1. Spatial Analysis & Vulnerability Studies START 2004 Advanced Institute IIASA, Laxenburg, Austria Colin Polsky May 12, 2004 Graduate School of Geography

2. International Geographical Union (IGU) Task Force on Vulnerability

3. I.What is spatially integrated social science? A. Qualitative dimensions B. Quantitative dimensions i. univariate ii. multivariate II.An example: Vulnerability to the Effects of Climate Change in the US Great Plains Outline

5. Necessary and sufficient conditions to achieve objective of vulnerability studies: Flexible knowledge base Multiple, interacting stresses Prospective & historical Place-based: local in terms of global Explores ways to increase adaptive capacity Source: Polsky et al., 2003

6. What variables cluster in geographic space? How do they cluster? Why do they cluster? Can you imagine any variables that are not clustered?

8. John Snow, Cholera, & the Germ Theory of Disease

9. Source: Fotheringham, et al. (2000)

10. Criticisms of quantitative social science: discovering global laws overly reductionist place can’t matter too deductive, sure of assumptions Localized quantitative analysis: exploring local variations and global trends holistic place can matter unabashedly inductive, questions assumptions

11. Source: Griffith and Layne (1999)

12. Spatial analysis (ESDA) is as valuable for hypothesis testing as for hypothesis suggesting … especially in data-sparse environments. ESDA helps explain why similar (or dissimilar) values cluster in geographic space: Social interactions (neighborhood effects) Spatial externalities Locational invariance: situation where outcome changes when locations of ‘ objects ’ change Source: Anselin, 2004

13. I.What is spatially integrated social science? A. Qualitative dimensions B. Quantitative dimensions i. univariate ii. multivariate II.An example: Vulnerability to the Effects of Climate Change in the US Great Plains Outline

14. “Steps” for Exploratory Spatial Data Analysis (ESDA): 1.Explore global/local univariate spatial effects 2.Specify & estimate a-spatial (OLS) model 3.Evaluate OLS spatial diagnostics 4.Specify & estimate spatial model(s) 5.Compare & contrast results

15. What does spatially random mean?

16. Spatial autocorrelation: Cov[y i,y j ]  0, for neighboring i, j or “values depend on geographic location” Is this a problem to be controlled & ignored or an opportunity to be modeled & explored?

17. Spatial regression/econometrics: spatial autocorrelation reflects process through regression mis-specification The “many faces” of spatial autocorrelation: map pattern, information content, spillover effect, nuisance, missing variable surrogate, diagnostic, …

18. Univariate spatial statistics

19. Source: Munroe, 2004 Spatial Weights Matrices & Spatially Lagged Variables

20. Moran’s I statistic

21. Local Moran’s I statistic

23. Multivariate spatial statistics

24. What you know, and what you don ’ t know … y = X  +  What you know What you don ’ t know

25. OLS assumptions: Var(e i ) = 0 no residual spatial/temporal autocorrelation errors are normally distributed no measurement error linear in parameters no perfect multicollinearity E(e i ) = 0

26. Ignoring residual spatial autocorrelation in regression may lead to: Biased parameter estimates Inefficient parameter estimates Biased standard error estimates Limited insight into process spatiality

27. bias versus inefficiency Source: Kennedy (1998)

28. Alternative hypothesis: there are significant spatial effects Large-scale: spatial heterogeneity Small-scale: spatial dependence Null hypothesis: no spatial effects, i.e., y = X  +  works just fine y = X  + W  +  y =  Wy + X  +  y = X  +  i, i=0,1 y = X i  i +  i, i=0,1

29. Large-scale: spatial heterogeneity – dissimilar values clustered discrete groups or regions, widely varying size of observation units Small-scale: spatial dependence – similar values clustered “ nuisance ” = external to y~x relationship, e.g., one-time flood reduces crop yield, sampling error “ substantive ” = internal to y~x relationship, e.g., innovation diffusion, “ bandwagon ” effect

30. Which Alternative Hypothesis? observationally equivalent

31. I.What is spatially integrated social science? A. Qualitative dimensions B. Quantitative dimensions i. univariate ii. multivariate II.An example: Vulnerability to the Effects of Climate Change in the US Great Plains Outline

32. “Economic Scene: A Study Says Global Warming May Help U.S. Agriculture” 8 September 1994

33. Agricultural land value = f (climatic, edaphic, social, economic) Ricardian Climate Change Impacts Model

34. Source: Mendelsohn, et al. (1994:768) Climate Change Impacts: Agricultural Land Values

35. The US Great Plains

36. Great Plains wheat yields & seeded land abandoned: 1925-91 Source: Peterson & Cole, 1995:340

38. Source: Polsky (2004)

39. ddd dd dd Land Value, 1992 Random?

40. Local Moran’s I Statistics, 1969-92

46. spatial lag/GHET model: y =  Wy + X  +  i, i=0,1

47. Source: Polsky (2004)

49. Space, Time & Scale: Climate Change Impacts on Agriculture Source: Polsky, 2004

50. end