This document discusses using R for spatial data analysis. It notes that spatial data has unique characteristics like geometry and attributes, map projections, and large multivariate and time series datasets. It compares GIS and R, noting that R allows for more flexible analysis, attributes as important, creativity, repeatability, and speed of development. It covers representing spatial data in R using classes like SpatialPointsDataFrame and reading/writing spatial data. It also summarizes types of spatial analysis and statistics that can be performed in R including queries, transformations, exploration, optimization, inference, modeling, point pattern analysis, geostatistics, and inference. Finally, it provides examples of performing spatial analysis and visualization in R.

1. The good, the bad & the pretty
Spatial data analysis with R
Robert Hijmans
University of California, Davis
May 2013

2. Spatial is special
• Complex: geometry and attributes
• Earth is flat? Map projections
• Size: lots and lots of it, multivariate, time series
• Special plots: maps
• First Law of Geography: nearby things are similar
– Statistical assumptions: violated
– Interpolation: possible

3. GIS* –
● Visual interaction –
• Data management –
• Geometric operations –
• Standard workflows –
• Single map production –
• Click, click, click & click –
• Speed of execution –
• Cumbersome –
Don't we have GIS for that?
– R
– Data & model focused ●
– Analysis ●
– Attributes as important ●
– Creativity & innovation ●
– Many (simpler) maps ●
– Repeatability (single script) ●
– Speed of development ●
– Easy & powerful (& free) ●
* there are many different GISs and they evolve

4. Geometry of spatial objects (‘vector’)
points, lines, polygons
X
Y

6. (Xmin, Ymax)
dimX
dimY
(Xmax, Ymin)
Geometry of spatial field (grid / raster data)
row 1
row 6
col 1 col 5
1 2 3 4 5
6 7
26 27 28 29 30
24 25

7. MODIS, 22 May, 2013

8. Representing spatial data
sp classes:
SpatialPointsDataFrame
SpatialLinesDataFrame
SpatialPolygonsDataFrame
SpatialGridDataFrame
SpatialPixelsDataFrame
rgdal
read/write of object (vector) and raster data,
(shapefiles, geotiff)
> library(rgdal)
> city <- readOGR('d:/data', 'city')
> elev <- readGDAL('d:/data/elevation.tif')

9. Map projections
coordinate reference system
Class: CRS
proj4string(city) <- CRS('+proj=lonlat +datum=WGS84')
cityutm <- sptransform(city, CRS('+proj=utm +zone=51'))

10. Types of spatial analysis*
• Query and reasoning
Where is? How much is this here? How to get from A to B?
• „Measurement
Area, Distance, Length, Slope
• „Transformation
Buffering, overlay, interpolation
• „Exploration and description
clusters, trends, spatial dependence, fragmentation
• „Optimization
Site selection, re-districting, traveling salesman
• „Inference
Samples from a population, problem of spatial autocorrelation
• Modeling
Climate change effects, impact of nuclear accident, dispersal
* After Michael Goodchild: http://www.csiss.org/aboutus/presentations/files/goodchild_qmss_oct02.pdf

11. Spatial statistics
• Point pattern analysis
• Geostatistics (kriging)
• Inference (hypothesis testing)

12. 1. Location of points is of prime interest
2. Points are not a sample
3. Points are within a defined study area
4. Points should be true incidents (not centroids)
Point patterns

13. Point patterns
> library(spatstat); library(maptools)
> cityOwin <- as(city, “owin”)
> pts <- coordinates(crime)
> p <- ppp(pts[,1], pts[,2], window=cityOwin)
> s <- smooth.ppp(p)
> e <- envelope(p) http://www.spatstat.org/

15. Geostatistics
> library(gstat)
> data(meuse)
> coordinates(meuse) <- ~x+y
> spplot(meuse, 'zinc')
1. Measurements are of prime interest (not locations)
2. Points are a sample
3. Unbiased estimates for locations that were not sampled

16. > x <- krige(log(zinc)~1, meuse, meuse.grid, model = m)
> spplot(x["var1.pred"], main="ordinary kriging predictions")
> spplot(x["var1.var"], main = "ordinary kriging variance")

17. > f <- houseValue ~ age + nBedrooms
> m <- lm(f1, data=hh)
> summary(m)
Call:
lm(formula = f1, data = hh)
Residuals:
Min 1Q Median 3Q Max
-222541 -67489 -6128 60509 217655
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -628578 233217 -2.695 0.00931 **
age 12695 2480 5.119 4.05e-06 ***
nBedrooms 191889 76756 2.500 0.01543 *
Regression with spatial data

18. Analyse the model residuals for SA (e.g. Moran's I)

19. > library(spdep)
> cb <- poly2nb(ca)
> lw <- nb2listw(cb)
> plot(ca)
> plot(lw, coordinates(ca),
add=TRUE, col="red")
> moran.test(residuals, lw)
Moran's I test under randomisation
Moran I statistic standard deviate = 2.6926, p-value = 0.003545
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
0.158977893 -0.010101010 0.003943149

20. If SA ‘significant’ then you could
• Re-specify your model
• Permit the coefficients,  , to vary spatially
(GWR)
• Modify the regression model to incorporate the SA
• Proceed and ignore SA?

21. OLS: Y = Xβ + e
Autogregressive model: Y = ρWY + e
Simultaneous Autoregressive Models:
SAR-lag: Y = ρWY + Xβ + e
(endogenous, inherent spat. autocorrelation, diffusion )
SAR-err: Y = Xβ + λWu + e
(exogenous, induced spatial autocorrelation)
SAR-mix: Y = ρWY + Xβ + WXγ + e
CAR

22. raster package
• new classes (‘S4’) for raster data
• no file size restrictions
• file formats: gdal, ncdf, ‘native’
• > 200 functions

23. RasterLayer
> library(raster)
>
> x <- raster(ncol=10, nrow=5)
>
> x <- raster('volcano.tif')
>
> x
class : RasterLayer
dimensions : 87, 61, 5307 (nrow, ncol, ncell)
resolution : 10, 10 (x, y)
extent : 2667400, 2668010, 6478700, 6479570 (xmin, xmax, …
coord. ref. : +proj=nzmg +lat_0=-41 +lon_0=173 +x_0=251
values : d:datavolcano.tif
min value : 94
max value : 195

24. > str(x)
Formal class 'RasterLayer' [package "raster"] with 16 slots
..@ file :Formal class '.RasterFile' [package "raster"] with 9 slots
. . .. ..@ name : chr “d:datavolcano.tif“
.. .. ..@ driver : chr "gdal"
..@ data :Formal class '.SingleLayerData' [package "raster"] with 11 slots
.. .. ..@ values : logi(0)
.. .. ..@ inmemory : logi FALSE
.. .. ..@ min : num 94
. . .. ..@ max : num 195
..@ extent :Formal class 'Extent' [package "raster"] with 4 slots
.. .. ..@ xmin: num 2667400
.. .. ..@ xmax: num 2668010
.. @ rotation :Formal class '.Rotation' [package "raster"] with 2 slots
.. .. ..@ geotrans: num(0)
.. .. ..@ transfun:function ()
..@ ncols : int 61
..@ nrows : int 87
..@ crs :Formal class 'CRS' [package "sp"] with 1 slots
.. .. ..@ projargs: chr " +proj=nzmg +lat_0=-41 +lon_0=173 +x_0=2510000 +y_0=6023150
..@ layernames: chr "volcano”
RasterLayer

25. Multiple layers
RasterStack - many files
RasterBrick - single files
> s <- stack(x, x*2, sqrt(x))
>
> s
class : RasterStack
dimensions : 87, 61, 5307, 3 (nrow, ncol, ncell,
nlayers)
resolution : 0.01639344, 0.01149425 (x, y)
extent : 0, 1, 0, 1 (xmin, xmax, ymin, ymax)
coord. ref. : NA
min values : 94.0, 188.0, 9.7
max values : 195, 390, 14
layer names : layer.1, layer.2, layer.3

26. 0
1 – 10
11 – 25
26 – 50
51 – 100
> 100
Daily rainfall

27. Some functions
ncell(x)
xyFromCell(x, 10)
getValues(x, row)
adjacent(x, 10)
writeRaster(x, filename, …)
merge, crop, project, aggregate,
reclass, resample,
rasterize, distance, focal …
“High level”
“Low level”

28. r <- raster(nc=10, nr=10)
values(r) <- 1:ncell(r)
q <- sqrt(r)
x <- (q + r) * 2
s <- stack(r, q, x)
ss <- s * r
Raster algebra

29. > elev <- getData('worldclim', var='alt', res=2.5)
> usa1 <- getData('GADM', country='USA', level=1)
> ca <- usa1[usa1$NAME_1 == 'California', ]
> bio <- getData('worldclim', var='bio', res=5)
> library(dismo)
> bg <- sampleRandom(bio, ext=extent(ca), size=1000)
> obs <- extract(bio, bigfoot)
> alt <- crop(elev, ca)
> alt <- mask(alt, ca)
> plot(alt)
> points(bigfoot)
Modeling bigfoot
(after Hickerson et al., 2008)
data from:
http://www.bfro.net/news/google_earth.asp

30. Likelihood
of occurrence
> d <- data.frame(pa=c(rep(1, nrow(obs)), rep(0, nrow(bg))),
rbind(obs, bg))
> library(randomForest)
> rf <- randomForest(pa~., data=d)
> pred <- predict(bio, rf)
> plot(pred)
> plot(ca, add=T)
> points(sel2, col='blue', pch=20)

31. Visualization
plot
plotRGB
contour
plot3D
…

32. > library(rasterVis)
> plot(s, addfun=function()plot(esp, add=T))

33. > library(rasterVis)
> alt <- getData('worldclim', var='alt', res=2.5)
> usa1 <- getData('GADM', country='USA', level=1)
> ca <- usa1[usa1$NAME_1 == 'California', ]
> alt <- crop(alt, extent(ca)+ 0.5)
> alt <- mask(alt, ca)
> levelplot(alt, par.settings=GrTheme)

34. http://www.revolutionanalytics.com/news-events/free-webinars/2012/ggplot2-with-hadley-wickham/
http://spatialanalysis.co.uk/2012/02/great-maps-ggplot2/

35. > library(dismo)
> g <- gmap('Mountain View, CA')
> plot(g, interpolate=T)
> xy <- geocode("2600 Casey Ave, Mountain View, CA")
> points(Mercator(xy[,2:3]), col='red', pch='*', cex=5)

36. http://flowingdata.com/2011/05/11/how-to-map-connections-with-great-circles/
> library(geosphere)
> inter <- gcIntermediate(lonlat1, lonlat2, n=100)
> lines(inter, col=colors, lwd=lwd)

37. .
http://cran.r-project.org/web/views/Spatial.html
More info