations, otherwise inference based on this model is invalid. inference based on this model is invalid. Y = X β + ρWea + er Y = X β + ρWea + er ea is the autoregressive portion of the error and er ea is the autoregressive portion of the error and er is the random portion of the error. W is the weight is the random portion of the error. W is the weight for two locations. for two locations. 2) For spatial interpolation 2) For spatial interpolation

5. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 5 2. Measures of Spatial Autocorrelation: 2.1 Feature types, spatial adjacency, and attribute types 2.1 Feature types, spatial adjacency, and attribute types 2.1.1 Feature types: 2.1.1 Feature types: (1) area features: (1) area features: (2) linear features (2) linear features (3) point features (3) point features 2.1.2 Spatial neighborhood stationarity – spatial adjacency: 2.1.2 Spatial neighborhood stationarity – spatial adjacency: (1) absolute adjacency (1, 0) (1) absolute adjacency (1, 0) (2) adjacency defined as distance between objects (2) adjacency defined as distance between objects (3) length of shared edges (3) length of shared edges 2.1.3 Attribute types 2.1.3 Attribute types (1) Interval/Ratio (1) Interval/Ratio (2) Nominal/Ordinal (2) Nominal/Ordinal

6. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 6 2. Measures of Spatial Autocorrelation: (continued…) 2.2 Common framework: 2.2 Common framework: 2.2.1 Common notations: 2.2.1 Common notations: 2.2.2 The basic idea: 2.2.2 The basic idea: 2.2.3 The logic of statistical testing: 2.2.3 The logic of statistical testing: 1) A null hypothesis about the map of values 1) A null hypothesis about the map of values 2) A probability distribution of the statistics 2) A probability distribution of the statistics 3) Comparison of the observed with the expected 3) Comparison of the observed with the expected

7. Geog. 579: GIS and Spatial Analysis - Lecture 10 Overheads 7 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? the null hypothesis for testing spatial autocorrelation? Questions