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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