- Moran's I homework returned. You'll need to be able to do this for the test next Friday....
- I hope that I'll get each group's report today, so that we can
finalize the survey.
- I've been asked to provide a little guidance on the test, which is
coming up next Friday.
- I expect you to know basic stats (e.g. mean and median)
- Understand Pascal's triangle: how to construct it, how it's related to counting, powers of 2, etc.
- Graphs --
- History (Euler, Konigsberg)
- Simple graphs: constructing them
- Duality
- Labelled simple graphs, and using Pascal to count
- Directed, and weighted graphs (e.g. "Enemy of my enemy")
- Dynamics of graphs (e.g. Google)
- Moran's I
- Definition
- Adjacency matrices
- Calculation
Once we know how to do that, I'll turn you loose to collect some more data so that we can compute a few more Moran's Is for Newport, including over time.
- Moran's I
In the case of Newport, the median incomes look like this (for 2013 ACS):
19779 ;; 501 51071 ;; 504 28507 ;; 505 24538 ;; 506 37917 ;; 524 55711 ;; 525 37772 ;; 532
0 0 0 1 0 0 1 ;; 501 0 0 1 0 1 0 1 ;; 504 0 1 0 1 1 1 1 ;; 505 1 0 1 0 0 1 0 ;; 506 0 1 1 0 0 1 0 ;; 524 0 0 1 1 1 0 0 ;; 525 1 1 1 0 0 0 0 ;; 532
- Some sample calculations of MI for Newport Median Income
- In doing calculations for this data, I observed something about the adjacency graph: it's got some symmetry in it (that Moran's I won't be able to detect). Let's take a look at that, and for our example Moran's I case on the 2x2 square.
- So how do we proceed for earlier years, when census tracts 501 and 502 merge into 532? How can we compare over time? What data would we use for 2000 and 1990? Let's decide, and compute some Moran's Is.
- There are patterns that Moran's I can, and can't
distinguish. Let's turn our attention back to the simpler case of the
2x2 example, but using different data.
Compute Moran's I for the data
- [1,0,0,-1],
- [1,1,-1,-1], and
- [-1,1,1,-1]