Sebaran Spasial Dua TipeTitik

Praktikum Statistika Spasial | Pertemuan 3

rrahmaanisa@apps.ipb.ac.id

MultiType Point Patterns

• A marked point pattern in which the marks are a categorical variable is usually called a multitype point pattern. The ‘types’ are the different values or levels of the mark variable

Inst

alle

d D

ata

Set

Ants Data Set

Species Semut yg Diamati

Messor wasmanni Cataglyphis bicolor

Load Ants Data Set

Metode Kuadran

• CAB=Banyaknya sel yang berisi kedua himpunan PA dan PB=14

• CA0=Banyaknya sel yang hanya berisi himpunan PA =0

• C0B=Banyaknya sel yang hanya berisi himpunan PB =4

• C00=Banyaknya sel kosong =6

• CA= CAB + CA0 =14

• CB= CAB + C0B =18

• C = CAB + CA0+ C0B + C00 =24

CAB=14 C0B=4 CB=18

CA0=0 C00=6 C-CB=6

CA=14 C-CA=10 C=24

CAB=14 C0B=4 CB=18

CA0=0 C00=6 C-CB=6

CA=14 C-CA=10 C=24

𝑌𝐴𝐵 =14(18)

24= 10.5 𝑌0𝐵 =

10(18)

24= 7.5

𝑌𝐴0 =14(6)

24= 3.5 𝑌00 =

10(6)

24= 2.5

𝜒ℎ𝑖𝑡𝑢𝑛𝑔2 =

14 − 10.5 2

10.5+

4 − 7.5 2

7.5+

0 − 3.5 2

3.5+

6 − 2.5 2

2.5= 11.2

𝜒𝑡𝑎𝑏𝑒𝑙2 = 𝜒0.05(1)

2 = 3.84

Hipotesis:

H0: Titik-titik pada Himpunan PA dan PB

adalah menyebar secara independen

H1: Titik-titik pada Himpunan PA dan PB

adalah menyebar secara tidak independen(Mereka berkorelasi secara spasial antarasesamanya)

𝜒ℎ𝑖𝑡𝑢𝑛𝑔2 > 𝜒𝑡𝑎𝑏𝑒𝑙

2 cukup bukti untuk menolak H0. Artinya, dapat disimpulkan bahwa pada 𝛼 = 5%, sebaran spasial

dari kedua species semut tersebut tidak saling bebas.

Metode Tetangga Terdekat

The estimator Kest ignores marks. Its counterparts for multitype point patterns are Kcross, Kdot, and for general marked point patterns see Kmulti.

Ripley’s K estimator for Mulitype Point

Function Description

Kdot For a multitype point pattern, estimate the multitype K function which counts the expected number of other points of the process within a given distance of a point of type i.

Kcross For a multitype point pattern, estimate the multitype K function which counts the expected number of points of type j within a given distance of a point of type i.

Kmulti For a marked point pattern, estimate the multitype K function which counts the expected number of points of subset J within a given distance from a typical point in subset I.

Metode Tetangga Terdekat

# diagnostic plot for independence

between Messor and other species

plot(envelope(ants, Kcross,

i="Messor",

j="Cataglyphis", nsim=99,

fix.n=T, fix.marks=T))

• If the process of type i points were independentof the process of type j points, then Kij(r) wouldequal pi * r^2.

• Deviations between the empirical Kij curve andthe theoretical curve pi * r^2 may suggestdependence between the points of types i and j.

mad.test(ants, Kcross, i="Messor", j="Cataglyphis", nsim=99,

fix.n=T, fix.marks=T)

Lansing 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

plot(split(lansing))

Metode Kuadranplot(quadratcount(split(lansing)))

Metode Kuadran

Metode Tetangga Terdekat

Referensi

1. Baddeley, A. (2008). Analysing spatial point patterns in R.

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