Tugas 2. Analisa Pola Titik Spasial
Felasofa Rahmatanti - M0501241033
2025-09-13
Analisa Pola Titik Spasial
Pola titik dalam ruang spasial dibagi menjadi 3 jenis yaitu:
- Acak : setiap titik mempunyai peluang yang sama untuk menduduki suatu ruang dan tidak dipengaruhi oleh titik yang lain
- Uniform : setiap titik adalah sejauh mungkin dari titik-titik tetangganya.
- Cluster : Banyak titik terkonsentrasi menduduki pada ruang yang sama, dan ruang yang lain sangat sedikit ditempati oleh titik.
Dalam menentukan pola titik digunakan dua pendekatan, yaitu :
- Metode Kuadran
- Empirical K-Function
Adapun tahapan analisa pola titik dalam ruang spasial sebagai berikut :
Package
Berikut package yang digunakan:
library(sf) #Mengelola data spasial dengan standar Simple Features (sf)## Linking to GEOS 3.13.1, GDAL 3.11.0, PROJ 9.6.0; sf_use_s2() is TRUElibrary(dplyr)#Manipulasi data seperti filter, select, mutate, dan summarise##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2) # Membuat grafik statistik dengan pendekatan Grammar of Graphics
library(spatstat.geom) # ppp, owin, quadratcount, as.ppp## Loading required package: spatstat.data## Loading required package: spatstat.univar## spatstat.univar 3.1-4## spatstat.geom 3.5-0library(spatstat.explore) # Kest, Lest, quadrat.test## Loading required package: spatstat.random## spatstat.random 3.4-1## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## spatstat.explore 3.5-2library(rosm)
library(ggspatial)1. Import Data
Data yang digunakan adalah data inaturalist yang dapat diakses
langsung menggunakan package rinat.
library(rinat) #Mengambil data naturalispc <- get_inat_obs(taxon_name = "Protea cynaroides",
bounds = c(-35, 18, -33.5, 18.5),
maxresults = 1000)
head(pc)## scientific_name datetime description
## 1 Protea cynaroides 2025-09-11 12:32:57 +0200
## 2 Protea cynaroides 2025-09-10 11:20:48 +0200
## 3 Protea cynaroides 2025-09-10 10:45:06 +0200
## 4 Protea cynaroides 2025-09-10 10:04:21 +0200
## 5 Protea cynaroides 2025-09-05 17:05:00 +0200
## 6 Protea cynaroides 2025-08-21 11:03:34 +0200 Botanical Gardens
## place_guess latitude longitude
## 1 Circular Drive, Cape Point, Western Cape, ZA -34.29180 18.43589
## 2 Silver Mine (Nature Reserve), Cape Town, South Africa -34.10265 18.44050
## 3 Muizenberg Mountains, Cape Town, 7945, South Africa -34.09606 18.44572
## 4 Table Mountain National Park, ZA-WC-CT, ZA-WC, ZA -34.09361 18.43426
## 5 Silver Mine (Nature Reserve), Cape Town, South Africa -34.07445 18.39816
## 6 Wynberg NU (2), Cape Town, 7824, South Africa -33.98979 18.42769
## tag_list common_name url
## 1 King Protea https://www.inaturalist.org/observations/313170699
## 2 King Protea https://www.inaturalist.org/observations/312964582
## 3 King Protea https://www.inaturalist.org/observations/312963501
## 4 King Protea https://www.inaturalist.org/observations/312962228
## 5 King Protea https://www.inaturalist.org/observations/312641000
## 6 King Protea https://www.inaturalist.org/observations/309437763
## image_url
## 1 https://inaturalist-open-data.s3.amazonaws.com/photos/565512840/medium.jpg
## 2 https://inaturalist-open-data.s3.amazonaws.com/photos/565119182/medium.jpg
## 3 https://inaturalist-open-data.s3.amazonaws.com/photos/565117193/medium.jpg
## 4 https://inaturalist-open-data.s3.amazonaws.com/photos/565114431/medium.jpg
## 5 https://inaturalist-open-data.s3.amazonaws.com/photos/564500630/medium.jpg
## 6 https://inaturalist-open-data.s3.amazonaws.com/photos/558389840/medium.jpg
## user_login id species_guess iconic_taxon_name taxon_id
## 1 bobsteelephoto 313170699 King Protea Plantae 132848
## 2 dryfveer 312964582 King Protea Plantae 132848
## 3 dryfveer 312963501 King Protea Plantae 132848
## 4 dryfveer 312962228 King Protea Plantae 132848
## 5 jrgale 312641000 King Protea Plantae 132848
## 6 kentashi 309437763 King Protea Plantae 132848
## num_identification_agreements num_identification_disagreements
## 1 1 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 1 0
## 6 2 0
## observed_on_string observed_on time_observed_at time_zone
## 1 2025-09-11 12:32:57 2025-09-11 2025-09-11 10:32:57 UTC Pretoria
## 2 2025-09-10 11:20:48 2025-09-10 2025-09-10 09:20:48 UTC Pretoria
## 3 2025-09-10 10:45:06 2025-09-10 2025-09-10 08:45:06 UTC Pretoria
## 4 2025-09-10 10:04:21 2025-09-10 2025-09-10 08:04:21 UTC Pretoria
## 5 2025/09/05 5:05 PM 2025-09-05 2025-09-05 15:05:00 UTC Pretoria
## 6 2025-08-21 11:03:34 2025-08-21 2025-08-21 09:03:34 UTC Pretoria
## positional_accuracy public_positional_accuracy geoprivacy taxon_geoprivacy
## 1 6 6 open
## 2 4 4 open
## 3 4 4 open
## 4 4 4 open
## 5 15 15 open
## 6 104 104 open
## coordinates_obscured positioning_method positioning_device user_id
## 1 false 3047144
## 2 false 2173153
## 3 false 2173153
## 4 false 2173153
## 5 false 3762511
## 6 false gps gps 9681215
## user_name created_at updated_at quality_grade
## 1 Bob Steele 2025-09-11 19:16:19 UTC 2025-09-11 23:53:44 UTC research
## 2 Santie Gouws 2025-09-10 19:20:01 UTC 2025-09-10 19:20:39 UTC needs_id
## 3 Santie Gouws 2025-09-10 19:14:17 UTC 2025-09-10 19:14:59 UTC needs_id
## 4 Santie Gouws 2025-09-10 19:07:32 UTC 2025-09-10 19:08:18 UTC needs_id
## 5 John Gale 2025-09-09 08:57:34 UTC 2025-09-09 09:31:03 UTC research
## 6 Kent Jennings 2025-08-27 08:26:12 UTC 2025-09-01 13:44:16 UTC casual
## license sound_url oauth_application_id captive_cultivated
## 1 CC-BY-NC NA 843 false
## 2 CC-BY-NC NA 2 false
## 3 CC-BY-NC NA 2 false
## 4 CC-BY-NC NA 2 false
## 5 CC-BY-NC NA NA false
## 6 CC-BY-NC NA 2 truenames(pc)## [1] "scientific_name" "datetime"
## [3] "description" "place_guess"
## [5] "latitude" "longitude"
## [7] "tag_list" "common_name"
## [9] "url" "image_url"
## [11] "user_login" "id"
## [13] "species_guess" "iconic_taxon_name"
## [15] "taxon_id" "num_identification_agreements"
## [17] "num_identification_disagreements" "observed_on_string"
## [19] "observed_on" "time_observed_at"
## [21] "time_zone" "positional_accuracy"
## [23] "public_positional_accuracy" "geoprivacy"
## [25] "taxon_geoprivacy" "coordinates_obscured"
## [27] "positioning_method" "positioning_device"
## [29] "user_id" "user_name"
## [31] "created_at" "updated_at"
## [33] "quality_grade" "license"
## [35] "sound_url" "oauth_application_id"
## [37] "captive_cultivated"Lakukan Filter pada data dengan kriteria tertentu supaya bebas noise.
pc <- pc %>%
filter(
!is.na(latitude), !is.na(longitude),
positional_accuracy < 46, # akurasi posisi <= 46 m
latitude < 0, # belahan selatan (cek saja)
captive_cultivated == "false",quality_grade =="research")class(pc)## [1] "data.frame"Seperti terlihat pada keluaran di atas,
objek pc merupakan kelas data frame, dimana terdapat kolom
koordinat bujur dan lintang di dalamnya. Namun, R belum mengenali objek
tersebut sebagai objek spasial. Konversi data frame menjadi objek
spasial dapat dilakukan menggunakan fungsi st_as_sf().
2. Mengubah data frame ke dalam sf point (ppp)
pc <- st_as_sf(pc, coords = c("longitude", "latitude"), crs = 4326)
class(pc)## [1] "sf" "data.frame"names(pc)## [1] "scientific_name" "datetime"
## [3] "description" "place_guess"
## [5] "tag_list" "common_name"
## [7] "url" "image_url"
## [9] "user_login" "id"
## [11] "species_guess" "iconic_taxon_name"
## [13] "taxon_id" "num_identification_agreements"
## [15] "num_identification_disagreements" "observed_on_string"
## [17] "observed_on" "time_observed_at"
## [19] "time_zone" "positional_accuracy"
## [21] "public_positional_accuracy" "geoprivacy"
## [23] "taxon_geoprivacy" "coordinates_obscured"
## [25] "positioning_method" "positioning_device"
## [27] "user_id" "user_name"
## [29] "created_at" "updated_at"
## [31] "quality_grade" "license"
## [33] "sound_url" "oauth_application_id"
## [35] "captive_cultivated" "geometry"3. Membuat visualisasi
ggplot() +
annotation_map_tile(type = "osm", progress = "none") +
geom_sf(data = pc, size = 1) +
labs(title = "Observasi iNaturalist: Protea cynaroides",
subtitle = "Cape Peninsula (WGS84 lon/lat)")
4. Menyiapkan window dan konversi ke Pola Titik (ppp)
# a) Jendela dari bounding box data
bbox_ll <- st_bbox(pc) # dalam lon/lat
# b) Untuk K-function: reproject ke UTM (meter). Cape Town ~ UTM 34S = EPSG:32734
pc_utm <- st_transform(pc, 32734)
bbox_utm <- st_bbox(pc_utm)
# Buat window (owin) dan objek ppp (meter)
win_utm <- owin(xrange = c(bbox_utm["xmin"], bbox_utm["xmax"]),
yrange = c(bbox_utm["ymin"], bbox_utm["ymax"]))
coords <- st_coordinates(pc_utm)
X <- ppp(x = coords[,1], y = coords[,2], window = win_utm)## Warning: data contain duplicated pointsKarena data x masih mengandung duplikat maka hapus terlebih dahulu :
X <- unique(X) # unique.ppp: singkirkan duplikat di objek ppp
X## Planar point pattern: 661 points
## window: rectangle = [253937.34, 266793.64] x [6201377, 6242922] units5. Identifikasi Pola Titik
1. Metode GRID/Quadrat
q <- quadratcount(X)
q # hitungannya## x
## y [2.54e+05,2.57e+05] (2.57e+05,2.59e+05]
## (6.235e+06,6.243e+06] 0 31
## (6.226e+06,6.235e+06] 1 51
## (6.218e+06,6.226e+06] 13 2
## (6.21e+06,6.218e+06] 0 8
## [6.201e+06,6.21e+06] 0 0
## x
## y (2.59e+05,2.62e+05] (2.62e+05,2.64e+05]
## (6.235e+06,6.243e+06] 158 74
## (6.226e+06,6.235e+06] 65 3
## (6.218e+06,6.226e+06] 26 88
## (6.21e+06,6.218e+06] 23 0
## [6.201e+06,6.21e+06] 5 46
## x
## y (2.64e+05,2.67e+05]
## (6.235e+06,6.243e+06] 3
## (6.226e+06,6.235e+06] 0
## (6.218e+06,6.226e+06] 47
## (6.21e+06,6.218e+06] 1
## [6.201e+06,6.21e+06] 16plot(q, main = "Quadrat counts (5 x 5, UTM meters)")
plot(X, add=T, pch=20, cex = 0.5)
Melakukan uji hipotesis CSR berbasis Quadrat
qt <- quadrat.test(X, nx = 5, ny = 5)
qt##
## Chi-squared test of CSR using quadrat counts
##
## data: X
## X2 = 1307.2, df = 24, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 5 by 5 grid of tilesKesimpulan :
- H0: CSR (Complete Spatial Randomness ~ proses Poisson homogen)
- Jika p-value kecil (<0.05), tolak H0 → pola tidak acak (clustered atau regular).
- Karena p-value <0.05 artinya tolak H0 sehingga pola titik bersifat tidak acak ( bisa begerombol atau reguler)
2. Metode K-Function (Ripley)
K <- Kest(X, correction = "Ripley")
plot(K, main = "Ripley's K (meter)", legend=FALSE)
E<-envelope(X,Kest, 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.plot(E)
mad.test(X, Kest, nsim=99, alternative="two.sided")## 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.##
## Maximum absolute deviation test of CSR
## Monte Carlo test based on 99 simulations
## Summary function: K(r)
## Reference function: theoretical
## Alternative: two.sided
## Interval of distance values: [0, 3214.07437876331]
## Test statistic: Maximum absolute deviation
## Deviation = observed minus theoretical
##
## data: X
## mad = 77709583, rank = 1, p-value = 0.01Kesimpulan :
Dengan pendekatan K-Function, diperoleh plot data observasi atau data empiris berada diatas plot garis Poisson dan nilai p-value < 0,05 yang berarti Tolak Ho, sehingga dapat dikatakan bahwa pola titik menyebar secara bekelompok (clustered)