Praktikum 3 - Spasial
Nofrida Elly
2/26/2021
setwd ("D:/PASCASARJANA/Semester 3/3. SPASIAL/02. Praktikum/03")library(spatstat)## Warning: package 'spatstat' was built under R version 3.6.3## Loading required package: spatstat.data## Warning: package 'spatstat.data' was built under R version 3.6.3## Loading required package: nlme## Loading required package: rpart## Warning: package 'rpart' was built under R version 3.6.3##
## spatstat 1.64-1 (nickname: 'Help you I can, yes!')
## For an introduction to spatstat, type 'beginner'##
## Note: R version 3.6.1 (2019-07-05) is more than a year old; we strongly recommend upgrading to the latest versionSebaran Spasial Dua Tipe Titik
Loads Ants Data Set
data(ants)
ants## Marked planar point pattern: 97 points
## Multitype, with levels = Cataglyphis, Messor
## window: polygonal boundary
## enclosing rectangle: [-25, 803] x [-49, 717] units (one unit = 0.5 feet)Pada data ini dapat terlihat bahwa data ini berupa “planar point pattern” dengan 2 levels yaitu Cattaglyphis dan Messor.
plot antara Cataglysis dan Messor
plot(ants)
plot terpisah (plot Cataglyphis dan plot Messor)
plot(split(ants))
Metode Kuadran
Ingin membagi Cataglyphis dan Messor dalam kuadran dimana tidak ditentukan jumlah kuadrannya (berdasar default saja)
kuadran <- quadratcount(split(ants))
plot(kuadran)
Hipotesisnya adalah :
H0 : Titik-titik pada Himpunan PA dan PB adalah menyebar secara independen vs
H1 : Titik-titik pada Himpunan PA dan PB adalah menyebar secara tidak independen (Mereke berkorelasi secara spasial antara sesamanya)
Jika Khi-Kuadrat hitung > Khi-Kuadrat Tabel maka keputusan Tolak Ho. Artinya telah cukup bukti untuk mengatakan bahwa pada alpha 5%, sebaran spasial dari kedua spesies semut (Cattaglysis dan Messor) tidak saling bebas (mereka berkorelasi secara spasial antara sesamanya)
catag <- kuadran[[1]]
mess <- kuadran[[2]]
obs <- matrix(NA, 2, 2)
rownames(obs) <- c("A", "O")
colnames(obs) <- c("B", "0")
obs[1,1] <- sum(((catag > 0) + (mess > 0)) == 2) #ab
obs[2,1] <- sum(((catag > 0) - (mess > 0)) == 1) #a0
obs[1,2] <- sum(((catag > 0) - (mess > 0)) == -1) #0b
obs[2,2] <- sum(((catag > 0) + (mess > 0)) == 0) #00
tes <- chisq.test(obs) ## Warning in chisq.test(obs): Chi-squared approximation may be incorrectchi_hitung <- sum((obs-tes$expected)^2/tes$expected)
chi_tabel <- qchisq(0.05, df=1, lower.tail = F)
p_valuechi <- pchisq(chi_hitung,1,lower.tail=F)
chisq.test(obs, correct = F)## Warning in chisq.test(obs, correct = F): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: obs
## X-squared = 11.2, df = 1, p-value = 0.000818Metode K-function pada data “ants”
Kest{spatstat}
unique(ants$marks)## [1] Messor Cataglyphis
## Levels: Cataglyphis MessorKh <- Kdot(ants, "Messor")
plot(Kh)
Plot diatas menggambarkan independensi antara Messor dan spesies lainnya.
f1 <- function (X) {marks(X) == "Messor"}
f2 <- function (X) {marks(X) == "Cataglyphis"}
K <- Kmulti(ants, f1, f2)
plot(K)
Dengan Kcross, melihat antara Messor dan Cataglyphis saja
K01 <- Kcross(ants, "Messor", "Cataglyphis")
plot(K01)
Plot ants dengan menggunakan Kcross
plot(envelope(ants, Kcross,i="Messor",j="Cataglyphis",nsim=99,fix.n=T,fix.marks=T))## Generating 99 simulations of CSR with fixed number of points of each type ...
## 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.
Plot ants dengan menggunakan Kmulti
plot(envelope(ants, Kmulti,
I=f1, J=f2, nsim=99,
fix.n=T, fix.marks=T))## Generating 99 simulations of CSR with fixed number of points of each type ...
## 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.
Mad Test
mad.test(ants, Kcross, i="Messor", j="Cataglyphis", nsim=99, fix.n=T, fix.marks=T)## Generating 99 simulations of CSR with fixed number of points of each type ...
## 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.##
## Maximum absolute deviation test of CSR
## Monte Carlo test based on 99 simulations with fixed number of points
## of each type
## Summary function: Kcross["Messor", "Cataglyphis"](r)
## Reference function: theoretical
## Alternative: two.sided
## Interval of distance values: [0, 191.5] units (one unit = 0.5 feet)
## Test statistic: Maximum absolute deviation
## Deviation = observed minus theoretical
##
## data: ants
## mad = 5161, rank = 71, p-value = 0.71Lansing Wood Data
Here is the famous Lansing Woods dataset recording the positions of 2251 trees of 6 different species (hickories, maples, red oaks, white oaks, black oaks and miscellaneous trees).
Load the data
data(lansing)
lansing## Marked planar point pattern: 2251 points
## Multitype, with levels = blackoak, hickory, maple, misc, redoak, whiteoak
## window: rectangle = [0, 1] x [0, 1] units (one unit = 924 feet)summary(lansing)## Marked planar point pattern: 2251 points
## Average intensity 2251 points per square unit (one unit = 924 feet)
##
## *Pattern contains duplicated points*
##
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units (one unit = 924 feet)
##
## Multitype:
## frequency proportion intensity
## blackoak 135 0.05997335 135
## hickory 703 0.31230560 703
## maple 514 0.22834300 514
## misc 105 0.04664594 105
## redoak 346 0.15370950 346
## whiteoak 448 0.19902270 448
##
## Window: rectangle = [0, 1] x [0, 1] units
## Window area = 1 square unit
## Unit of length: 924 feetplot(lansing)
Ingin memisahkan plot masing-masing
plot(split(lansing))
plot(density(split(lansing)), ribbon = F)
hick <- split(lansing)$hickory
plot(hick)
Metode Kuadran
plot(quadratcount(split(lansing)))
Metode K-function
Kh_lansing <- Kdot(lansing, "hickory")
plot(Kh_lansing)