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

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 statistic Non-mappable Mappable GIS-unfriendly GIS –friendly Aspatial or spatially limited Spatial Emphasize similarities across space Emphasize differences across space Search for regularities or ‘laws’ Search for exceptions or “local hot spots’ Example – classic regression Example – GWR geog. weighted regression Source: 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

y = b 0 +  k b k x ij + e i (u i, v i ) = (X T W (u i, v i ) X) -1 X -T W (u i, v i )y where the bold type denotes a matrix, represents an estimate of β, and W (u i, v i ) 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 (u i, v i ) denote the coordinates of the ith point in space and k (u i, v i ) is a realization of the continuous function surface β k (u i, v i ) at point i. GWR modeling

GWR kernel From Fotheringham, Brundson and Charlton Geographically Weighted Regression GWR with fixed kernelGWR with adaptive kernel Points are weighted based on distance from center of kernel e.g. Gaussian kernel where weighting is given by: w i (g) = exp[-1/2(d ij /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 Estimates (Coefficient And median for GWR) Ghobarah et al. (2003) Estimates Replication – Global Regression GWR – Capitals Coord Adaptive GWR – Capitals Fixed - 500kms GWR – Capitals Fixed kernel – 800kms GWR – Geog.centro ids Adaptive GWR –.centroids Fixed 500kms GWR – centroids Fixed 800 kms Intercept6.65 (0.50) 7.84 (0.60) (0) 9.65 (18) (5) (17) (10) (10) Civil War Deaths (1.71) 0.21 (1.75) 0.12** (0) 0.66 (10) 0.07 (15) 0.15 (2) -0.11** (9) 0.09 (12) Contiguous Civil Wars 7.84 (2.74) 7.75 (2.72) 0.45 (12) -.09 (10) (4) 1.32 (14) (9) (6) Health Spending (-1.35) (-1.27) (6) (7) (5) (2) (2) (10) Education-3.74 (-0.99) (-1.11) 2.45 (0) 2.81 (9) 3.01 (12) (17) (4) 1.35 (23) Urban Growth 5.93 (4.26) 5.85 (4.22) 0.67 (0) 1.31 (2) 1.69 (1) 1.31 (17) (15) 1.29 (13) Income Gini (2.88) (2.83) (0) (9) (3) (0) (5) (0) Tropical Country 4.61 (1.29) 4.49 (1.29) 2.17** (0) 3.06 (3) 7.22 (0) (0) 5.48 (2) 5.98 (0) Polity Score 0.22 (0.98) 0.22 (0.99) 0.64 (6) (9) 0.02 (7) 0.24 (27) 0.06 (22) 0.06 (9) Ethnic Heterogenei ty 0.62 (0.50) 0.41 (0.34) 0.49 (0) 0.70 (6) 0.24 (17) 0.55 (2) 0.24 (6) (6) Adjusted R F-rationa 8.86 # # 7.85 # # AICna

Table 2: Geographically-Weighted Regression estimates for DALYs lost in different Disease Categories – Females and Males aged Estimates (Coefficient and median – GWR) Females Aged All Diseases Females Aged AIDS Males Aged AIDS Ghobarah et al. (2003) Estimates Global Estimates GWR Capitals Adaptive Global Estimates GWR Capitals Adaptive Global Estimates GWR Capitals Adaptive Intercept5.99 (0.34) 8.72 (0.50) (7) (-1.07) 0.49 (2) (-1.00) 1.17 (8) Civil War Deaths (1.78) 0.30 (1.78) 0.15 (13) 0.06 (0.65).001 (13) 0.07 (0.64) (24) Contiguous Civil Wars (3.27) (3.24) 1.90** (8) 3.59 (3.37) 1.87** (6) 9.30 (3.52) (7) Health Spending (0.74) (-0.65) (0) 1.58 (1.41) 0.09 (3) 2.21 (1.54) 0.03 (19) Education-7.41 (-1.46) (-1.64) (28) (-1.54) -.51 (25) (-1.77) (24) Urban Growth 8.54 (4.57) 8.38 (4.51) 0.57 (7) 3.59 (3.63) -.02 (14) 4.16 (3.25) (19) Income Gini (2.06) (1.98) (6) (1.01) 0.84 (4) (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) Polity Score 0.05 (0.18) 0.05 (0.20) 0.03 (3) (-0.27).001 (3) (-0.41).000 (6) Ethnic Heterogeneit y 0.59 (0.35) 0.18 (.11) 0.70 (22) (-0.18) (31) (-0.24) -.01 (19) Adjusted R F-ratio - GWR na 7.87 # na6.42 # na8.07 AICna

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 ” for Males 15-44, DALYs lost due to All Causes

Distribution of R 2 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

Uniform popn. 800 kms radius

Popn. Density 500 kms radius

Popn. Density 500 kms radius

Popn. Density 800 kms radius