Crime Mapping and Spatial Data Analysis using R

At the center of all spatial analysis is the concept of place. People identify with places of various sizes and shapes, from the parcel of land, to the neighbourhood, city, country, state or nation state. Places often have names, and people use these to talk about and distinguish them. Names can be official or unofficial. Places also change continually as people move. In geospatial analysis, the basis of rigorous and precise definition of place is a coordinate system. A coordinate system is a set of measurements that allows place to be specified unambiguously and in a way that is meaningful across different users, analysts, mappers, and researchers.

In Environmental Criminology, place has acquired different meanings through history. The first geographical studies of crime during the 19th century looked at variation across provinces in France [229], Belgium [235], and England [230]. Later on, in the first decades of the 20th century, the Chicago School of Sociology focused on the study of neighbourhoods [233] [238]. With the emergence of Environmental Criminology [223] [226] [227] a shift towards a greater interest in microplaces, such as street segments or particular addresses, can be seen [228]. Although an interest in variation across large administrative units (as “place”) remains within criminology, there has been a trend towards understanding place as particular locations, and focusing on risky places for crime.

However we define “place”, it is the central concept to crime mapping, and spatial data analysis. Most human activity takes place in a specific location, and accounting for this spatial information is a key task for criminologists, crime analysts, and social and data scientists more broadly.

Attribute has become the preferred term for any recorded characteristic or property of a place. It is what more generally in statistics we may call a variable and in data science a feature. A place’s name is an obvious example of an attribute. But there can be other pieces of information, such as number of crimes in a neighbourhood, or the GDP of a country. Within geographic information science (GIS) the term ’attributes’ usually refers to records in a data table associated with individual elements in a spatial data file. These data behave exactly as data you may have encountered in past experience with non-spatial statistics. The rows represent observations, and the columns represent variables. The variables can have different levels of measurement (numeric (interval or ratio, discrete or continuous) or categorical (binary, nominal, ordinal)), and depending on what they are, you can apply different methods to making sense of them. The difference between a non-spatial data set and an attribute table associated with spatial data is that the unit of analysis will be some places or locations; each row will include elements that allow us to place it on a map.

In spatial analysis it is customary to refer to places as objects. These objects can be a whole country, or a road. In forestry, the objects of interest might be trees, and their location will be represented as points. On the other hand, studies of social or economic patterns may need to consider the two-dimensional extent of places, which will therefore be represented as areas. These representations of the world are part of what is called the vector data model: a representation of the world using points, lines, and polygons. Vector models are useful for storing data that have discrete boundaries, such as country borders, land parcels, and streets. This is made up of points, lines, and areas (polygons):

df <- data.frame(x = c(1, 4, 3, 2, 1),
                 y = c(2, 0, 2, 4, 2))

p1 <- ggplot(df) +
  geom_point(aes(x = x, y = y), size = 5) +
  xlim(c(0,5)) +
  ylim(c(-1,5)) +
  theme_void() +
  labs(title = "Points") +
  theme(panel.border = element_rect(colour = "black", fill=NA, size=3))

p2 <- ggplot(df, aes(x = x, y = y)) +
  geom_point(size = 5) +
  geom_line(size = 2) +
  xlim(c(0,5)) +
  ylim(c(-1,5)) +
  theme_void() +
  labs(title = "Line") +
  theme(panel.border = element_rect(colour = "black", fill=NA, size=3))

p3 <- ggplot(df, aes(x = x, y = y)) +
  geom_point(size = 5) +
  geom_path(size = 2) +
  xlim(c(0,5)) +
  ylim(c(-1,5)) +
  theme_void() +
  labs(title = "Polygon") +
  theme(panel.border = element_rect(colour = "black", fill=NA, size=3))

gridExtra::grid.arrange(p1, p2, p3, nrow = 1)

Spatial objects may also be stored as raster data. Raster data are made up of pixels (or cells), and each cell has an associated value. Simplifying slightly, a digital photograph is an example of a raster dataset where each pixel value corresponds to a particular colour. In GIS, the pixel values usually represent continuous data such as elevation above sea level, or chemical concentrations, or rainfall, etc. The key point is that all of this data is represented as a grid of (usually square or hexagonal) cells.

We already mentioned lines that constitute objects of spatial data, such as streets, roads, railroads, etc. Networks constitute one-dimensional structures embedded in two or three dimensions. Discrete point objects may be distributed on the network, representing phenomena such as landmarks; or observation points. Mathematically, a network forms a graph, and many techniques developed for graphs have application to networks. These include various ways of measuring a network’s connectivity, or of finding the shortest path between pairs of points on a network. We elaborate on networks further in Chapter 8 of this book.