Spatial Scan Kulldorf 1

Spatial Scan Kulldorf 1 - Further Methods for Point Pattern...

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1 Lecture 11 October 7, 2003 Further Methods for Point Pattern Analysis Bailey and Gatrell Chapter 4 n Certain types of events will exhibit clustering due to heterogeneity in the underlying distribution Variations in Population e.g disease cases or crimes will tend to cluster where the population is higher n In such cases we need to “correct” for the the underlying variations in the population Use of Kernel Estimates ( 29  - = = t t l t i n i s s k s 1 2 1 ˆ § Kernel estimate estimates events per unit area § Reconsider as estimate of events per unit population § Divide estimated intensity at location s by an estimate of population density at s § How to estimate population density at s?
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2 Estimations of Population Density § Can take population count for a census unit and convert to density by dividing by the census unit area § For the population density at s, use the population density for the census unit in which s falls s ( 29 ) ( 1 ˆ 1 2 s pd s s k s j i n i  - = = t t r t j j j A p pd = Population for unit j Area for unit j Estimations of Population Density m j j y , , 1 L = Population values ( 29 j j m j y s s k s - = = t t l t 1 2 1 ˆ Estimate of population per unit area m j j s , , 1 L = Locations where populations are recorded + + + + + + + + + + 1 s 2 s 4 s 3 s 8 s 5 s 6 s 7 s 10 s 9 s Estimations of Events per Unit Population ( 29 j j m j i n i y s s k s s k s - - = = = t t t t r t 1 2 1 2 1 1 ˆ Divide estimate of events per unit area by population per unit area § Generally use same kernel and bandwidth for each estimate, but not necessary § Good estimates of either alone may not lead to good estimates of the ratio § Small changes in the estimates of population density in regions where value is low lead to large variations in ratio
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Spatial Scan Kulldorf 1 - Further Methods for Point Pattern...

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