Chapter 12 Activity 5: Point Pattern Analysis II
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.
12.1 Practice questions
Answer the following questions:
- How does the quadrat-based test of independence respond to a small number of quadrats?
- How does the quadrat-based test of independence respond to a large number of quadrats?
- What are the limitations of quadrat analysis?
- What is a kernel function?
- How does the bandwidth affect a kernel function?
12.2 Learning objectives
In this activity, you will:
- Explore a dataset using quadrats and kernel density.
- Experiment with different parameters (number/size of kernels and bandwidths).
- Discuss the impacts of selecting different parameters.
- Hypothesize about the underlying spatial process based on your analysis.
12.3 Suggested reading
O’Sullivan D and Unwin D (2010) Geographic Information Analysis, 2nd Edition, Chapter 5. John Wiley & Sons: New Jersey.
12.4 Preliminaries
It is good practice to begin with a clean session to make sure that you do not have extraneous items there when you begin your work. The best practice is to restart the R
session, which can be accomplished for example with command/ctrl + shift + F10
. An alternative to only purge user-created objects from memory is to use the R
command rm
(for “remove”), followed by a list of items to be removed. To clear the workspace from all objects, do the following:
Note that ls()
lists all objects currently on the worspace.
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) # Companion Package for Book An Introduction to Spatial Data Analysis and Statistics
library(spatstat) # Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests
library(tidyverse) # Easily Install and Load the 'Tidyverse'
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. Begin by loading the data that you will use in this activity:
This dataset was sourced from the Scandinavia Bear Project, a Swedish-Noruegian collaboration that aims to study the ecology of brown bears, to provide decision makers with evidence to support bear management, and to provide information regarding bears to the public. You can learn more about this project here.
The project involves tagging bears with GPS units, so that their movements can be tracked.
The dataset includes coordinates of one bear’s movement over a period of several weeksin 2004. The dataset was originally taken from the adehabitatLT
package but was somewhat simplified for this activity. Instead of full date and time information, the point pattern is marked more simply as “Day Time” and “Night Time”, to distinguish between diurnal and nocturnal activity of the bear.
Summarize the contents of this dataframe:
## x y marks
## Min. :515743 Min. :6812138 Day Time :502
## 1st Qu.:518995 1st Qu.:6813396 Night Time:498
## Median :519526 Median :6816724
## Mean :519321 Mean :6816474
## 3rd Qu.:519983 3rd Qu.:6818111
## Max. :522999 Max. :6821440
The Min. and Max. of x
and y
give us an idea of the region covered by this dataset. We can use these values to approximate a window for the region (as an experiment, you could try changing these values to create regions of different sizes):
Next, we can convert the dataframe into a ppp
-class object suitable for analysis using the package spatstat
:
You can check the contents of the ppp
object by means of summary
:
## Marked planar point pattern: 1000 points
## Average intensity 1.176471e-05 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
## Day Time 502 0.502 5.905882e-06
## Night Time 498 0.498 5.858824e-06
##
## Window: rectangle = [515000, 523500] x [6812000, 6822000] units
## (8500 x 10000 units)
## Window area = 8.5e+07 square units
Now that you have loaded the dataframe and converted to a ppp
object, you are ready for the next activity.
12.5 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
- Analyze the point pattern for the movements of the bear using quadrat and kernel density methods. Experiment with different quadrat sizes and kernel bandwidths.
Activity Part II
Explain your choice of parameters (quadrat sizes and kernel bandwidths) to a fellow student.
Decide whether these patterns are random, and support your decision.
Do you see differences in the activity patterns of the bear by time of day? What could explain those differences, if any?
Discuss the limitations of your conclusions, and of quadrat/kernel (density-based) approaches more generally.