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# Building maps with analysis

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Presentation given at NACIS 2013 by Linda Beale

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### Building maps with analysis

1. 1. NACIS Annual Meeting Oct 9-11, 2013 | Greenville, South Carolina Workshop More than just colouring in: building maps with a solid analytical foundation Linda Beale PhD
2. 2. Visualization process • Based on clear need and purpose - Who is the audience? - • What is the intended purpose? What medium is to be used? These goals can not all accomplished by visual tricks
3. 3. What does GIS offer cartography? • Is it a hammer to crack a walnut? - Combining different data to get new information - • Bringing data together from disparate sources Part of the process of making informative and different maps Is statistical analysis really needed? - The development and application of methods to collect, analyze and interpret data - The science of learning from data
4. 4. Spatial analysis is about solving problems • • • • • • • What is inside an area? What is nearby? Where are the events concentrated? Where do things move over time? Why things occur where they do? How can we estimate values for a whole area? What is a suitable location for …? • Maps are needed to communicate the result
5. 5. Getting clarity • Descriptive statistics - Help understand the data as part of analysis or to quantify data - Commonly aspatial i.e. result is not dependant on location - Some spatial methods
6. 6. Basic descriptors Method Use ArcGIS tools Total Count or sum of values  Smallest and largest values  Minimum, Maximum    Mode Most commonly occurring  Median Central value     Mean Average value   Summary Statistics / Spatial Join / Frequency / Tabulate Intersection Neighborhood & Zonal Statistics (Spatial Analyst) Statistics / Summary Statistics / Spatial Join Histogram (Geostatistics) Neighborhood & Zonal Statistics / Get & set raster properties (Spatial Analyst) Spatial Join Neighborhood & Zonal Statistics (Spatial Analyst) Spatial Join Histogram (Geostatistics) Neighborhood & Zonal Statistics (Spatial Analyst) Statistics / Summary Statistics/ Spatial Join Neighborhood & Zonal Statistics (Spatial Analyst)
7. 7. Data distributions Method Use ArcGIS Range Max-min   Standard deviation Average deviation about the mean  nth Quantile Value that is nth way through a sorted list    Summary Statistics / Spatial Join Neighborhood & Zonal Statistics (Spatial Analyst) Summary Statistics Neighborhood & Zonal Statistics (Spatial Analyst) Display Properties Histogram (Geostatistics)
8. 8. Demo Finding quantity by area Summarizing by area
9. 9. Demo Finding percentage area Tabulate Intersection
10. 10. Spatial descriptors Method ArcGIS tools Mean  Central value  Distribution     Mean Center Linear Directional Mean Central Feature Median Center Standard Distance Directional Distribution
11. 11. Demo Finding direction Linear directional mean
12. 12. Normalization • Aspatially: - Normalization is to transform a set of measurements so that they may be compared in a meaningful way - • Examples: Standard score (z values), coefficient of variation Spatially: - Normalization transforms measures of magnitude (counts or weights) into measures of intensity - Using normalization we can take into account the differences between the areas (e.g. size of area, population size etc)
13. 13. Understanding quantity • We see quantity related to size
14. 14. As we often see it….
15. 15. Or… • So, we must map ‘like’ with ‘like’
16. 16. Demo Normalization
17. 17. Distributions and patterns • Density surfaces of count per unit area - Looking at concentrations of features - Seeing patterns of features - • Hotspots, Heat maps A density surface reflects the likelihood of an event occurring in each cell (bivariate probability density function)
18. 18. Demo Showing distribution Density analysis
19. 19. Maps can lie…so can statistics • Assumptions must be met for example, statistical tests are either: - • Parametric: Data distribution assumptions must be met Non-parametric: Distribution-free Analysis often concerned with explaining differences - Hypothesis testing - Statistical significance does not mean ‘important’
20. 20. Demo Identifying Clusters Hotspot analysis
21. 21. Demo Temporal patterns Coxcombs or Rose diagrams
22. 22. Demo Comparisons Percentage Difference
23. 23. Spatial autocorrelation • “Everything is related to everything else, but near things are more related than distant things." Tobler (1970) • Spatial autocorrelation statistics evaluate the degree of spatial dependency among observations
24. 24. Interpolation • from Latin interpolates - • Meaning: to estimate a value that lies between two other values Interpolation is required when: - We have samples from something that is continuous - A discrete surface has a different resolution (or cell size) to that required
25. 25. Spatial interpolation • Spatial interpolation is based on the notion that points which are close together in space tend to have similar attributes (Tobler’s First Law of Geography) • If the relationship between points and their values is determined by: - distance between points = isotropy - distance and direction = anisotropy Interpolated values are reliable only to the extent that the spatial dependence of the phenomenon can be assumed
26. 26. Interpolation in ArcGIS • IDW • Kriging • Natural Neighbor • Spline • Spline with Barriers • Topo to Raster • Topo to Raster by File • Trend • Global polynomial • Local polynomial • Inverse distance weighted • Radial basis functions • Diffusion kernel • Kernel smoothing • Ordinary kriging • Simple kriging • Universal kriging • Indicator kriging • Probability kriging • Disjunctive kriging • Gaussian geostatistical simulation • Areal interpolation • Empirical Bayesian kriging
27. 27. Deterministic methods • The data contains the full range of possible values • Things close to one another are more alike than those farther apart • The outcome is exactly known and based on the input
28. 28. Natural neighbor • Weighted average technique based Voronoi Delauney triangulation (in dotted lines) on top of voronoi • Delauney triangulation: The geometric dual of Voronoi i.e. natural bisection between voronoi which reverses the face inclusion
29. 29. IDW (inverse distance weighting) • Output is limited to the range of the values used to interpolate • Based on the assumption that the interpolating surface should be influenced most by the nearby points and less by the more distant points - • Assumes the surface is driven by local variation Weights assigned diminish with distance from the interpolation point - Sample points should have an even distribution
30. 30. Demo Interpolation to area Natural Neighbor and IDW
31. 31. Geostatistical methods • Uses the relationships between your data locations and their values, assuming: Data is normally distributed - Data exhibits stationary (no local variation) - Data has spatial autocorrelation - Data is not clustered - - - simple kriging has declustering options Data has no local trends - local trends can be removed during interpolation (and these trends are accounted for in the prediction calculations)
32. 32. Kriging Assumes that spatial variation can be decomposed into 3 main components: 1. Deterministic variation or trend/drift Trend analysed by trend surface analysis techniques 2. Spatially correlated, random variation Spatially correlated variation analysed by computing the semivariance 3. Spatially uncorrelated variation (noise) Provides measures of the certainty or accuracy of the predictions
33. 33. Normal distribution - Histogram - A normal QQ plot (probability plot) - Bell-shaped - No outliers - Mean ≈ Median - Skewness ≈ 0 - Kurtosis ≈ 3
34. 34. Transformations • Transformations can be used to bring data to a normal distribution e.g. logarithms, box-cox, square root
35. 35. Data stationarity • Statistical properties of data (e.g. mean, variance) are independent of absolute location • Covariance depends on only on the relative locations of the sites (e.g. the distance and direction between them) and not their exact location • Create a Voronoi map symbolized by: • Entropy • Standard Deviation
36. 36. Trend • Systematic changes in the mean of the data values across the area of interest - Can be difficult to distinguish from autocorrelation and anisotropy - Trend removal options
37. 37. Dealing with outliers Outliers statistically affect your data • They may be real and important or may be errors (such as input errors) Possible solution: • Remove outliers from the modeling step (semivariogram) • Use the full dataset for prediction
38. 38. The semivariogram Shows the spatial autocorrelation of the measured sample points semivariance • sill partial sill range nugget 0 • lag Semivariogram(distanceh) = 0.5 * average[(valuei – valuej)2]
39. 39. Empirical Bayesian Kriging • Spatial relationships are modeled automatically • Results often better than interactive modeling • Uses local models to capture small scale effects - Doesn’t assume one model fits the entire data
40. 40. Using EBK • Advantages Requires minimal interactive modeling - Standard errors of prediction are more accurate than other kriging methods - More accurate than other kriging methods for small or nonstationary datasets - • Disadvantages Processing is slower than other kriging methods - Limited customization -
41. 41. Selecting the best model • Predictions should be unbiased Mean prediction error should be near zero (depends on the scale of the data) so, - standardised mean nearest to 0 - • Predictions should be close to known values - • Small root mean prediction errors Correctly assessing the variability: average standard-error nearest the root-mean-square prediction error - standardised root-mean-square prediction error nearest to 1 -
42. 42. Demo Interpolation to area Empirical Bayes Kriging
43. 43. Take away points… • Good analysis is an important part of cartography • Even basic statistics can be powerful • Spatial data is more complex… but often reveals so much more
44. 44. Demo Think before you map…