Taking ‘Geography’ Seriously:

Disaggregating the Study of Civil Wars.

John O’Loughlin and Frank Witmer

Institute of Behavioral ScienceUniversity of Colorado at Boulder

Boulder, CO 80309-0487johno@colorado.eduwitmer@colorado.edu

GlobalStatistics Local_Statistics___________________Summarize data for whole region (e.g. Morans I)

Local disaggregations of global statistics (e.g. G*i)Single-valued statistic Multi-valued statisticNon-mappable

MappableGIS-unfriendly

GIS –friendlyAspatial or spatially limited

SpatialEmphasize similarities across space

Emphasize differences across spaceSearch for regularities or ‘laws’

Search for exceptions or “local hot spots’Example – classic regression

Example – GWR geog. weighted regressionSource: Fotheringham et al 2002

•Separate regression is run for each observation, using a spatial kernel that centers on a given point and weights observations subject to a distance decay function.

•Can used fixed size kernel or adaptive kernel to determine number of local points that will be included in each local regression

• Adaptive kernels used when data is not evenly distributed

Geographically Weighted Regression

ik kiikii exvuvuxY ),(),()(

y = b0 + kbkxij + ei

(ui , vi ) = (XT W (ui , vi ) X)-1 X-T W (ui , vi )y

where the bold type denotes a matrix, represents an estimate of β, and W (ui , vi ) is an n x n matrix whose diagonal elements are the geographical weighting for each of the n observed data for regression point i. Uses weighted least squares approach

where (ui , vi ) denote the coordinates of the ith point in space and k (ui , vi) is a realization of the continuous function surface β k (ui , vi) at point i.

GWR modeling

GWR kernel

From Fotheringham, Brundson and Charlton. 2002. Geographically Weighted Regression

GWR with fixed kernel GWR with adaptive kernel

Points are weighted based on distance from center of kernele.g. Gaussian kernel where weighting is given by:

wi(g) = exp[-1/2(dij/b)2 where b is bandwidth

Bias and variance tradeoff•Tradeoff between bias and standard error

•The smaller the bandwidth, the more variance but the lower the bias, the larger the bandwidth, the more bias but the more variance is reduced

•This is because we assume there are many betas over space and the more it is like a global regression, the more biased it is.

•AIC minimization provides a way of choosing bandwidth that makes optimal tradeoff between bias and variance.

•We expect all parameters to have slight spatial variations; is that variation sufficient to reject the null hypothesis that it is globally fixed?

•If so, then any permutation of regression variable against locations is equally likely, allowing us to model a null distribution of the variance

•A Monte Carlo approach is adopted to create this distribution in which the geographical coordinates of the observations are randomly permuted against the variables n times; results in n values of the variance of the coefficient of interest which we use as an experimental distribution

•We can then compare the actual value of the variance against these values to obtain the experimental significance

Monte Carlo test for parameter variation

Table 1: Replication of Ghobarah et al (2003) results and Geographically-Weighted Regression extensions.

DALYs lost to All Disease Categories – Males aged 15-44.

Estimates(CoefficientAnd median for GWR)

Ghobarah et al. (2003)Estimates

Replication – Global Regression

GWR –Capitals CoordAdaptive

GWR –CapitalsFixed -500kms

GWR – CapitalsFixed kernel – 800kms

GWR –Geog.centroidsAdaptive

GWR –.centroidsFixed 500kms

GWR –centroidsFixed 800 kms

Intercept 6.65(0.50)

7.84(0.60)

10.31(0)

9.65(18)

10.75(5)

27.25(17)

27.51(10)

33.51(10)

Civil War Deaths 91-97

2.15(1.71)

0.21(1.75)

0.12**(0)

0.66(10)

0.07(15)

0.15(2)

-0.11**(9)

0.09(12)

ContiguousCivil Wars

7.84(2.74)

7.75(2.72)

0.45(12)

-.09(10)

-0.13(4)

1.32(14)

-0.78(9)

-0.01(6)

Health Spending

-2.12(-1.35)

-1.98(-1.27)

-3.19(6)

-2.31(7)

-3.29(5)

-3.11(2)

-2.32(2)

-3.06(10)

Education -3.74(-0.99)

-4.157(-1.11)

2.45(0)

2.81(9)

3.01(12)

-0.18(17)

-1.17(4)

1.35(23)

UrbanGrowth

5.93(4.26)

5.85(4.22)

0.67(0)

1.31(2)

1.69(1)

1.31(17)

-0.30(15)

1.29(13)

IncomeGini

52.24(2.88)

51.61(2.83)

35.42(0)

36.08(9)

22.37(3)

48.89(0)

27.22(5)

24.63(0)

Tropical Country

4.61(1.29)

4.49(1.29)

2.17**(0)

3.06(3)

7.22(0)

10.40(0)

5.48(2)

5.98(0)

PolityScore

0.22(0.98)

0.22(0.99)

0.64(6)

0.002(9)

0.02(7)

0.24(27)

0.06(22)

0.06(9)

EthnicHeterogeneity

0.62(0.50)

0.41(0.34)

0.49(0)

0.70(6)

0.24(17)

0.55(2)

0.24(6)

-3.06(6)

Adjusted R2 .46 .45 .82 .26 .91 .77 .43 .88

F-ratio na na 8.86# 0.69 9.77# 7.85# 0.96 6.72#

AIC na 1537 1420 2871 1601 1439 2442 1737

Table 2: Geographically-Weighted Regression estimates for DALYs lost in different Disease Categories – Females and Males aged 15-44.

Estimates(Coefficientand median –GWR)

FemalesAged 15-44All Diseases

FemalesAged 15-44

AIDS

MalesAged 15-44

AIDS

Ghobarah et al. (2003)Estimates

Global Estimates

GWRCapitalsAdaptive

GlobalEstimates

GWRCapitalsAdaptive

GlobalEstimates

GWRCapitals Adaptive

Intercept 5.99(0.34)

8.72(0.50)

13.75(7)

-9.92(-1.07)

0.49(2)

-11.96(-1.00)

1.17(8)

Civil War Deaths 91-97

2.99(1.78)

0.30(1.78)

0.15(13)

0.06(0.65)

.001(13)

0.07(0.64)

-0.30(24)

ContiguousCivil Wars

12.52(3.27)

12.42(3.24)

1.90**(8)

3.59(3.37)

1.87**(6)

9.30(3.52)

-0.004(7)

Health Spending

-1.56(0.74)

-1.36(-0.65)

-3.08(0)

1.58(1.41)

0.09(3)

2.21(1.54)

0.03(19)

Education -7.41(-1.46)

-8.18(-1.64)

-0.97(28)

-4.10(-1.54)

-.51(25)

-6.07(-1.77)

-0.13(24)

UrbanGrowth

8.54(4.57)

8.38(4.51)

0.57(7)

3.59(3.63)

-.02(14)

4.16(3.25)

-0.02(19)

IncomeGini

50.10(2.06)

48.47(1.98)

26.89(6)

13.26(1.01)

0.84(4)

16.40(0.97)

.10(7)

Tropical Country

4.34(0.90)

4.17(0.86)

2.26**(1)

3.63(1.41)

0.28**(8)

4.40(1.32)

.000(7)

PolityScore

0.05(0.18)

0.05(0.20)

0.03(3)

-0.04(-0.27)

.001(3)

-0.08(-0.41)

.000(6)

EthnicHeterogeneity

0.59(0.35)

0.18(.11)

0.70(22)

-0.16(-0.18)

-0.13(31)

-0.27(-0.24)

-.01(19)

Adjusted R2

.44 .44 .83 .25 .72 .24 .77

F-ratio - GWR

na na 7.87# na 6.42# na 8.07

AIC na 1643 1549 1417 1347 1509 1411

Distribution of parameter estimates for predictor “Civil war in contiguous state” for Males 15-44, DALYs lost due to All Causes

Distribution of parameter estimates for predictor “Civil war deaths 1991-97” for Males 15-44, DALYs lost due to All Causes

Distribution of R2 estimates for for Males 15-44,

DALYs lost due to All Causes (coordinates of capitals)

Distribution of parameter estimates for predictor “Location in tropical region” for Males 15-44, DALYs lost due to All Causes

Distribution of R2 estimate for Model for Males 15-44,

DALYs lost due to All Causes (geographic centroids)

Distribution of residual estimates for model of contiguous state” for Males 15-44, DALYs lost due to All Causes (coordinates of Capitals)

Distribution of parameter estimates for predictor “Civil war in contiguous state” for Females 15-44, DALYs lost due to AIDS

Uniform popn.

500 kms radius

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Uniform popn.

800 kms radius

Popn. Density

500 kms radius

001001

.001

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Popn. Density

500 kms radius

Popn. Density

800 kms radius

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