Key Concepts Learned + Notes
- Clustered Errors (Spatial Autocorrelation of Residuals)
- Recall the Tobler’s 1st Law of Geography. This autocorrelation can occur for errors when evaluating models as well. A model generalized to a city may have + residuals in certain areas, and - residuals in others. If the model is good, we should see random scattering, not clustering of errors in space.
- Moran’s I
- Measuring spatial autocorrelation. Ranging between -1 (Perfect negative correlation - dispersion), 0 (Random spatial pattern), and 1 (Perfect positive correlation - clustering).
- At a high level, the formula calculates the difference of an observation from the mean, multiplied by the observation’s neighbor from the mean. Summation of all of these pairs.
- Defining Neighbor
- Contiguity (polygons that share a border; queen, rook), Distance (all w/in X distance; fixed distance), k-Nearest (closest k-points; adaptive distance)
- Spatial Lag - average value of neighbors
- In spatial stats, we learned about Spatial Lag/Spatial Error models. This is not going to be used in this class (focused on predictive models)
- Why? Simultaneity Problem (we need new house prices, but don’t have them in a predictive model). OLS estimates are biased and inconsistent.
- Biased (expected value != true parameter). Inconsitent (doesn’t converge to true value as n -> inf)
Coding Techniques/Technical Notes
- library(spdep)
- Creating the spatial lag.
- knn2b (to create neearest neighbors)
- nb2listw (provide the nearest neighbors to create a weights matrix - observation x observation with binary values)
- moran.mc
## Questions & Challenges