Analysis and Visualization of Spatial Data

1. Analysis and Visualization of Spatial Data Richard Pugh Product Specialist MathSoft International

2. Overview Introduction S+SpatialStats 1.5 S-PLUS for ArcView GIS 1.2 EnvironmentalStats for S-PLUS 2.0 Working with S-PLUS

3. Data Analysis in S-PLUS Great Interactive Graphics Complete Set of Statistical Algorithms Visualize Explore S-PLUS Model Powerful S Programming Language Full Interoperability and Deployability

4. S-PLUS • A state-of-the-art solution for exploratory data analysis, statistical modeling, and advanced data visualization • Combines the S object-oriented programming language with over 4200 prewritten functions • Offers the most comprehensive set of robust, classical and modern statistical methods available anywhere

5. Over 80 2D & 3D Graph Types Fully Object-Oriented Graphics Trellis (Conditional) Plots Dynamic Brush & Spin Linked Plots Embed Data in Graphs Exclude points from curve fits Interactive Plots Multiple Axes Multiple Plots on Graphs Multiple Graphs/Page Tabbed Graph Pages S-PLUS 2000: Graphics

6. Basic Statistics ANOVA & Regression GLMs, GAMs and NLMs Non Parametric & Local Regression Multivariate Statistics Robust Methods Survival Analysis Tree Models Quality Control Charts Mixed Effects Models Clustering Bootstrap / Jackknife Smoothing Time Series Power / Sample Size / Design Missing Data Imputation S-PLUS 2000: Statistics

7. S-PLUS Integration • C, C++, & FORTRAN object code links • OLE Automation: Server/Client • Interaction with UNIX & DOS O/S • Active X • DDE • JAVA

8. S-PLUS Add-On Modules • S+SpatialStats • S-PLUS for ArcView GIS • EnvironmentalStats for S-PLUS • S+NUOPT • S+GARCH • S+Wavelets • S+SeqTrial

9. S+SpatialStats • Geostatistical Data • Spatial Point Patterns • Lattice data

10. S-PLUS for ArcView GIS • Link between S-PLUS and ArcView • Import Data Easily • Unparalleled Graphics • Superior Analytical Power

11. EnvironmentalStats for S-PLUS • Data from Monitoring Networks • Display of Probability Distributions • Goodness-of-fit Tests • Sample Size Calculation • Prediction and Tolerance Intervals • Risk Assessment • Type I singly and multiply censored data

12. Geostatistical Data • Also called random field data • Measurements taken at fixed locations • Examples include: • mineral concentrations in a mine • rainfall recorded at weather stations • Small-scale variation / spatial correlation • closer sites generally have more similar data values

13. Analyzing Geostatistical Data • Producing Empirical Variograms • Fitting Theoretical Variogram Models • Exploration for Anisotropy • Performing Point and Block Kriging • Simulating Geostatistical Data

14. Lattice Data • Observations associated with spatial regions • Examples: • remote sensed images (regular) • cancer rates for Washington counties (irregular) • Neighbourhood structure • Neighbouring regions may have correlated data

15. Analyzing Lattice Data • Defining a neighborhood structure • Testing for spatial autocorrelation • Fitting spatial linear models • Model selection

16. Spatial Point Patterns • Locations are the variable of interest • Locations of objects in a spatial region • Examples: • trees in a forest • earthquake epicentres • Aim to identify: • spatial randomness • clustering or regularity • models for process

17. Analyzing Spatial Point Patterns • Testing for CSR • Nearest-neighbour methods • Intensity estimation • K-functions (second order properties) • Simulating point process data

18. SpatialStats Graphical User Interface

19. S-PLUS for ArcView GIS: • An ArcView GIS extension • Integrates the powerful statistics, data analysis, and presentation quality graphics capabilities of S-PLUS with the cartographic rendering and data management abilities of ArcView GIS • S-PLUS for ArcView GIS dramatically extends the ArcView analysis charting capabilities • For the first time in ArcView, you get accurate statistical inference which accounts for the spatial dependency pattern • S-PLUS data tables with analyses results can be imported back into ArcView for plotting in a wide range of map projections • Powerful complement to ARC/INFO via data conversion to ArcView GIS formats

20. S-PLUS for ArcView GIS: Graphics • Import existing S-PLUS Graphs • Colour classification plots and pie / bar charts • Two Step Graph Wizard with Plot Gallery • 2D, 3D, Pie, Matrix, Multiple Axis,... • Trellis plots made easy!

21. Spatial Neighbors builds weights between neighboring polygons Global Spatial Auto-correlation Indexes Moran’s I & Geary’s C measures Local Index of Spatial Association Spatial Linear Regression Model variables selected from themes or S-PLUS data frames Spatial Statistics Menu

22. S+EnvironmentalStats • Add-on Module for S-PLUS • Monitoring Water, Soil, and Air Use Statistics to Compare to “Background” and Look for Trends

23. EnvironmentalStats Features • Probability Density and Cumulative Density Plots • QQ Plots for all Probability Distributions • Estimation of Distribution Parameters and Quantiles, and C.Intervals • Maximum Likelihood and Minimum Variance Unbiased • Method of Moments • L-Moments • Additional Prob. Distributions • Generalized Extreme Value • Lognormal Mixture • 3 Parameter Lognormal • Goodness-of-Fit Tests • Chi-Square • Kolmogorov-Smirnov • PPCC • Shapiro-Wilk • Shapiro-Francia

24. EnvironmentalStats Features • Prediction and Tolerance Intervals • Special Nonparametric Hypothesis Tests for Trend and Shift • Seasonal Kendall’s Tau for Trend • Quantile Test for Shift in Upper Tail • Methods for Type I Singly and Multiply Censored Data • Sample Size and Power Calculations and Plots • Tools for Probabilistic Risk Assessment • Latin Hypercube Sampling • Generate Random Numbers from Different Distributions With a Specified Rank Correlation • Built-In Data Sets and Extensive Help System “The Help System Alone is Worth the Price of Admission”

25. EnvironmentalStats 2.0 (Beta) • Version 2.0 (in Beta) Has: • Pull-Down Menus • Power and Sample Size for Lognormal Distribution • Optimal Box-Cox Transformations • Simultaneous Prediction Intervals • Nonparametric von Neumann Test for Serial Correlation

26. S-PLUS GIS Users Natural Resources - Amoco, Commonwealth Edison, Hydro Quebec, Kimberly Clark, Koch Industries, Phillip Morris, Weyerhauser, Willamette Industries... Marketing - AC Nielsen, Amazon.com, Canada Post, CTB McGraw Hill, Dairy Queen, JD Powers & Associates, McDonalds, Rand Corporation, Readers Digest, Sears Roebuck & Co, Time Warner … Transportation - Airborne Express, American Airlines, Enterprise Rent A Car, Transport Canada... Government - Centers for Disease Control, Department of Fisheries and Oceans, DOE, EPA, FAA, FCC, FDA, Federal Housing Administration, IRS, NIH, NIST, NOAA, Social Security Admin, US Air Force, US Forest Service, US Geological Survey, SAPD ... Worldwide – NASA, US EPA, USGS, Centres for Disease Control UK – NERC - Centre for Ecology and Hydrology – British Geological Survey, British Antarctic Survey, Macauley Land Use Research Institute, BIOSS, CEFAS, MAFF, Marlab

27. EnvironmentalStats Users • Government Agencies • EPA, USGS, etc. • Commercial Consultants • CH2M Hill, Exponent • Academics • Environmental Engineering, Biostatistics, Environmental Health, Mathematics, etc. • Students • People Outside the Environmental Field! • Merck • Lockheed Martin

28. ? Questions Posed • Point Patterns 1 - Random / Clustered - Intensity • Point Patterns 2 - Cross Spectral Analysis • Point Patterns 3 – Mark Correlation Functions • Lattice Data 1 – Spatial Regression Methods for Normal Data • Lattice Data 2 – Spatial Regression Methods for Non-Normal Data • Lattice Data 3 – Spatial Smoothing Methods • Geostatistical Data 1 – Variograms and Kriging • Hybrid Patterns 1 – Cross Spectral Analysis • Hybrid Patterns 2 – Bayesian Hierarchical Models

29. Live Demo Time! • Writing a Presentation on Spatial Statistics • User Input (mostly at a Spatial Conference) • 2 Major Advantages …

30. 1) S-PLUS GIS Toolbox • Geostatistical Data • Variogram plots and boxplots and clouds • Directional variograms and Correlograms for Exploring Anisotrophy • Empirical Variogram Estimation including Robust Methods • Variogram Models including Spherical and Exponential • Ordinary and Universal Kriging • Block and Point Kriging Prediction at arbitrary Location with Standard Errors • Parametric and Non-parametric Trend Surfaces • Point Patterns • Point Maps that Include Region Boundaries • Spatial Randomness Tests • Ripley’s K-Function • Simultation of Spatial Random Processes • Local Intensity Estimation • Lattice Data • “Binning” of High Density Data into a Regular Lattice of Counts • Geary and Moran Spatial Autocorrelation coefficients • Spatial Regression Models including Conditional and Simultaneous Autoregressive Models • Nearest Neighbour Search • Visualisation of Neighbour Structures

31. 2) It’s in S-PLUS! • Advanced Graphics • Exclusive Trellis Graphics • 3D Plotting and Spinning • Contour Plots • Overlaying Plots • Brush and Spin Environment • Export to Large Number of Formats • Java Graphlets • Imaging Plots • Hexagonal Binning • “S” Language • Powerful Language • Excel Integration • Call from ArcView with Link • Full Visability and Customisation • C, C++, Fortran and Java Connectivity • 100,000 + User Community • Statistics • Cluster Analysis • Tree Models • Advanced Regression • Data Mining Tools • Linear and Non-Linear Mixed Effects • Missing Data

32. Now What? For User Manuals (pdf) email rpugh@mathsoft.co.uk Questions?