taking ‘geography’ seriously: disaggregating the study of civil wars
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Taking ‘Geography’ Seriously: Disaggregating the Study of Civil Wars. John O’Loughlin and Frank Witmer Institute of Behavioral Science University of Colorado at Boulder Boulder, CO 80309-0487 [email protected] [email protected]. - PowerPoint PPT PresentationTRANSCRIPT
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 [email protected]@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
.001
.01
.1
.001
.01
.1.001
.01
.1
Uniform popn.
800 kms radius
Popn. Density
500 kms radius
001001
.001
.01
.1
.001
.01
.1
Popn. Density
500 kms radius
Popn. Density
800 kms radius
.001
.01
.1