CSRの帰無仮設を棄却する検定手順（３）F関数とF統計量（データクリーニング後）

f:id:ttcrossroads09:20181203101443p:plain

CSR検定手法として、Diggle(2003),p28が二つの手法、すなわち、G関数の検定とF関数の検定を勧める。G検定の結果はすでにブログに載せました。ここではF 検定の手順と結果を載せます。

古谷(2009)*1参照:

F関数とF統計量は任意の地点から他の最近隣地点までの距離について、F関数を使って得られる統計量です。F関数は任意の地点からの半径ｒを用いて、次式のように表されます。

Rでは、Fest()関数を用いてF統計量をけいさんすることができます。ここでCSRのエンベロープシミュレーション*2 *3を用いて行います。各地図に示される地点から計算された結果、本ポストの図に示します。

CSRのモンテカルロ・シミュェーション


> library(lattice)
> library(spatstat)
> r <- seq(0, sqrt(2)/6, by = 0.001)
> FenvSagaFukuoka <- envelope(as(pppSagaFukuoka,"ppp"), fun = Fest, r=r, nrank=2, nsim=99)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
> FenvFukuokaChikushino <- envelope(as(pppFukuokaChikushino,"ppp"), fun = Fest, r=r, nrank=2, nsim=99)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
> FenvChuoHakata <- envelope(as(pppChuoHakata,"ppp"), fun = Fest, r=r, nrank=2, nsim=99)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
> FenvKasuga <- envelope(as(pppKasuga,"ppp"), fun = Fest, r=r, nrank=2, nsim=99)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
> Fresults <- rbind(FenvSagaFukuoka, FenvFukuokaChikushino, FenvChuoHakata,FenvKasuga )
> Fresults <- cbind(Fresults, DATASET = 
+ rep(c("Saga-Fukuoka Prefs", "Fukuoka-Chikushino Cities","Chuo-Hakata Wards","Kasuga"), each = length(r)))
> png(file="Fest-Saga-FukuokaC.png", width=600, height=480)
> print(xyplot(obs~theo|y , data=Fresults, type="l", 
+ xlab = "theoretical", ylab = "observed",
+ panel=function(x, y, subscripts) {
+    lpolygon(c(x, rev(x)), 
+    c(Fresults$lo[subscripts], rev(Fresults$hi[subscripts])),
+    border="gray", col="gray"
+ )
+ llines(x, y, col="black", lwd=2)
+ }))
> dev.off()