Function in R - Kernel Density Estimation (KDE) - Statistics Assessment Answer

Assessment Task:

Assessment Part 1 

This assessment tests your ability to think about the ways data can be processed and analysed. The task is to write a simple function in R. The function itself should perform one or a number of spatial analysis routines and produce an output file and/or visualisation of a dataset we have used in class or that you have sourced yourself. You should submit the code as part of the appendix. The marker may request original R files from the student if there are concerns about plagiarism (this is done anonymously via the student office) so all original files should be kept. Examples will be provided in class. 

Things to consider:
1. The final function should address a clear problem and turn the raw data into information. 2. You may wish to integrate the plotting of data into the function, but this may not always be appropriate.
3. The function should offer a number of clearly explained parameters for the user to adjust if they wish to experiment with a range of results. 

The accompanying write-up should take the form of a manual for the function’s use. It should include: 

1. A flow diagram to demonstrate the sequence of steps in the function. 

2. Explanation of the R object format required – such as what variables are required. 

3. A worked example of the function in action. 

You should include:
1. The need for such a function to be written and a rationale for your approach. 

2. A description of the data used to demonstrate the function. 

3. The scientific basis and a brief description of the analysis implemented. 

4. Testing you have performed to ensure the outputs are reliable. 

5. Potential applications of the function beyond those demonstrated. 

6. Limitations. 

7. R-Markdown

The function itself is worth 30 points, with 20 points available for the manual. 

The function should be created based on what has been done during the classes. This is what has been done:

• Discrete object fields

• Rasters vectors

• Projections

• Ecological fallacy and maup

• Spatial autocorrelation

• Importance of pattern

• Quadrat Analysis

• Location Quotient

• Gerry’s C

• Moran’s I

• Simpsons’ Paradox

• GWR

• Quadrant Analysis

• Ripley’s K(d) Function

• Geographical Weighted Regression

• Nearest Neighbour Analysis

• Kernel Density Estimation (KDE)

PART 2: Creating a function in R 

Rationale for function 

Kernel Density Estimation (KDE) is frequently utilized as a probability density function to produce a ‘risk analysis’ of spatial events. However, the singular use of KDE functions in statistical packages can result in an over-generalised representation of spatial point trends. 

Being purely statistical, it does not reflect important attribute and environmental data that may have contributed to the occurrence of the point event in the first place (Anderson, 2009). 

To obtain a spatial representation of statistics representing qualitative trends, k-means analysis could be used to identify clusters of events sharing similar attributes (Anderson, 2009). However, the resulting map product of a singular k-means analysis does not provide the smooth probability density map useful to assessing risk that KDE analysis offers (Anderson, 2009). Recognising this, a function is designed to integrate k-means analysis into existing KDE functions. 

Design of function 

This function (Figure 6) allows a KDE to be computed for individual typologies of spatial point events. To use this function, a k-means clustering analysis should be conducted a priori to classify each individual point event into a group based on similar k-means centres defined statistically. The procedure of the k-means clustering method, as described by Tan et al. (2006), is provided in Figure 7. The outputs of the k-means clustering analysis would serve as the key variables required for the function subsequently. Based on these variables, the function computes the KDE for each classification group defined in the previous k-means clustering analysis and provides a spatial visualization of the respective density estimations.

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