An Introduction to Spatial Statistics: Data Types, Statistical Tools and Computer Software Moira A. Mugglestone MRC Institute for Environment and Health mam14@le.ac.uk http://www.le.ac.uk/ieh/ spatial.1
Plan for the talk Data types: point patterns, lattice data, geostatistical data and hybrid patterns. Statistical tools: for description, regression, interpolation and smoothing. Computer software: which tools are available as a single command or a worked example in standard packages (as far as I know). Today s other talks: illustration of some of the tools available in GenStat and S-PLUS. spatial.2
Point patterns example 1 0 50 100 150 200 250 0 50 100 150 200 250 Wacapous at Paracou, French Guyana. spatial.3
Point patterns example 1 Research questions: random, clustered or regular? variations in intensity? Statistical tools: empirical distributions of inter-event distances (including the -function); spectral analysis; kernel density estimation. Software: GenStat and S-PLUS. spatial.4
Point patterns example 2 0 50 100 150 200 250 0 50 100 150 200 250 Mahots noirs at Paracou. spatial.5
Point patterns example 2 Research questions: association between mahots noirs and wacapous? Statistical tools: empirical distributions of inter-event distances (including bivariate -functions); cross-spectral analysis. Software: GenStat and S-PLUS. spatial.6
Point patterns example 3 0 50 100 150 200 250 0 50 100 150 200 250 Size of wacapous at Paracou. spatial.7
Point patterns example 3 Research questions: association between size and location? Statistical tools: mark-correlation functions. Software: not available in standard packages? spatial.8
Lattice data example 1 sqrt(number of beetles) at date 2 crop height at date 2 0 0 2 2 4 4 rows 6 rows 6 8 8 10 10 12 12 0 2 4 6 8 10 12 14 columns 0 2 4 6 8 10 12 14 columns Beetle counts and crop height at IACR Long Ashton. spatial.9
Lattice data example 1 Research questions: random distribution of beetles? association between beetle counts and crop height? Statistical tools: spatial regression methods for normal data. Software: GenStat and SAS. spatial.10
Lattice data example 2 830 820 northings 810 800 790 780 770 ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο 760 present ο ο ο ο absent 290 300 310 320 330 340 350 360 eastings Presence/absence of red deer in Grampian Region, Scotland. spatial.11
Lattice data example 2 Research questions: association between presence/absence of deer and habitat-related covariates? Statistical tools: spatial regression methods for non-normal data. Software: not available in standard packages? spatial.12
Lattice data example 3 Population counts in Leicestershire. spatial.13
Lattice data example 3 Research questions: disease incidence varies across the region? Statistical tools: spatial smoothing methods. Software: BUGS. spatial.14
Geostatistical data example 1 0 2000 4000 6000 0 2000 4000 6000 Sampling locations for measurements of soil depth. spatial.15
Geostatistical data example 1 Research questions: association between depth at different locations? spatial prediction? Statistical tools: variograms and kriging. Software: GenStat, S-PLUS and SAS. spatial.16
Hybrid patterns example 1 0 50 100 150 200 250 0 50 100 150 200 250 Wacapous and altitude at Paracou. spatial.17
Hybrid patterns example 1 Research questions: association between altitude and wacapous? Statistical tools: cross-spectral analysis. Software: not available in standard packages? spatial.18
Summary Data types: point patterns, lattice data, geostatistical data and hybrid patterns. Statistical tools: for description, regression, interpolation and smoothing. Computer software: GenStat, S-PLUS, SAS and BUGS contain tools for analysis of spatial data. spatial.19
Acknowledgements Paracou data: CIRAD-Forêt, France. Beetle data: George Thomas and Massimo Bressan, IACR Long Ashton. Deer data: Red Deer Commission. Leicestershire map: Bob Harris, IEH. Soil data: Michel Goulard, INRA Toulouse, France. spatial.20