spatial analysis & vulnerability studies start 2004 advanced institute iiasa, laxenburg, austria...
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Spatial Analysis & Vulnerability Studies
START 2004 Advanced InstituteIIASA, Laxenburg, Austria
Colin PolskyMay 12, 2004
Graduate School of Geography
International Geographical Union (IGU) Task Force on Vulnerability
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
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
What variables cluster in geographic space?
How do they cluster?
Why do they cluster?
Can you imagine any variables that are not clustered?
Southwark and Lambeth
Vauxhall
Cholera Deaths
1263 98
Households 40046 26107
John Snow, Cholera, & the Germ Theory of Disease
Source: Fotheringham, et al. (2000)
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
Source: Griffith and Layne (1999)
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
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
“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
What does spatially random mean?
Spatial autocorrelation:
Cov[yi,yj] 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?
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, …
Univariate spatial statistics
Source: Munroe, 2004
Spatial Weights Matrices &Spatially Lagged Variables
Moran’s I statistic
Local Moran’s I statistic
Multivariate spatial statistics
What you know, and what you don’t know…
y = X +
What you know
What you don’t know
OLS assumptions:
• Var(ei) = 0
• no residual spatial/temporal autocorrelation
• errors are normally distributed• no measurement error• linear in parameters• no perfect multicollinearity
• E(ei) = 0
Ignoring residual spatial autocorrelation in regression may lead to:
• Biased parameter estimates
• Inefficient parameter estimates
• Biased standard error estimates
• Limited insight into process spatiality
bias versus inefficiency
Source: Kennedy (1998)
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 = Xii + i , i=0,1
Large-scale:• spatial heterogeneity – dissimilar values clustereddiscrete 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
substantived iffus io n
biased p.e.'sincons is ten t p.e.'s
nuisanceig n o red fac to rsinef f ic ien t p.e.'sbiased s .e.e.'s
dependence
groupw ise he te r 'yreg io n a l varian ces
inef f ic ien t p.e.'s
spatia l regim esreg io n a l e ffec tsinef f ic ien t p.e.'s
heterogene ity
la te ra l
nes ted assoc ia tionssca la r varia tio n s
inef f ic ien t p.e.'sbiased s .e.e.'s
hierarchica l
SPA T IA L E F F EC T S
Which Alternative Hypothesis?
observationally equivalent
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
“Economic Scene:A Study Says Global Warming May Help U.S. Agriculture”
8 September 1994
Agricultural land value = f (climatic, edaphic, social, economic)
Ricardian Climate Change Impacts Model
Source: Mendelsohn, et al. (1994:768)
Climate Change Impacts: Agricultural Land Values
The US Great Plains
Great Plains wheat yields & seeded land abandoned: 1925-91
Source: Peterson & Cole, 1995:340
Source: Polsky (2004)
1992 AG LAND VALUE78 - 195197 - 290291 - 369370 - 503504 - 2417
States.shpddd
dddd
Land Value, 1992
Random?
Local Moran’s I Statistics, 1969-92
spatial lag/GHET model:
y = Wy + X + i , i=0,1
Source: Polsky (2004)
% chg $/acre, 1982-36 - -3-3 - 11 - 55 - 88 - 19
% chg $/acre, 1974-38 - -5-5 - 33 - 88 - 1414 - 47
Space, Time & Scale: Climate Change Impacts on Agriculture
Source: Polsky, 2004
% chg $/acre, 1974-38 - -5-5 - 33 - 88 - 1414 - 47
% chg $/acre, 1982-36 - -3-3 - 11 - 55 - 88 - 19
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