Chapter 9 Spatial Dependence and Autocorrelation
This chapter begins to explore the analysis of spatial autocorrelation statistics. It has been long known that attribute values that are close together in space are unlikely to be independent. This is often referred to as Tobler’s first law of geography: "everything is related to everything else, but near things are more related than distant things". For example, if area \(n_i\) has a high level of violence, we often observe that the areas geographically close to \(n_i\) tend to also exhibit high levels of violence. Spatial autocorrelation is the measure of this correlation between near things.
The analysis of spatial dependence and global clustering is generally a first step before we explore the location of clusters. In spatial statistics we generally distinguish global clustering from the detection of local clusters. Some techniques, the focus of this chapter, are based on the global view and are appropriate for assessing the existence of dependence in the whole distribution, or clustering. It is important to first evaluate the presence of clustering before one explores the location of clusters, which we will cover in Chapter 10.
In this chapter we are going to discuss ways in which you can quantify the answer to this question. We will start introducing methods to assess spatial clustering with point pattern data, which typically start from exploring continuous distance between the location of the points. Then, we will discuss measures of global spatial autocorrelation for lattice data, which essentially aim to answer the degree to which areas (census tracts, police precincts, etc.) that are near each other tend to be more alike.
We will be making use of the following packages:
# Packages for reading data and data carpentry
library(readr)
library(dplyr)
library(lubridate)
# Packages for handling spatial data and for geospatial carpentry
library(sf)
library(sp)
# Specific packages for spatial point pattern analysis
library(spatstat)
library(spatstat.Knet)
# Packages to generate spatial weight matrix and compute measures of dependence
library(spdep)
library(rgeoda)
# Packages for mapping and visualisation
library(tmap)
library(ggplot2)
library(ggspatial)
