Area data

  • We are starting to explore area data this week.
  • Due to privacy concerns, especially in the social sciences, access to point-level data is rare.
  • For instance, publicly available Canadian census data is aggregated to census geography.

Modifiable Areal Unit Problem (MAUP)

  • When aggregating point data into different spatial units, the choice of spatial units impacts analysis results such as hypothesis tests.
  • This is because any variations within the spatial unit are lost during aggregation.

Scale effect

Zone effect

Gerrymandering

  • In representative electoral systems, carefully modifying electoral district boundaries can provide advantages to a particular party.

Rock and queen contiguity

Spatial weight matrix

\[ \textbf{W}=\left (\begin{array}{c c c c c c} 0 & 1 & 1 & 0\\ 1 & 0 & 0 & 1\\ 1 & 0 & 0 & 1\\ 0 & 1 & 1 & 0\\ \end{array} \right) \]

\[ \textbf{W}'=\left (\begin{array}{c c c c c c} 0 & 0.5 & 0.5 & 0\\ 0.5 & 0 & 0 & 0.5\\ 0.5 & 0 & 0 & 0.5\\ 0 & 0.5 & 0.5 & 0\\ \end{array} \right) \]

Linear algebra recap

\[ \mathbf{W} = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} \]

\[ \mathbf{X} = \begin{pmatrix} b_{11} \\ b_{21} \end{pmatrix} \]

\[ \mathbf{W} \cdot \mathbf{X} = \begin{pmatrix} a_{11}\cdot b_{11} + a_{12} \cdot b_{21} \\ a_{21}\cdot b_{11} + a_{22} \cdot b_{21} \end{pmatrix} \]

Colour scheme

https://colorbrewer2.org/

Activities for today

  • We will work on the following chapter from the textbook:
    • Chapter 20: Activity 9: Area Data I
    • Chapter 22: Activity 10: Area Data II
  • The hard deadline is Friday, February 28.

Reference