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Geospatial Statistics

Explore spatial data in geospatial statistics including points, polygons, and spatial mechanisms. Learn spatial dependence and modeling approaches with examples like income and cancer rates in NC. Dive into spatial error and lag models mathematically and create spatial weights matrices. Hands-on lab exercises included!

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Geospatial Statistics

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  1. LearnR! Fall 2014 Nathaniel MacNell Geospatial Statistics

  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 vectorX Covariate vector (including exposure)β Effect vector (slopes)ε Residual (“error”) vector

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

  10. What is W? • Spatial Weights Matrix • 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

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