CSRの帰無仮設を棄却する検定手順（１）背景と分析地区
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背景
点過程データを分析する際、その最初のステップとして、CSR（Complete Spatial Randomness）という帰無仮設を置き、最近隣距離法若しくは法格法を用いて、その仮設を棄却する確率を算出する。*1*2ここでは、Rのspatstatというパッケージ*3を用いて、佐賀県と福岡県の意匠登録者の空間点過程データをBivand, Pebesma, Gómez-Rubio (2008)が説明するDiggle(2003) の例に従って、分析する。
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分析地区
spパッケージのSpatialPointsオブジェクトに対して、spatstatがpppオブジェクトを利用するため、spatstatの機能を利用するようにspSagaFukuokaの地区を抽出した後、pppオブジェクトに変換しなければならない。
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佐賀県と福岡県の全地区(pppSagaFukuoka)
> ## Bivand, Pebesma, Gómez-Rubio (2008)pp156-158 > library(maptools) > summary(spSagaFukuoka) Object of class SpatialPoints Coordinates: min max x 129.81595 131.11875 y 33.00453 33.95653 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] Number of points: 1193 > library(spatstat) > ## convert to unit square > spSagaFukuokaSQ <- elide(spSagaFukuoka, scale=TRUE, unitsq = TRUE) > summary(spSagaFukuokaSQ) Object of class SpatialPoints Coordinates: min max [1,] 0 1 [2,] 0 1 Is projected: NA proj4string : [NA] Number of points: 1193 > pppSagaFukuoka <- as( spSagaFukuokaSQ, "ppp") > summary(pppSagaFukuoka) Planar point pattern: 1193 points Average intensity 1193 points per square unit *Pattern contains duplicated points* Coordinates are given to 8 decimal places Window: rectangle = [0, 1] x [0, 1] units Window area = 1 square unit -
福岡市―筑紫野市(pppFukuokaChikushino)
> ## done in earlier session > llCRS <- CRS("+proj=longlat +ellps=WGS84") > ## coordinates > Sr1 = Polygon(cbind( + c(130.191354,130.626400,130.626400,130.191354, 130.191354), + c(33.718652,33.718652,33.423697,33.423697,33.718652) + )) > Srs1 = Polygons(list(Sr1), "bbFukuokaChikushino") > spbbFukuokaChikushino = SpatialPolygons(list(Srs1), 1:1, proj4string = llCRS) > summary(spbbFukuokaChikushino) Object of class SpatialPolygons Coordinates: min max x 130.1914 130.62640 y 33.4237 33.71865 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] > spFukuokaChikushino <- spSagaFukuoka[spbbFukuokaChikushino,] > summary(spFukuokaChikushino) Object of class SpatialPoints Coordinates: min max x 130.19690 130.58931 y 33.42709 33.71665 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] Number of points: 566 >
> ## convert to unit square > plot(spFukuokaChikushino, pch=1) > spFCSQ <- elide(spFukuokaChikushino, scale=TRUE, unitsq = TRUE) > summary(spFCSQ) Object of class SpatialPoints Coordinates: min max [1,] 0 1 [2,] 0 1 Is projected: NA proj4string : [NA] Number of points: 566 > pppFukuokaChikushino <- as(spFCSQ, "ppp") > summary( pppFukuokaChikushino) Planar point pattern: 566 points Average intensity 566 points per square unit *Pattern contains duplicated points* Coordinates are given to 8 decimal places Window: rectangle = [0, 1] x [0, 1] units Window area = 1 square unit > png(file="pppFukuokaChikushino.png", width=600, height=480) > plot( pppFukuokaChikushino, pch=1) > dev.off()
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> ########## ChuoHakata > Sr2 = Polygon(cbind( + c(130.354992,130.486107,130.486107,130.354992, 130.354992), + c(33.613987,33.613987,33.535556,33.535556,33.613987) + )) > Srs2 = Polygons(list(Sr2), "bbChuoHakata") > spbbChuoHakata = SpatialPolygons(list(Srs2), 1:1, proj4string = llCRS) > summary(spbbChuoHakata) Object of class SpatialPolygons Coordinates: min max x 130.35499 130.48611 y 33.53556 33.61399 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] > spChuoHakata <- spSagaFukuoka[spbbChuoHakata,] > summary(spChuoHakata) Object of class SpatialPoints Coordinates: min max x 130.35518 130.48578 y 33.53611 33.61334 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] Number of points: 325 >
> ## convert to unit square > spCHSQ <- elide(spChuoHakata, scale=TRUE, unitsq = TRUE) > summary(spCHSQ) Object of class SpatialPoints Coordinates: min max [1,] 0 1 [2,] 0 1 Is projected: NA proj4string : [NA] Number of points: 325 > pppChuoHakata <- as(spCHSQ, "ppp") > summary(pppChuoHakata) Planar point pattern: 325 points Average intensity 325 points per square unit *Pattern contains duplicated points* Coordinates are given to 8 decimal places Window: rectangle = [0, 1] x [0, 1] units Window area = 1 square unit -
春日市(pppKasuga)
> ## Earlier Saga-Fukuoka, Fukuoka-Chikushino Cities, Chuo-Hakata Wards > ## subsets show high degrees of aggregation. But this is to be expected > ## from terrain and population. This subset is from an area of Kasuga City > ## Chikushino cities that has had a lot of planned development with > ## that are newer developments with large areas of single family dwellings. > ## 33.556279, 130.481984 > ## 33.516162, 130.409705 > latNE = 33.556279 > longNE = 130.481984 > latSW = 33.516162 > longSW = 130.409705 > Sr1 = Polygon(cbind( + c(longNE ,longNE ,longSW ,longSW , longNE ), + c(latNE,latSW ,latSW ,latNE,latNE) + )) > Srs1 = Polygons(list(Sr1), "bbKasuga") > spbbKasuga = SpatialPolygons(list(Srs1), 1:1, proj4string = llCRS) > summary(spbbKasuga) Object of class SpatialPolygons Coordinates: min max x 130.40971 130.48198 y 33.51616 33.55628 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] > spKasuga <- spSagaFukuoka[spbbKasuga,] > summary(spKasuga) Object of class SpatialPoints Coordinates: min max x 130.40993 130.4798 y 33.51632 33.5561 Is projected: FALSE proj4string : [+proj=longlat +ellps=WGS84] Number of points: 48 >
> ## convert to unit square > spKasugaSQ <- elide(spKasuga, scale=TRUE, unitsq = TRUE) > summary(spKasugaSQ) Object of class SpatialPoints Coordinates: min max [1,] 0 1 [2,] 0 1 Is projected: NA proj4string : [NA] Number of points: 48 > > pppKasuga <- as(spKasugaSQ, "ppp") > summary(pppKasuga) Planar point pattern: 48 points Average intensity 48 points per square unit *Pattern contains duplicated points* Coordinates are given to 8 decimal places Window: rectangle = [0, 1] x [0, 1] units Window area = 1 square unit
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