RSS : Software for Spatial Analysis

Analysis and Visualization

of Spatial DataRichard Pugh

Product SpecialistMathSoft International

Overview

IntroductionS+SpatialStats 1.5S-PLUS for ArcView GIS 1.2EnvironmentalStats for S-PLUS 2.0Working with S-PLUS

Great Interactive Graphics

Powerful S Programming

Language

Complete Set of Statistical Algorithms

Full Interoperability and Deployability

S-PLUSExplore

Model

Visualize

Data Analysis in 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

S-PLUS

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

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C, C++, & FORTRAN object code links

OLE Automation: Server/Client Interaction with UNIX & DOS O/S Active X DDE JAVA

S-PLUS Integration

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These two components explain 96.07 % of the point variability.

S+SpatialStats S-PLUS for ArcView GIS EnvironmentalStats for S-

PLUS S+NUOPT S+GARCH S+Wavelets S+SeqTrial

S-PLUS Add-On Modules

Geostatistical Data Spatial Point Patterns Lattice data

S+SpatialStats

S-PLUS for ArcView GIS

Link between S-PLUS and ArcView

Import Data Easily Unparalleled Graphics Superior Analytical Power

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

EnvironmentalStats for S-PLUS

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

Geostatistical Data

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

Analyzing Geostatistical 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

Lattice Data

Defining a neighborhood structure Testing for spatial autocorrelation Fitting spatial linear models Model selection

Analyzing Lattice Data

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

Spatial Point Patterns

Testing for CSR– Nearest-neighbour methods

Intensity estimation K-functions (second order properties) Simulating point process data

Analyzing Spatial Point Patterns

SpatialStats Graphical User Interface

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

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!

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

S+EnvironmentalStats

Add-on Module for S-PLUS Monitoring Water, Soil, and Air Use Statistics to Compare

to “Background” and Look for Trends

Lognormal Mixture Density with(mean1=5, cv1=1, mean2=20, cv2=0.5, p.mix=0.5)

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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

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Histogram of Observed Datawith Fitted Normal Distribution

Order Statistics for TcCB andNormal(mean=0.5985106, sd=0.2836408) Distribution

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Empirical CDF for TcCB (solid line)with Fitted Normal CDF (dashed line)

Quantiles of Normal(mean = 0.5985106, sd = 0.2836408)

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Results of Shapiro-Wilk GOF

HypothesizedDistribution: Normal

Estimated Parameters: mean = 0.5985106sd = 0.2836408

Data: TcCB in epa.94b.tccb.df

Subset With: Area == "Reference"

Sample Size: 47

Test Statistic: W = 0.9179198

Test Statistic Parmeter: n = 47

P-value: 0.002830172

Results of Shapiro-Wilk GOF Test for TcCB

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

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Half-Width vs. Sample Size for Confidence Interval for p,with Confidence Level = 0.95, and p Hat = 0.5

“The Help System Alone is Worth the Price of Admission”

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

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

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

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

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Live Demo Time!

Writing a Presentation on Spatial Statistics User Input (mostly at a Spatial Conference) 2 Major Advantages …

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

1) S-PLUS GIS Toolbox

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

Now What?

For User Manuals (pdf)email rpugh@mathsoft.co.uk

Questions?