Everything happens somewhere and spatial analysis attempts to use location as an explanatory variable. Such analysis is made complex by the very many ways we habitually record spatial location, the complexity of spatial data structures, and the wide variety of possible domain-driven questions we might ask. One option is to develop and use software for specific types of spatial data, another is to use a purpose-built geographical information system (GIS), but determined work by R enthusiasts has resulted in a multiplicity of packages in the R environment that can also be used.

1. Finding Meaning in Points, Areas
and Surfaces: Spatial Analysis in
R
Revolution Analytics
Wednesday 13th June 1300 EST

2. The instructor
• Dave Unwin
• Retired Geography
professor
• University of London,
UK
• Spatial analysis & GIS in
environmental sciences

3. Geography is everywhere?
• Everything happens somewhere
• Interest is on geo-spatial data at scales from a
few meters to the planet Earth

4. Spatial analysis is the name given to a
variety of methods of analysis in which we
use LOCATION as an explanatory variable
NB: Not all spatial analysis is spatial
statistical analysis and not all spatial
analysis is geospatial

5. Typical Questions
• Is there an unusual clustering of point objects such
as crimes/cases of a disease/trees/whatever here
that we need to worry about? If so does the point
pattern help explain why?
• Does this phenomenon in these areas (counties,
states, countries) show spatial variation I need to
know about? Does the pattern help explain why?
• What is the most probable value for a continuous
variable at this location?

6. Characteristics of spatial data?
• Almost always given: typically the analyst has no
choice in their acquisition, sometimes even their
formatting;
• They have additional structure that defines their
geometry (point, line/network, area/lattice,
surface/field/geostatistical)

7. Types of spatial data
Objects
can be points, lines/networks or areas/lattices with L0,
L1 and L2 dimension of length
Fields
are self-defining and spatially continuous: everywhere
has a value (e.g. temperature, mean annual rainfall, …)

8. Locating things on Planet Earth
• There are many ways by which we measure our location (place name,
address, ZIP/Post code , latitude/longitude, grid reference etc)
• How we locate depends on context and scale
• Spatial resolution of location measurements vary
• For analysis we (usually) need (x, y) co-ordinates in a projected system
• Need for keys to provide these data, often added after the data have been
collected
• GPS & GPS-enabled devices are changing this and LBS is a massive and
growing industry that is changing our spatial behaviour

9. Why R?
• A consistent environment for statistical computing
and graphics
• Relative proximity to the data
• Easy links to code in numerous languages and to
DBMS
• Easier development of new methods
• Packages available to perform most analyses
• Immensely supportive community

10. The sp Spatial
Class and its
subclasses

11. > library(sp)
> getClass("Spatial")
Class "Spatial" [package "sp"]
Slots:
Name: bbox proj4string
Class: matrix CRS
Known Subclasses:
Class "SpatialPoints", directly
Class "SpatialLines", directly
Class "SpatialPolygons", directly
Class "SpatialPointsDataFrame", by class "SpatialPoints", distance 2
Class "SpatialPixels", by class "SpatialPoints", distance 2
Class "SpatialLinesDataFrame", by class "SpatialLines", distance 2
Class "SpatialGrid", by class "SpatialPoints", distance 3
Class "SpatialPixelsDataFrame", by class "SpatialPoints", distance 3
Class "SpatialGridDataFrame", by class "SpatialPoints", distance 4
Class "SpatialPolygonsDataFrame", by class "SpatialPolygons", distance 2

12. What extra?
• A data matrix called • A spatial data frame
turbines: called turbines_spdf
> turbine_df that adds three bits of
lon lat ‘geography’
1 -0.8716027, 52.39353
1. lon/lat become spatial
2 -0.8781694, 52.39340
3 -0.8656111, 52.39398
coordinates
4 -0.8795611, 52.39626 2. A coordinate reference
5 -0.8804666, 52.39913 system (CRS) to which
6 -0.8726833, 52.39631 these relate, and
7 -0.8643472, 52.39723
3. A bounding box (for
display)

13. Why bother?
You can do a lot of spatial
analysis using a simple
Cartesian co-ordinate
system such as a unit
square, but what happens
when you want to merge
with other geographic
data?
Here is a simple example in
which turbines_spdf has
been written out in KML
and then ‘mashed ‘ onto
Google Earth to create a
‘pin’ map

14. Packages for spatial data
Contributed packages with spatial statistics
applications:
• Utilities: rgdal, sp, maptools
• Point patterns: spatstat, VR:spatial, splancs;
• Geostatistics: gstat, geoR, geoRglm, fields, spBayes,
• RandomFields, VR: spatial, sgeostat, vardiag;
• Lattice/area data: spdep, DCluster, spgwr, ade4.

15. Making sense of it all …
• This is the standard work,
written by the authors of sp
and some of the packages
• It contains just about all you
might want to know about
spatial analysis in R circa
2008
• Useful new packages have
emerged since then

16. For spatial and spatial statistical analysis?

17. Three use case examples
• Each illustrates the analysis of a particular class of
spatial data -- points L0, area L2 and surfaces L3

18. Patterns in drumlins?
Our bit
A ‘drumlin’ A ‘swarm of them in NI

19. Adding an ‘edge’ ….
Is the pattern CSR as predicted by Smalley
and Unwin (1968) over forty years ago?

20. Visualizing the pattern using kernel density estimation

21. Simple tests against CSR ….
Using Baddeley’s spatstat package ….
• > # nearest neighbor tests for comparison
• > clarkevans(drumlin_ppp)
• naive Donnelly cdf
• 1.249917 1.215380 1.233599
• > clarkevans(drumlin_rr)
• naive Donnelly cdf
• 1.238626 NA 1.215134

22. Ripleys K(d) function …
NB: Modification to L(est) on RHS due to Mark Rosenstein

23. In this case we conclude that the pattern is
more regular than random at short range,
but then we have no evidence that it is
other than CSR at longer ranges
The generic question is
Is there an unusual clustering of point objects
such as crimes/cases of a disease/trees/
whatever here that we need to worry about? If
so does the point pattern help explain why?

24. Patterns in disease incidence
• Where does this disease occur?
• Although disease affects individuals, almost always
the available information will be aggregated into
some areal unit such as a postal code, electoral
district, county, state or country
• Such data are called lattice data and they are
visualized using choropleth (‘area-value’) maps
• Our questions are essentially the same as before

25. Lip cancer incidence
in the Districts and
Islands of Scotland
(Clayton and Kaldor,
1987)
> lips <-
readShapePoly("C:s
cotlip",
IDvar="RECORD_ID")
> plot(lips)
Note this is an ESRI
‘shapefile’ a de facto
standard for such
lattice data

26. Plotting the raw
numbers?
>library(sp)
>spplot (lips,
“CANCER”)
This is a
complete NO
NO
NO

27. Plotting the rates?
The data are basically
Poisson and the numbers
are low, which means that
these rates are unstable to
quite small changes

28. Two alternatives
Probabilities Bayesian weighting

29. Chi-square mapping using ‘Pearsonian’ Residuals
> sum(lips$CANCER)
[1] 536
> sum(lips$POP)
[1] 14979894
>pop_exp<-
536*(lips$POP/14979894)
> chisq <- (lips$CANCER-
pop_exp)/sqrt(pop_exp)
> lips_chi <- spCbind(lips, chisq)
>spplot(lips_chi,"chisq")

30. But is does it have a ‘geography’?
Moran’s I is used globally
 w11 w12  w1n 
w w22  
W =  21 
    
 
 wn1   wnn 

31. We conclude that we are not fooling ourselves!
Geographic Structure Moran’s I Expected value Variance of (E) z-score
Scheme
Simple contiguity 0.363263693 -0.019230769 (n=52) 0.006769752 4.6488
Delauney 0.519599336 -0.018181818 0.005068704 7.5537
Distance k=3 0.543587908 -0.018181818 0.008287442 6.1709
Sphere of influence 0.483547126 -0.018181818 0.006087487 6.4306
Gabriel graph 0.371846634 -0.022222222 (n=45) 0.007022745 4.7024
Relative neighbors 0.38126027 -0.02500000 (n=40) 0.01206414 3.6988

32. We conclude that the pattern is
‘real’, the disease has a
geography of interest
The generic question is:
Does this phenomenon in these areas (counties,
states, countries) show spatial variation I need to
know about? Does the pattern help explain why?

33. Spatial interpolation of a continuous field
In effect we take a sample of ‘heights’ and use these to
estimate the value EVERYWHERE across the surface

34. Spatial interpolation
• The key property of the variable is that it is spatially continuous (everywhere has a
value and the gradient is likewise a continuous vector field)
• Given a scatter of sample measurements of the ‘height’ of some continuous
variable, what is the value of this field variable at this location?
• There are domain-dependent sub-questions such as: what is the gradient of the
field at this point? Or : how much of the variable is below the surface (e.g. rainfall
totals)
• Examples might be air temperature, rainfall over some period, values of some
mineral resource, ground height etc., etc.
• Sometimes results can be verified by further sampling, but equally often there is
no external way to test the results
• The process is called spatial interpolation and there are a great many ways of
doing it automatically

35. Interpolation by Inverse Distance Weighting (IDW)
• Estimate each and every location on a very
fine grid using an inverse distance weighted
sum of the height values of neighboring
control points
• Uses the gstat package:
• A parameter ‘e’ controls the degree of
smoothing

36. Rendering
IDW
e=2.0
IDW
e=1.0
IDW
e=3.0

37. Issues in IDW
• Produces ring contours or bull’s eyes
• No way of assessing the likely errors involved
• No theoretical reason for the choice of the
distance exponent to be used
• Undesirable side effects if the control data are
clustered
• But it corresponds fairly well to what a human
might draw

38. Geostatistics: making use of spatial dependence in
interpolation
• For points and areas spatial dependence can
complicate any statistical analysis using
standard methods
• Can we characterise the spatial dependence
across a field and use it to produce better
interpolations?

39. Variography: the semi-variogram ‘cloud’

40. Summary semi-variogram
We fit one or other of
the plausible models
to these data to derive
a function that
describes the spatial
dependence

41. Interpolation by Kriging
Error of the estimates can also
be mapped:

42. We have our estimates over the
entire area
The generic question is:
What is the most probable value for a
continuous variable at this location?

43. Some R-fun (1) : using dismo
>library(XML) #needs this
> library(rgdal) #and this
>library (dismo)
> place<-geocode("Maidwell, > size<-extent(unlist(place[4:7]))
Northamptonshire, UK") #the #what does this do?
address needs to have enough to be > map<-gmap(size,type="satellite")
recognized > plot(map)
> place # the place object is a vector > map<-gmap(size,type="roadmap")
of length 7 with a bounding box: > plot(map)
ID lon lat lonmin lonmax
latmin latmax To find places and plot
1 1 -0.9030642 52.38524 -0.938073 them using Google
-0.8710494 52.37016 52.40107 Earth and Maps™
location
1 Maidwell, Northamptonshire, UK

44. Where I live …
Google Maps™
Aerial photography

45. Or (slightly) better known?
> place<-geocode("The White
House, Washington, USA")
> size<-
extent(unlist(place[4:7]))
> map<-
gmap(size,type="satellite")
> plot(map)

46. Some R Fun (2): exporting KML
• Due to James Cheshire
UCL
• The London Bicycle Hire
system
> library(maptools)
> library(rgdal)
> cycle <-
read.csv("London_cycle_hire_locs.cs
v", header=TRUE)
> plot(cycle$X,cycle$Y)

47. Some R Fun (2): exporting KML
(continued)
• > coordinates(cycle)<- c("X","Y")
• > BNG<-CRS("+init=epsg:27700")
• > proj4string(cycle) <- BNG
• >p4s <- CRS("+proj=longlat
+ellps=WGS84 +datum=WGS84")
• > cycle_wgs84 <-
spTransform(cycle,CRS=p4s)
• > writeOGR(cycle_wgs84,
dsn="london_cycle_docks.kml",
layer= "cycle_wgs84",
driver="KML",
dataset_options=c("NameField=
name"))

48. The End
• Taking it further:
• Applied Spatial Data Analysis with R (Bivand,
Pebesma and Gomez-Rubio (2008)
• Spatial Statistics with R commences 14th
December 2012 at Statistics.com ™
QUESTIONS ARE WELCOME