Local Models for Spatial Analysis

by Lloyd, Christopher D.

• ISBN13: 9780415316811
• ISBN10: 0415316812
• Format: Hardcover
• Copyright: 2006-10-25
• Publisher: CRC Press

Summary

In both the physical and social sciences, there are now available large spatial data sets with detailed local information. Global models for analyzing these data are not suitable for investigating local variations; consequently, local models are the subject of much recent research. Collecting a variety of models into a single reference, Local Models for Spatial Analysis explains in detail a variety of approaches for analyzing univariate and multivariate spatial data.Different models make use of data in unique ways, and this book offers perspectives on various definitions of what constitutes "local," varying spatial scales, and nonstationary models. The author discusses analyses of single variables on grids, multiple variables, deterministic approaches to spatial prediction, geostatistical prediction, and point patterns. He uses numerous worked examples, illustrations, and case studies to shed light on issues involved in implementing the concepts in practice, and makes use of physical and social science data sets. In each chapter, the book follows a consistent format that introduces global approaches followed by corresponding local approaches, providing an assessment of the suitability of various methods in particular situations.Combining a valuable array of tools for GIScience and GISystems, Local Models for Spatial Analysis guides you in selecting and applying the most appropriate model for a given purpose and set of data.

Table of Contents

1 Introduction	1	(20)
1.1 Remit of this book	2	(1)
1.2 Local models and methods	2	(3)
1.3 What is local?	5	(1)
1.4 Spatial dependence	5	(1)
1.5 Spatial scale	6	(2)
1.5.1 Spatial scale in geographical applications	7	(1)
1.6 Stationarity	8	(1)
1.7 Spatial data models	8	(2)
1.7.1 Grid data	9	(1)
1.7.2 Areal data	9	(1)
1.7.3 Geostatistical data	9	(1)
1.7.4 Point patterns	9	(1)
1.8 Data sets used for illustrative purposes	10	(2)
1.8.1 Monthly precipitation in Great Britain in 1999	10	(1)
1.8.2 A digital elevation model (DEM) of Great Britain	11	(1)
1.8.3 Positions of minerals in a slab of granite	11	(1)
1.8.4 Landcover in Turkey	11	(1)
1.8.5 Digital orthophoto of Newark, New Jersey	12	(1)
1.8.6 Population of Northern Ireland in 2001	12	(1)
1.9 A note on notation	12	(1)
1.10 Overview	13	(8)
2 Local Modelling	21	(6)
2.1 Approaches to local adaptation	21	(3)
2.2 Stratification or segmentation of spatial data	24	(1)
2.3 Moving window/kernel methods	24	(1)
2.4 Locally-varying model parameters	25	(1)
2.5 Transforming and detrending spatial data	26	(1)
2.6 Overview	26	(1)
3 Grid Data	27	(34)
3.1 Exploring spatial variation in single variables	27	(1)
3.2 Global univariate statistics	27	(1)
3.3 Local univariate statistics	28	(1)
3.4 Analysis of grid data	28	(1)
3.5 Moving windows for grid analysis	28	(9)
3.5.1 Image smoothing: Low pass filtering	31	(2)
3.5.2 High pass filters	33	(1)
3.5.3 Edge detectors	33	(1)
3.5.4 Texture	34	(3)
3.5.5 Other approaches	37	(1)
3.6 Wavelets	37	(15)
3.6.1 Fourier transforms and wavelet transforms	38	(1)
3.6.2 Continuous wavelet transform	39	(1)
3.6.3 Discrete wavelet transform (DWT)	40	(1)
3.6.4 Wavelet basis functions	40	(3)
3.6.5 Implementation of the DWT	43	(1)
3.6.6 Fast wavelet transform: Illustrated example	44	(1)
3.6.7 Two-dimensional (2D) wavelet transforms	45	(5)
3.6.8 Other issues	50	(1)
3.6.9 Applications of wavelets	51	(1)
3.7 Segmentation	52	(3)
3.8 Analysis of digital elevation models	55	(3)
3.9 Overview	58	(3)
4 Spatial Relations	61	(30)
4.1 Spatial autocorrelation: Global measures	62	(3)
4.1.1 Testing for spatial autocorrelation	64	(1)
4.2 Spatial autocorrelation: Local measures	65	(5)
4.2.1 Local indicators of spatial association	65	(5)
4.3 Global regression	70	(2)
4.4 Local regression	72	(1)
4.5 Regression and spatial data	73	(1)
4.6 Spatial autoregressive models	73	(2)
4.7 Multilevel modelling	75	(1)
4.8 Allowing for local variation in model parameters	76	(3)
4.8.1 Spatial expansion method	77	(1)
4.8.2 Other approaches	78	(1)
4.9 Moving window regression (MWR.)	79	(1)
4.10 Geographically weighted regression (GWR)	79	(7)
4.10.1 Illustrated application of MWR and GWR	81	(2)
4.10.2 Selecting a spatial bandwidth	83	(1)
4.10.3 Testing the significance of the GWR model	84	(1)
4.10.4 Case study: MWR, and GWR	84	(2)
4.10.5 Other geographically weighted statistics	86	(1)
4.11 Spatially weighted classification	86	(1)
4.12 Overview	86	(5)
5 Spatial Prediction 1: Deterministic Methods	91	(40)
5.1 Point interpolation	92	(1)
5.2 Global methods	92	(2)
5.3 Local methods	94	(19)
5.3.1 Thiessen polygons: Nearest neighbours	94	(3)
5.3.2 Triangulation	97	(1)
5.3.3 Trend surface analysis and local polynomials	97	(1)
5.3.4 Linear regression	97	(1)
5.3.5 Inverse distance weighting (IDW)	98	(3)
5.3.6 Natural neighbours	101	(2)
5.3.7 Thin plate splines	103	(5)
5.3.8 Thin plate splines case study	108	(1)
5.3.9 Finite difference methods	109	(3)
5.3.10 Locally adaptive approaches for constructing digital elevation models	112	(1)
5.4 Areal interpolation	113	(1)
5.5 General approaches: Overlay	114	(2)
5.6 Local models and local data	116	(12)
5.6.1 Generating surface models from areal data	116	(3)
5.6.2 Population surface case study	119	(1)
5.6.3 Local volume preservation	120	(3)
5.6.4 Making use of prior knowledge	123	(4)
5.6.5 Uncertainty in areal interpolation	127	(1)
5.7 Limitations: Point and areal interpolation	128	(1)
5.8 Overview	128	(3)
6 Spatial Prediction 2: Geostatistics	131	(40)
6.1 Random function models	132	(1)
6.2 Stationarity	132	(2)
6.2.1 Strict stationarity	133	(1)
6.2.2 Second-order stationarity	133	(1)
6.2.3 Intrinsic stationarity	133	(1)
6.2.4 Quasi-intrinsic stationarity	134	(1)
6.3 Global models	134	(1)
6.4 Exploring spatial variation	134	(9)
6.4.1 The covariance and correlogram	135	(1)
6.4.2 The variogram	136	(2)
6.4.3 The cross-variogram	138	(1)
6.4.4 Variogram models	138	(5)
6.5 Kriging	143	(9)
6.5.1 Simple kriging	145	(1)
6.5.2 Ordinary kriging	146	(2)
6.5.3 Cokriging	148	(2)
6.5.4 Applying cokriging	150	(2)
6.6 Equivalence of splines and kriging	152	(1)
6.7 Conditional simulation	152	(1)
6.8 The change of support problem	152	(1)
6.9 Other approaches	153	(1)
6.10 Local approaches: Nonstationary models	153	(1)
6.11 Nonstationary mean	154	(2)
6.11.1 Trend or drift?	154	(1)
6.11.2 Modelling and removing large scale trends	155	(1)
6.12 Nonstationary models for prediction	156	(7)
6.12.1 Median polish kriging	156	(1)
6.12.2 Kriging with a trend model	156	(3)
6.12.3 Intrinsic model of order k	159	(1)
6.12.4 Use of secondary data	160	(3)
6.13 Nonstationary variogram	163	(1)
6.14 Variograms in texture analysis	164	(1)
6.15 Summary	165	(6)
7 Point Patterns	171	(24)
7.1 Point patterns	171	(1)
7.2 Visual examination of point patterns	172	(1)
7.3 Density and distance methods	173	(1)
7.4 Statistical tests of point patterns	174	(1)
7.5 Global methods	174	(1)
7.6 Distance methods	175	(4)
7.6.1 Nearest neighbour methods	175	(1)
7.6.2 The K function	176	(3)
7.7 Other issues	179	(1)
7.8 Local methods	180	(1)
7.9 Density methods	180	(6)
7.9.1 Quadrat count methods	180	(1)
7.9.2 Quadrat counts and testing for complete spatial randomness (CSR)	181	(2)
7.9.3 Density estimation	183	(3)
7.10 Accounting for the population at risk	186	(1)
7.11 The local K function	186	(1)
7.12 Point patterns and detection of clusters	187	(4)
7.13 Overview	191	(4)
8 Summary: Local Models for Spatial Analysis	195	(4)
8.1 Review	195	(1)
8.2 Key issues	196	(1)
8.3 Software	196	(1)
8.4 Future developments	197	(1)
8.5 Summary	198	(1)
References	199	(22)
Index	221