Lecture 7 Implementing Spatial Analysis (Cont.) 7-1. Spatial Autocorrelation Definition: Everything is related to everything else, but near thins are more inter-related than distant things. Spatial processes exhibit patterns which invalidate some basic assumptions of aspatial statistics. Provides useful measures and descriptions of the pattern of spatial processes. GIS can be used to manage data in a format suitable for calculating SA and visualizing results. 2018/11/17 Jun Liang, Geography @ UNC

7-1. Spatial Autocorrelation (Cont.) Examples of SA: The two households which are next to each other will have similar disposable incomes than two households which are far apart. (page 175) Demographic data (such as minority ratio in census tract). Crime rate. Air pollution. Temperature. 2018/11/17 Jun Liang, Geography @ UNC

7-1. Spatial Autocorrelation (Cont.) Chape hill, NC - Percent of Persons 65 Years and Over: 2000 block map Blocks next to each other tend to have similar percentage of senior than blocks which are far away from each other. 2018/11/17 Jun Liang, Geography @ UNC

Jun Liang, Geography @ UNC 7-2 Goodness of Fit A statistical test in which the validity of one hypothesis is tested without specification of an alternative hypothesis is called a goodness-of-fit test. A measure of how well a model matches some data. Being used to calibrate and infer processes. GIS: Can be used to mapping result and control the spatial resolution of matching. Choice of model specification and evaluation statistic may have significant influence. The most common tests for goodness-of-fit are the chi-square test, Kolmogorov test, Cramer-Smirnov-Von-Mises test, runs. 2018/11/17 Jun Liang, Geography @ UNC

7-3 Aggregate versus disaggregate Similar to scale problem (MAUP) GIS helps to visualize results under different strategies. Examples: – models of migration frequently work at the aggregate level, and utilize sum total flows between census areas. Or look at the migration of individuals. – models of crime pattern analysis often need to summarize crime rate for each street block. 2018/11/17 Jun Liang, Geography @ UNC

7-4 Spatial classification In spatial classification, members from the same group should close to each other in term of physical distance, and at the same time, group members should have high spatial autocorrelation (similar attributes). Purposes of doing spatial classification: Reducing large number individuals to a small number of groups (spatial clusters) – no predefined boundaries, like aggregation. Facilitate description and illustration. Similar for spatial aggregation. 2018/11/17 Jun Liang, Geography @ UNC

7-4 Spatial classification (Cont.) Simple examples of spatial classification: 2 4 3 3 4 Raster Classification Vector Classification 2018/11/17 Jun Liang, Geography @ UNC

7-5 Spatial analysis in current general-purpose commercial GIS ArcGIS Spatial Analyst Network Analyst Geostatistical Analyst 3D Analyst ERDAS-IMAGINE Image interpretation Spatial modelling (similar to Spatial Analyst in ArcGIS) Terrain analysis (Surface Interpolation and contouring) 2018/11/17 Jun Liang, Geography @ UNC