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### Transcript of Sebaran Spasial Dua Tipe Titik - stat.ipb.ac.id Spatial Statistics/P3... · PDF...

Sebaran Spasial Dua TipeTitik

Praktikum Statistika Spasial | Pertemuan 3

[email protected]

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

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

=14(18)

24= 10.5 0 =

10(18)

24= 7.5

0 =14(6)

24= 3.5 00 =

10(6)

24= 2.5

2 =

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

2 = 0.05(1)

2 = 3.84

Hipotesis:

H1: Titik-titik pada Himpunan PA dan PBadalah menyebar secara tidak independen(Mereka berkorelasi secara spasial antarasesamanya)

2 >

2 cukup bukti untuk menolak H0. Artinya, dapat disimpulkan bahwa pada = 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.

http://127.0.0.1:16418/library/spatstat/help/Kcrosshttp://127.0.0.1:16418/library/spatstat/help/Kdothttp://127.0.0.1:16418/library/spatstat/help/Kmulti

Ripleys 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.

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).

plot(split(lansing))