Session 1 Presentation, worksheet and data at

• presentation: http://rpubs.com/lexcomber/GWPCA_Session1_pres
• worksheet: http://rpubs.com/lexcomber/GWPCA_Session1
• data: https://bit.ly/2INkSsM

Lex Comber email: a.comber@leeds.ac.uk

Paul Harris (‘Harry’) email: paul.harris@rothamsted.ac.uk

There will be 5 sessions

• Introduction to Regression GWR (Lex)
• Introduction to PCA & GWPCA (Harry)
• GWPCA for Outlier Detection (Harry)
• GWPCA for Network Design (Harry)
• GWPCA for Spatial Classification (Harry!)

There will be breaks

• 10:30 - Coffee / Tea
• 12:30 - lunch
• 15:10 - Coffee / Tea

Aim to finish at 17:00

We have set aside time in the first session (Introduction) to make sure everything is set up

• You have R installed
• You can load all of the packages
• You have all of the materials on your computer
• To make sure that you establish robust workflows

• We will be working in R and RStudio
• R is the engine
• we encourage you to work in RStudio

Technical aspects

1. Code is entered by a console
2. You should write your code in a script (like a text file)
3. This is not a typing / English lesson - so copy and paste from the documents
4. You can run code from the script
5. This means your code is saved, can be easily changed and re-run etc

Technical aspects: RStudio start

Technical aspects: Open a script

Technical aspects: RStudio Components

Conceptual aspects

1. You are not expected to remember every R command, function, etc
2. BUT ….you are expected to understand what you are trying to do with your code
   • so ask if you need to!!!
3. For these reasons you should annotate your code - use the # in your script

Conceptual aspects

• Learning is R is learning to drive.
• It takes time to become a good driver
• Learning by doing is important

• R includes a very large number of tools, functions and packages
• R has the latest methods and tools
• New tools are in R 10-20 years before commercial software
• The tools in R are open (i.e. the source code is visible)
• This support research transparency
• Oh - and R is free!

In each session

• we will briefly introduce each Part (10-15 mins)
• then you will work through the exercise documents
• we will be going round the lab helping where it is needed
• you are not just expected to run the code but to play with it as well!

• Data
• Exploration
• Multiple Linear Regression
• Testing Assumptions
• Outliers

You will find Chapters 5 and Chapter 8 in An Introduction to R for Spatial Analysis and Mapping by Chris Brunsdon and Lex Comber useful.

• you will load data (.csv format)
• you will create spatial data
• you will load shapefiles (.shp)
• you will need to install some packages
• only needs to be done once

The data set contains a number of variables for a study area from Rothamsted Research where Harry works.

• Sulphur (S)
• Calcium (Ca)
• Iron (Fe)
• Phosphorus (P)
• Soil Organic Matter (SOM)
• pH
• Slope
• Aspect
• coordinates (Easting and Northing)

We are interested in predicting S .

Assume associated with

• Sulphur (S)
• Calcium (Ca)
• Iron (Fe)
• Phosphorus (P)
• Soil Organic Matter (SOM)
• pH
• Slope
• Aspect

The equation for a regression is:

\(y_i = \beta_{0} + \sum_{m}^{k=1}\beta_{k}x_{ik} + \epsilon_i \textsf{ for } i \in 1 \cdots n\)

• \(y_i\) is S here
• The \(x_{ij}\)’s are SOM etc.

for example

m <- lm(S~Ca+Fe+P+SOM+pH+Slope+Aspect, data = df) 

## tmap mode set to interactive viewing

“the full range of conditions anywhere on the Earth’s surface could in principle be found packed within any small area. There would be no regions of approximately homogeneous conditions to be described by giving attributes to area objects. Topographic surfaces would vary chaotically, with slopes that were everywhere infinite, and the contours of such surfaces would be infinitely dense and contorted. Spatial analysis, and indeed life itself, would be impossible.” (de Smith et al 2007, p44)

Coefficients change

Coefficients change over the map:

Some coefficients flip…