1. Geospatial Statistics
LearnR!
Fall 2014
Nathaniel MacNell

2. What do we do with spatial data?

3. What approach should I use?
Start: the [spatial] “support” of the data
What type spatial data do you have?
Points (e.g. GPS coordinates) per observation
Polygons (“areal units”) per observation
Could be different for exposure/covariates/outcome
Also: background information
What is the mechanism of action?
Also: hypothesis/research questions
What are you trying to show?

4. Today: Spatial Dependence
A dataset where observations are polygons
Census data
SEER (cancer) data
Patients coded to areas
Variety of designs
Cross-sectional
Cohort
Time series

5. Example: Income & Cancer in NC
Research question: do NC counties with lower mean income have higher rates of lung cancer? Poverty → Lung Cancer

6. Potential Spatial Mechanisms:
Effects of the “space” itself
Core/periphery areas (agriculture → poverty)
Supply of tobacco (agriculture → smoking)
Often: “unmeasured [spatial] confounders”
Effect of neighbors
“Contagiousness” of smoking/income behavior
Social norms (you smoking → me smoking)
Inheritance of poverty (parent poverty → child poverty)

7. To Modeling Approaches
Spatial Error Model
“residuals” of nearby observations not independent
I.e. effects of unmeasured spatial factors
Spatial Lag Model
Observations affected by nearby observations
Value of independent variable
Value of dependent variable
i.e. effects of “echoes” of measured spatial factors

8. Spatial Models Mathematically
Generalized Linear Model (non-spatial)
Y = Xβ + ε
Y Outcome vector X Covariate vector (including exposure) β Effect vector (slopes) ε Residual (“error”) vector

9. Spatial Models Mathematically
Spatial Error Model
Y = Xβ + u u = λWu + ε
Spatial Lag Model
Y = Xβ + ρWY + ε

10. What is W? Spatial Weights Matrix Many different coding schemes
Who are my neighbors?
How “close” am I to each one? (measure of impact)
Many different coding schemes
Binary: all neighbors affect me equally
Row-standardized: all neighbors add up to 1

11. Example W

12. How to get W Option 1: Define it (educated guess)
E.g. social network analysis
Option 2: Figure out something empirically
Find all my neighbors in space
Choose a coding scheme (still educated guess!)

13. To the lab! Import spatial data Build a neighbors object
Build some weights matrices
Try spatial lag and spatial error models