Chapter 14 Activity 6: Point Pattern Analysis III

NOTE: The source files for this book are available with companion package {isdas}. The source files are in Rmarkdown format and packed as templates. These files allow you execute code within the notebook, so that you can work interactively with the notes.

14.1 Practice questions

Answer the following questions:

  1. List and explain two limitations of quadrat analysis.
  2. What is clustering? What could explain a clustering in a set of events?
  3. What is regularity? What could explain it?
  4. Describe the concept of nearest neighbors.
  5. What is a cumulative distribution function?

14.2 Learning objectives

In this activity, you will:

  1. Explore a dataset using distance-based approaches.
  2. Compare the characteristics of different types of patterns.
  3. Discuss ways to evaluate how confident you are that a pattern is random.

14.3 Suggested reading

O’Sullivan D and Unwin D (2010) Geographic Information Analysis, 2nd Edition, Chapter 5. John Wiley & Sons: New Jersey.

14.4 Preliminaries

It is good practice to clear the working space to make sure that you do not have extraneous items there when you begin your work. The command in R to clear the workspace is rm (for “remove”), followed by a list of items to be removed. To clear the workspace from all objects, do the following:

rm(list = ls())

Note that ls() lists all objects currently on the workspace.

Load the libraries you will use in this activity. In addition to tidyverse, you will need spatstat, a package designed for the analysis of point patterns (you can learn about spatstat here and here):

library(isdas)
library(maptools) # Needed to convert `SpatialPolygons` into `owin` object
library(tidyverse)
library(sf)
library(spatstat)

In the practice that preceded this activity, you learned about the concepts of intensity and density, about quadrats, and also how to create density maps. For this practice, you will use the data that you first encountered in Activity 4, that is, the business locations in Toronto.

Begin by reading the geospatial files, namely the city boundary of Toronto. You need the sf object, which will be converted into a spatstat window object:

data("Toronto")

Convert the sf object to an owin object (via SpatialPolygons, hence as(x, "Spatial"):

Toronto.owin <- as.owin(as(Toronto, "Spatial")) # Requires `maptools` package

Next the data that you will use in this activity needs to be loaded. Each dataframe is converted into a ppp object using the as.ppp function, again after extracting the coordinates of the events from the sf object:

data("Fast_Food")
Fast_Food.ppp <- as.ppp(st_coordinates(Fast_Food), W = Toronto.owin)
# Add the classes of fast food to the ppp object:
marks(Fast_Food.ppp) <- Fast_Food$Class

data("Gas_Stands")
Gas_Stands.ppp <- as.ppp(st_coordinates(Gas_Stands), W = Toronto.owin)

data("Paez_Mart")
Paez_Mart.ppp <- as.ppp(st_coordinates(Paez_Mart), W = Toronto.owin)

If you inspect your workspace, you will see that the following ppp objects are there:

  • Fast_Food.ppp
  • Gas_Stands.ppp
  • Paez_Mart.ppp

These are locations of fast food restaurants and gas stands in Toronto (data are from 2008). Paez Mart on the other hand is a project to cover Toronto with convenience stores. The points are the planned locations of the stores.

You can check the contents of ppp objects by means of summary:

summary(Fast_Food.ppp)
## Marked planar point pattern:  614 points
## Average intensity 9.681378e-07 points per square unit
## 
## Coordinates are given to 1 decimal place
## i.e. rounded to the nearest multiple of 0.1 units
## 
## Multitype:
##           frequency proportion    intensity
## Chicken          82  0.1335505 1.292953e-07
## Hamburger       209  0.3403909 3.295453e-07
## Pizza           164  0.2671010 2.585906e-07
## Sub             159  0.2589577 2.507067e-07
## 
## Window: polygonal boundary
## 10 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1       4185 630935000.0      9.95e-01
## polygon 2        600   2536260.0      4.00e-03
## polygon 3        193    237206.0      3.74e-04
## polygon 4         28     26539.7      4.18e-05
## polygon 5         52    142793.0      2.25e-04
## polygon 6         67    158439.0      2.50e-04
## polygon 7         41     83470.2      1.32e-04
## polygon 8         30     42934.1      6.77e-05
## polygon 9         36     33866.6      5.34e-05
## polygon 10         8     11069.2      1.75e-05
## enclosing rectangle: [609550.5, 651611.8] x [4826375, 4857439] units
##                      (42060 x 31060 units)
## Window area = 634207000 square units
## Fraction of frame area: 0.485

Now that you have the data that you need in the right format, you are ready for the next activity.

14.5 Activity

NOTE: Activities include technical “how to” tasks/questions. Usually, these ask you to practice using the software to organize data, create plots, and so on in support of analysis and interpretation. The second type of questions ask you to activate your brainware and to think geographically and statistically.

Activity Part I

  1. Calculate the event-to-event distances to nearest neighbors using the function nndist(). Do this for all fast food establishments (pooled) and then for each type of establishment (i.e, “Chicken”, “Hamburger”, “Pizza”, “Sub”).

  2. Create Stienen diagrams using the distance vectors obtained in Question 1.

  3. Plot the empirical G-function for all fast food establishments (pooled) and then for each type of establishment (i.e, “Chicken”, “Hamburger”, “Pizza”, “Sub”).

Activity Part II

  1. Discuss the diagrams that you created in Question 2 with a fellow student.

  2. Is there evidence of clustering/regularity?

  3. How confident are you to make a decision whether the patterns are not random? What could you do to assess your confidence in making a decision whether the patterns are random? Explain.