Penerapan Analisis Multidimensional Scaling Pada Pemetaan Karakteristik IPM pada Kabupaten di Papua
Meilinda Ayu Khoriyah
2023-11-09
# install.packages("knitr")
# install.packages("rmarkdown")
# install.packages("prettydoc")
# install.packages("equatiomatic")PENDAHULUAN
1.1 Latar Belakang Kasus
Indeks Pembangunan Manusia (IPM) merupakan suatu indikator apakah penduduk berhasil dalam membangun kualitas hidupnya atau tidak. Indikator IPM ada umur panjang dan hidup sehat yang dapat dilihat dari angka harapan hidup (AHH), pendidikan yang dapat dilihat dari angka melek huruf (AMH), dan standar hidup layak dapat dilihat dari persentase kemiskinan. Data yang akan digunakan adalah data faktor-faktor yang mempengaruhi IPM dengan variabel AMH, AHH, dan kemiskinan yang berada di wilayah Papua pada tahun 2013. Sumber data berasal dari jurnal karya Syahrul Eka dkk tahun 2017.
1.2 Metode
Metode yang digunakan dalam menganalisis data adalah Mutidimensional Scaling dimana untuk mengetahui kemiripan IPM di wilayah Papua ditinjau dari AMH, AHH, dan kemiskinan.
1.3 Tinjauan Pustaka
Multidimensional Scaling merupakan metode yang didasarkan kedekatan antar objek atau subjek yang mengungkapkan kesamaan atau ketidaksamaan untuk menemukan titik dalam dimensi rendah yang mencerminkan konfigurasi relatif objek data berdimensi tinggi. Konfigurasi dalam dimensi tinggi diwakili oleh matriks jarak. Multidimensional Scaling digunakan untuk mengungkap hubungan atau pola dalam data yang divisualisasikan dalam gambar geometri sederhana. Terdapat 2 jenis penskalaan pada Multidimensional Scaling yaitu Metric Multidimensional Scaling berbasis kedekatan yang diukur dalam skala rasio dan Nonmetric Multidimensional Scaling berbasis kedekatan yang diukur dalam skala ordinal. Tahapan Metric Multidimensional Scaling:
Menghitung matriks jarak D menggunakan rumus jarak euclidian.
Setelah didapatkan matriks jarak, menghitung matriks B.
Mencari nilai eigen dan vektor eigen.
Membentuk koordinat objek.
Visualisasi dalam gambar 2 dimensi.
Tahapan Nonmetric Multidimensional Scaling :
Menghitung jarak euclidian dari koordinat yang terbentuk.
Menghitung nilai STRESS. Nilai STRESS mendekati 0 berarti model memiliki tingkat kelayakan yang sempurna.
Menentukan titik koordinat akhir.
1.4 Tujuan
Mengetahui kemiripan dari kabupaten-kabupaten yang ada di Papua dengan variabel AMH, AHH, dan Kemiskinan untuk menilai IPM.
Data
Data AMH, AHH, dan Kemisikinan berdasarkan Kabupaten/Kota di Papua (2013).
library (readxl)
data <- read_excel("E:/IPM.xlsx")
View(data)Sumber : Jurnal karya Syahrul Eka A.L dkk.
2 SOURCE CODE DAN HASIL
Library yang Dibutuhkan
library(MASS)2.1 Statistika Deksriptif Data
summary(data)## Kab/Kota AMH AHH Kemiskinan
## Length:29 Min. :28.08 Min. :63.85 Min. :12.33
## Class :character 1st Qu.:33.50 1st Qu.:66.58 1st Qu.:27.69
## Mode :character Median :53.08 Median :66.87 Median :37.23
## Mean :59.72 Mean :67.18 Mean :33.21
## 3rd Qu.:88.27 3rd Qu.:67.74 3rd Qu.:40.33
## Max. :99.86 Max. :70.88 Max. :47.52Statistika deskriptif karakteristik pendidikan (AMH) pada tiap kabupaten/kota di Papua menunjukkan kabupaten Intan Jaya dengan karakteristik pendidikan terendah senilai 28,08 dan kota Jayapura dengan karakteristik pendidikan tertinggi senilai 99.86.
Statistika deskriptif karakteristik kesehatan (AHH) pada tiap kabupaten/kota di Papua menunjukkan kabupaten Merauke dengan karakteristik kesehatan terendah senilai 63,85 dan kabupaten Mimika dengan karakteristik kesehatan tertinggi senilai 70.88.
Statistika deskriptif karakteristik standar hidup layak (Kemiskinan) pada tiap kabupaten/kota di Papua menunjukkan kabupaten Merauke dengan karakteristik standar hidup layak terendah senilai 12,33 dan kabupaten Deiyai dengan karakteristik standar hidup layak tertinggi senilai 47.52.
2.2 Membentuk Matriks Jarak dengan Rumus Jarak Euclidian
MJ<-as.matrix(dist(data[,-1]))
MJ## 1 2 3 4 5 6 7
## 1 0.000000 46.21960 10.848511 16.637368 17.942539 21.021851 38.060858
## 2 46.219600 0.00000 50.352003 33.767040 39.929905 47.355526 10.139906
## 3 10.848511 50.35200 0.000000 16.852851 13.378718 12.844937 41.014228
## 4 16.637368 33.76704 16.852851 0.000000 7.466157 15.529540 24.214155
## 5 17.942539 39.92990 13.378718 7.466157 0.000000 8.379027 30.002623
## 6 21.021851 47.35553 12.844937 15.529540 8.379027 0.000000 37.389684
## 7 38.060858 10.13991 41.014228 24.214155 30.002623 37.389684 0.000000
## 8 27.932895 33.81767 24.634009 12.618201 11.436332 15.553842 23.866347
## 9 10.683674 41.40254 9.877616 9.066581 9.507881 15.104572 32.213177
## 10 54.600208 25.40452 62.231774 48.615918 55.962580 64.071233 32.216241
## 11 57.992405 22.68806 64.986179 50.319585 57.501027 65.511259 31.103230
## 12 61.369187 23.31011 68.003739 52.913411 59.956531 67.923935 32.426233
## 13 63.887245 20.37067 69.372759 53.291933 59.842351 67.502756 30.374674
## 14 61.250716 20.95601 67.510424 52.004575 58.903631 66.737934 30.543898
## 15 60.733525 19.89801 66.862163 51.250377 58.103239 65.908826 29.564590
## 16 6.092077 42.23509 9.512034 10.857412 12.286550 16.861839 33.486016
## 17 12.163671 43.58442 7.358716 9.852660 6.479707 9.607471 34.044033
## 18 27.050983 25.68207 27.306514 11.135390 15.162130 21.825859 15.790288
## 19 30.421627 43.68235 23.954812 19.047504 13.741532 11.455645 33.866436
## 20 31.956547 14.48953 35.914027 19.515320 26.128195 33.821527 6.703879
## 21 64.111794 22.58541 70.195231 54.496379 61.292187 69.052080 32.447755
## 22 60.518415 16.27171 65.739821 49.510327 55.966249 63.534055 26.345527
## 23 60.527196 18.63427 66.394363 50.590290 57.341720 65.100650 28.448784
## 24 61.635329 19.41665 67.449716 51.598281 58.315786 66.059556 29.293195
## 25 63.817249 20.93396 69.459327 53.498659 60.126907 67.857440 30.857352
## 26 57.547123 20.74343 64.228497 49.265284 56.360696 64.361279 29.386740
## 27 67.437610 25.00097 73.331551 57.480001 64.170839 71.896895 34.972369
## 28 67.471255 22.75903 72.627537 56.306300 62.642667 70.113876 32.804904
## 29 12.923703 53.37041 3.164727 19.822848 15.876782 14.218815 43.990019
## 8 9 10 11 12 13 14
## 1 27.932895 10.683674 54.600208 57.992405 61.369187 63.887245 61.250716
## 2 33.817667 41.402537 25.404521 22.688059 23.310112 20.370668 20.956011
## 3 24.634009 9.877616 62.231774 64.986179 68.003739 69.372759 67.510424
## 4 12.618201 9.066581 48.615918 50.319585 52.913411 53.291933 52.004575
## 5 11.436332 9.507881 55.962580 57.501027 59.956531 59.842351 58.903631
## 6 15.553842 15.104572 64.071233 65.511259 67.923935 67.502756 66.737934
## 7 23.866347 32.213177 32.216241 31.103230 32.426233 30.374674 30.543898
## 8 0.000000 19.834225 54.042099 54.195146 55.983563 54.165326 54.280905
## 9 19.834225 0.000000 53.194517 55.831548 58.764280 60.137290 58.313687
## 10 54.042099 53.194517 0.000000 6.950719 10.941115 19.731128 13.854057
## 11 54.195146 55.831548 6.950719 0.000000 4.245574 12.964093 6.946251
## 12 55.983563 58.764280 10.941115 4.245574 0.000000 9.563629 3.851454
## 13 54.165326 60.137290 19.731128 12.964093 9.563629 0.000000 6.159424
## 14 54.280905 58.313687 13.854057 6.946251 3.851454 6.159424 0.000000
## 15 53.329201 57.667414 14.469029 7.661756 4.917316 5.462326 1.199708
## 16 22.256729 5.075677 52.839778 55.720339 58.846071 60.650986 58.481387
## 17 17.629915 6.106963 57.222001 59.434429 62.231428 63.002243 61.488891
## 18 9.030908 20.138173 45.178249 45.382654 47.307333 45.988873 45.710018
## 19 10.142495 23.183604 64.014205 64.235247 66.030812 64.020943 64.262675
## 20 22.190523 27.109622 31.968162 32.168887 34.267048 33.900531 32.925287
## 21 56.250572 61.004570 16.734665 9.797821 6.024102 4.415699 3.197014
## 22 50.063285 56.584136 20.178627 13.870836 11.509761 4.257182 7.851707
## 23 52.265754 57.185419 15.936816 9.302989 6.718698 4.182212 3.078571
## 24 53.122562 58.231556 16.724117 9.983146 6.991802 3.159383 3.326860
## 25 54.698056 60.187366 18.524379 11.746365 8.196011 1.498065 5.018556
## 26 52.712691 54.998692 8.572917 2.368713 3.845530 11.184297 5.513801
## 27 58.796213 64.094242 19.707648 12.878001 8.769664 4.884527 6.650601
## 28 56.308585 63.476204 24.212511 17.343927 13.698515 4.654127 10.419798
## 29 27.087301 12.500104 65.025372 67.886724 70.926087 72.361339 70.481280
## 15 16 17 18 19 20 21
## 1 60.733525 6.092077 12.163671 27.050983 30.42163 31.956547 64.111794
## 2 19.898012 42.235087 43.584420 25.682074 43.68235 14.489531 22.585413
## 3 66.862163 9.512034 7.358716 27.306514 23.95481 35.914027 70.195231
## 4 51.250377 10.857412 9.852660 11.135390 19.04750 19.515320 54.496379
## 5 58.103239 12.286550 6.479707 15.162130 13.74153 26.128195 61.292187
## 6 65.908826 16.861839 9.607471 21.825859 11.45564 33.821527 69.052080
## 7 29.564590 33.486016 34.044033 15.790288 33.86644 6.703879 32.447755
## 8 53.329201 22.256729 17.629915 9.030908 10.14249 22.190523 56.250572
## 9 57.667414 5.075677 6.106963 20.138173 23.18360 27.109622 61.004570
## 10 14.469029 52.839778 57.222001 45.178249 64.01421 31.968162 16.734665
## 11 7.661756 55.720339 59.434429 45.382654 64.23525 32.168887 9.797821
## 12 4.917316 58.846071 62.231428 47.307333 66.03081 34.267048 6.024102
## 13 5.462326 60.650986 63.002243 45.988873 64.02094 33.900531 4.415699
## 14 1.199708 58.481387 61.488891 45.710018 64.26268 32.925287 3.197014
## 15 0.000000 57.880205 60.776152 44.795948 63.29750 32.090020 3.406905
## 16 57.880205 0.000000 7.323626 21.703790 25.42265 27.791619 61.239367
## 17 60.776152 7.323626 0.000000 19.975190 18.78671 29.251349 64.059221
## 18 44.795948 21.703790 19.975190 0.000000 18.89193 13.268640 47.801803
## 19 63.297505 25.422647 18.786711 18.891932 0.00000 32.158475 66.176723
## 20 32.090020 27.791619 29.251349 13.268640 32.15847 0.000000 35.243842
## 21 3.406905 61.239367 64.059221 47.801803 66.17672 35.243842 0.000000
## 22 6.715102 57.134621 59.257298 41.932546 59.87405 30.056467 7.564047
## 23 1.926889 57.510648 60.193057 43.833089 62.20939 31.310006 4.016329
## 24 2.397102 58.588861 61.221409 44.738039 63.05135 32.290619 3.264858
## 25 4.495086 60.667541 63.171388 46.445458 64.60512 34.175310 3.306872
## 26 5.979707 55.049147 58.519406 43.973962 62.77194 30.834599 8.598541
## 27 6.831413 64.451193 67.110446 50.498786 68.68289 38.155364 3.549507
## 28 9.853451 64.071850 66.082514 48.399509 65.98528 36.853321 7.866823
## 29 69.841012 12.381644 10.260058 30.223292 25.59734 38.955018 73.180428
## 22 23 24 25 26 27 28
## 1 60.518415 60.527196 61.635329 63.817249 57.547123 67.437610 67.471255
## 2 16.271709 18.634270 19.416653 20.933960 20.743433 25.000970 22.759029
## 3 65.739821 66.394363 67.449716 69.459327 64.228497 73.331551 72.627537
## 4 49.510327 50.590290 51.598281 53.498659 49.265284 57.480001 56.306300
## 5 55.966249 57.341720 58.315786 60.126907 56.360696 64.170839 62.642667
## 6 63.534055 65.100650 66.059556 67.857440 64.361279 71.896895 70.113876
## 7 26.345527 28.448784 29.293195 30.857352 29.386740 34.972369 32.804904
## 8 50.063285 52.265754 53.122562 54.698056 52.712691 58.796213 56.308585
## 9 56.584136 57.185419 58.231556 60.187366 54.998692 64.094242 63.476204
## 10 20.178627 15.936816 16.724117 18.524379 8.572917 19.707648 24.212511
## 11 13.870836 9.302989 9.983146 11.746365 2.368713 12.878001 17.343927
## 12 11.509761 6.718698 6.991802 8.196011 3.845530 8.769664 13.698515
## 13 4.257182 4.182212 3.159383 1.498065 11.184297 4.884527 4.654127
## 14 7.851707 3.078571 3.326860 5.018556 5.513801 6.650601 10.419798
## 15 6.715102 1.926889 2.397102 4.495086 5.979707 6.831413 9.853451
## 16 57.134621 57.510648 58.588861 60.667541 55.049147 64.451193 64.071850
## 17 59.257298 60.193057 61.221409 63.171388 58.519406 67.110446 66.082514
## 18 41.932546 43.833089 44.738039 46.445458 43.973962 50.498786 48.399509
## 19 59.874050 62.209393 63.051352 64.605124 62.771944 68.682887 65.985276
## 20 30.056467 31.310006 32.290619 34.175310 30.834599 38.155364 36.853321
## 21 7.564047 4.016329 3.264858 3.306872 8.598541 3.549507 7.866823
## 22 0.000000 4.813408 4.720392 5.227715 11.780565 9.024910 6.963541
## 23 4.813408 0.000000 1.145775 3.596929 7.386339 6.947381 8.680219
## 24 4.720392 1.145775 0.000000 2.490843 8.163553 5.891324 7.671023
## 25 5.227715 3.596929 2.490843 0.000000 10.037545 4.206352 5.799319
## 26 11.780565 7.386339 8.163553 10.037545 0.000000 11.812421 15.715909
## 27 9.024910 6.947381 5.891324 4.206352 11.812421 0.000000 6.246111
## 28 6.963541 8.680219 7.671023 5.799319 15.715909 6.246111 0.000000
## 29 68.747580 69.380551 70.435781 72.435319 67.142571 76.313066 75.636776
## 29
## 1 12.923703
## 2 53.370412
## 3 3.164727
## 4 19.822848
## 5 15.876782
## 6 14.218815
## 7 43.990019
## 8 27.087301
## 9 12.500104
## 10 65.025372
## 11 67.886724
## 12 70.926087
## 13 72.361339
## 14 70.481280
## 15 69.841012
## 16 12.381644
## 17 10.260058
## 18 30.223292
## 19 25.597338
## 20 38.955018
## 21 73.180428
## 22 68.747580
## 23 69.380551
## 24 70.435781
## 25 72.435319
## 26 67.142571
## 27 76.313066
## 28 75.636776
## 29 0.000000Matriks jarak menunjukkan bahwa kabupaten Mamberamo Tengah dan kabupaten Yalimo memiliki jarak terdekat sebesar 1,145775 diantara kabupaten/kota lainnya. Hal tersebut menunjukkan bahwa kabupaten Mamberamo Tengah dan kabupaten Yalimo memiliki karakteristik IPM yang mirip. Kabupaten Intan Jaya dan kota Jayapura memiliki jarak terjauh sebesar 76,313066 diantara kabupaten/kota lainnya.
2.3 Mencari Nilai Eigen dan Vektor Eigen
A <- MJ^2
I <- diag(29)
J <- matrix(rep(1,29),nrow=29,ncol=29)
V <- I-(1/29)*A
B <- (-1/2)*V*A*V
eigen(B)## eigen() decomposition
## $values
## [1] 5.277866e+08 3.308936e+07 8.372430e+06 1.418726e+06 5.150207e+05
## [6] 3.473715e+05 8.854509e+04 5.788570e+04 4.037655e+04 1.381370e+04
## [11] 5.201443e+03 3.177489e+03 1.212308e+03 3.995768e+02 1.256623e+02
## [16] 7.358805e+00 6.773788e-01 1.933393e-01 1.671374e-03 -5.612249e+01
## [21] -2.633756e+03 -9.190686e+03 -1.207150e+05 -3.662324e+05 -8.302627e+05
## [26] -1.855859e+06 -7.914035e+06 -3.238757e+07 -5.282537e+08
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.179367238 -0.27907919 -0.13064861 -0.449805478 -0.19352029
## [2,] -0.026557093 0.06703135 -0.27618483 0.118834597 -0.41036226
## [3,] 0.307055871 -0.13903935 0.09309630 0.064017782 -0.06296748
## [4,] 0.065409565 -0.01460892 -0.24191395 0.070204701 0.16500140
## [5,] 0.133448683 0.06142957 -0.22707870 0.216916934 0.05206766
## [6,] 0.276452244 0.24915736 0.03183970 0.220210286 -0.37314739
## [7,] -0.004716181 0.03560297 -0.15359777 0.070365925 -0.18964004
## [8,] 0.078964765 0.17029958 -0.18957437 -0.058099676 0.32008788
## [9,] 0.130323606 -0.10781023 -0.24001491 0.087371735 0.17041533
## [10,] -0.118726328 -0.41706767 0.04284025 0.459243890 -0.06598001
## [11,] -0.145700938 -0.27073895 -0.03787281 -0.011963574 -0.03652128
## [12,] -0.187741653 -0.21480446 0.06389520 -0.092803775 0.04462140
## [13,] -0.200244291 0.13541047 -0.07364689 0.101630329 0.19775323
## [14,] -0.175297576 -0.07460538 -0.07943026 -0.202050522 -0.06888248
## [15,] -0.164218763 -0.03862257 -0.14041426 -0.178582476 -0.03814271
## [16,] 0.134571834 -0.15513933 -0.23366630 -0.101463943 -0.09309809
## [17,] 0.175537151 -0.03589566 -0.19796770 0.175204644 -0.17650132
## [18,] 0.028852017 0.04773392 -0.16871139 -0.022495857 0.22495807
## [19,] 0.213748891 0.49594760 0.02038077 -0.334390165 0.03343390
## [20,] 0.001103198 0.00471791 -0.12505281 -0.006590833 -0.05627445
## [21,] -0.220103647 -0.01342476 0.07865024 -0.234122630 -0.22468847
## [22,] -0.142350035 0.15232352 -0.28869776 0.105784768 -0.02653803
## [23,] -0.155531568 0.01955972 -0.19922812 -0.100493725 0.04454045
## [24,] -0.170849490 0.03701193 -0.15370958 -0.080351031 0.06548361
## [25,] -0.203350331 0.08453074 -0.03938262 0.070244806 0.29486943
## [26,] -0.133508620 -0.18954310 -0.13421817 -0.009987947 0.19752162
## [27,] -0.285480837 0.05766290 0.39311171 -0.096893266 -0.15737648
## [28,] -0.261266072 0.31749080 0.16880124 0.329494799 -0.03964467
## [29,] 0.395282906 -0.15999045 0.37039251 0.037529353 0.30998937
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.160542262 0.14359036 0.077416329 -0.248166510 -0.02570704
## [2,] 0.301393225 0.06660744 0.418009669 0.098930070 0.05589297
## [3,] -0.015654716 -0.38854743 -0.056657247 0.072722190 -0.26550736
## [4,] -0.164411669 0.41797497 0.059992507 0.362873184 -0.17445611
## [5,] -0.006624844 0.11437230 0.260374103 -0.268147120 -0.24756715
## [6,] -0.155702060 0.15283412 -0.182897701 -0.209355078 0.34110018
## [7,] 0.209060752 -0.29301148 -0.384118475 0.079109081 0.17933624
## [8,] -0.172626141 -0.23242242 0.227504000 -0.196183933 0.14030440
## [9,] 0.477677259 0.03451181 -0.176878433 -0.184888996 0.16911867
## [10,] -0.097000516 0.20247641 -0.080172893 -0.144484553 0.03293967
## [11,] -0.085296078 -0.18266068 0.024618264 0.240823328 -0.02008786
## [12,] 0.254289077 0.04525501 -0.122109123 0.231542485 -0.30532174
## [13,] 0.118976732 0.06467891 -0.183961979 -0.044641658 -0.02039744
## [14,] -0.124699636 -0.03858252 -0.060019054 0.015211466 0.01891170
## [15,] -0.153900078 -0.03986628 0.025536463 -0.058798437 0.07263525
## [16,] 0.104006686 -0.03792813 -0.095477643 0.275812322 0.29635878
## [17,] -0.019346857 -0.23285699 0.094137852 0.207022837 -0.21118664
## [18,] -0.333506581 -0.03952710 -0.261561380 0.167422167 0.25750813
## [19,] 0.197206825 0.01227709 -0.001579805 0.159844207 -0.17111112
## [20,] -0.045749093 -0.14655049 -0.276246426 -0.449663844 -0.46870950
## [21,] -0.145447080 0.09130723 -0.199649339 -0.008807083 -0.04691313
## [22,] -0.076067343 0.28954960 -0.035437427 0.118524995 -0.13706481
## [23,] -0.085374184 0.02395711 0.088236389 -0.115220113 0.07901139
## [24,] -0.039510634 0.04895119 -0.029642959 -0.106430447 0.03819951
## [25,] 0.277981729 0.03287112 -0.132460591 -0.096062816 0.02047301
## [26,] 0.022660559 -0.33653510 0.356661895 -0.070323534 0.17692149
## [27,] 0.219692679 0.08838242 0.232110737 -0.108113268 0.14034698
## [28,] -0.264712332 -0.24872088 0.069327679 0.129246027 -0.04973588
## [29,] -0.009354613 0.17346106 0.068302750 0.053186046 0.07843788
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.205833367 0.00473399 -0.064085846 0.028726142 -0.10798427
## [2,] -0.105141954 -0.18417687 -0.099098104 0.052609018 0.21726888
## [3,] -0.012987062 -0.28249440 -0.049625718 -0.170259204 0.33891484
## [4,] 0.145671438 -0.14616297 0.013791589 -0.176215440 0.08581718
## [5,] -0.277710981 0.38048830 0.116540709 0.050924668 0.25646890
## [6,] 0.018055048 -0.07668136 -0.300538092 0.002494722 -0.05126030
## [7,] 0.014550585 0.32904639 0.195800956 -0.142246350 -0.12150875
## [8,] 0.453550530 -0.13032227 -0.194049874 -0.057161754 -0.07246485
## [9,] -0.206385319 -0.20618485 -0.198415999 0.025827739 -0.13957475
## [10,] 0.088796541 0.03045370 0.203371560 -0.113836956 0.07230655
## [11,] -0.105514460 -0.43893220 -0.018877183 0.202105670 -0.14384564
## [12,] -0.070163398 0.31243680 -0.552378004 -0.146324604 -0.12047988
## [13,] 0.038594887 -0.16108772 0.132839304 0.175394912 -0.03108563
## [14,] -0.034201229 -0.05293008 0.047947990 -0.209485418 0.09889140
## [15,] -0.045021096 -0.01088950 0.079307156 -0.464382821 0.08190968
## [16,] 0.441793978 0.21482121 -0.012129855 0.004007354 0.24465796
## [17,] 0.017561822 0.03131065 0.407371969 0.106136929 -0.44770802
## [18,] -0.502362123 -0.05975445 -0.004687872 0.137482858 0.03767024
## [19,] -0.082818395 0.03100522 0.160887692 0.002304117 0.02882187
## [20,] 0.212781606 -0.09081995 -0.074117907 0.066901867 -0.06086849
## [21,] 0.138000703 0.10581194 0.093858717 0.519482527 0.31549579
## [22,] 0.168532311 -0.01149892 -0.158600773 0.190737421 -0.25379293
## [23,] -0.038634831 0.06749314 0.140744325 -0.262180965 -0.11727048
## [24,] -0.012690635 0.10530002 0.074336515 -0.049095535 -0.18422970
## [25,] -0.007899277 -0.14579441 0.186394629 -0.019940756 0.34118054
## [26,] -0.014922878 0.23023253 -0.114255608 0.336331507 0.02809669
## [27,] 0.053001636 -0.14055891 0.151325485 -0.079058794 -0.20655344
## [28,] -0.122100482 0.14072668 -0.240262815 -0.083601564 0.03041133
## [29,] 0.059168429 0.16028526 0.076543865 0.072605914 -0.12015044
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.02448647 -0.003607556 0.007288671 0.0007776998 0.09668843
## [2,] 0.22030738 -0.080537036 0.062590457 0.0213981349 0.08517334
## [3,] -0.10614602 0.047664261 -0.025606356 -0.0022680844 -0.29659321
## [4,] 0.10730630 -0.043692184 0.038900045 0.0085771213 0.03101417
## [5,] -0.13976353 0.088826165 -0.030473480 0.0009961325 -0.25070605
## [6,] 0.02615981 -0.029914829 -0.006773623 -0.0020841683 0.05497776
## [7,] -0.09295518 0.037769623 -0.022005951 -0.0040352291 -0.04153906
## [8,] 0.08158922 -0.069091040 0.012485444 -0.0036932288 0.09005328
## [9,] 0.02338942 -0.015625370 -0.001258154 -0.0015115225 0.11224661
## [10,] 0.04048502 0.018397544 0.015233590 -0.0155681747 0.01109457
## [11,] -0.17339693 -0.193105967 -0.026116883 0.0511456975 -0.18726346
## [12,] 0.11607388 -0.070541606 -0.052732702 0.0669390641 0.06806541
## [13,] 0.53314943 0.376871766 -0.125417402 0.3074754042 -0.24245486
## [14,] 0.23776121 0.411158892 0.033855298 -0.6815898517 0.13159957
## [15,] -0.16717626 0.213127056 0.193698573 0.6002369929 0.25554571
## [16,] -0.06987078 0.008662723 -0.029099865 -0.0013043553 -0.22472943
## [17,] 0.11159137 -0.037324675 0.043623515 -0.0008590371 0.35226758
## [18,] -0.07613200 0.053894222 -0.023991026 0.0014855257 -0.05401876
## [19,] -0.02161493 0.022491493 0.001750550 0.0019495037 -0.03402816
## [20,] -0.02626549 -0.002203317 -0.009641843 -0.0107331718 0.01157490
## [21,] 0.08908337 -0.194519942 -0.046937669 0.1355461804 0.17405656
## [22,] -0.53162318 0.269661988 -0.061056147 -0.0961747576 -0.05725776
## [23,] 0.07748278 -0.407330308 -0.691379260 -0.0471966979 -0.14542637
## [24,] 0.13578739 -0.378156655 0.663039313 -0.1075390480 -0.40560910
## [25,] -0.27282433 -0.258665685 0.072195930 -0.1716115698 0.39052041
## [26,] -0.04778152 0.214141833 0.007669957 0.0045698584 0.05777532
## [27,] -0.23036395 0.156420827 -0.035387777 -0.0234038575 -0.21170008
## [28,] 0.08040791 -0.113790056 0.020907391 -0.0336737966 0.11389432
## [29,] 0.05077125 -0.020956986 0.014666783 0.0021494493 0.11509364
## [,21] [,22] [,23] [,24] [,25]
## [1,] -0.055838320 0.193870532 0.070159081 -0.200653305 0.1890092328
## [2,] 0.098110125 -0.143157350 -0.001695684 -0.060561817 -0.3625525004
## [3,] -0.344689605 -0.148376668 0.182245546 -0.066010500 0.0549268805
## [4,] -0.372524161 0.269109164 -0.350158103 -0.073599087 -0.1738940360
## [5,] 0.243392900 0.233638558 0.151546993 0.026467751 -0.0831305783
## [6,] -0.007303794 0.103898695 -0.121555675 -0.245746045 0.1673487551
## [7,] -0.217816571 0.440169856 0.057717533 -0.097203958 -0.3605743846
## [8,] 0.015185814 0.056195834 0.424250360 -0.050525552 -0.2641707193
## [9,] -0.147280365 -0.028488375 -0.001614902 0.525397900 0.0260394881
## [10,] -0.091975540 -0.189592674 0.104197341 0.110702143 0.0567458349
## [11,] 0.360465913 0.438511706 -0.043643893 0.099011530 -0.0008072954
## [12,] 0.075895180 -0.106411766 0.155854661 -0.251069818 -0.0583390786
## [13,] 0.090718744 0.100820744 0.077913950 -0.203942999 0.1584691029
## [14,] 0.126691477 0.062497184 0.032536956 0.154727192 -0.0449985510
## [15,] 0.104878920 -0.032898118 -0.036898414 0.165517603 -0.0086174784
## [16,] 0.370857814 -0.190539424 -0.183833812 0.041571985 0.1691506147
## [17,] 0.047883346 -0.210401184 0.080471817 -0.122575219 0.1220285063
## [18,] 0.063796497 -0.398824463 -0.021250077 -0.191572673 -0.3494085236
## [19,] -0.026715652 -0.064219902 -0.098410712 0.179667175 0.1380045625
## [20,] 0.187806209 -0.139320643 -0.494078243 -0.010884029 -0.2916026089
## [21,] -0.212034234 -0.004707496 0.199255047 0.240929413 -0.1704132822
## [22,] -0.082727938 -0.099291810 0.210789609 0.073880215 0.0622108528
## [23,] -0.071649085 -0.120478822 -0.066041690 0.058991660 0.0503792847
## [24,] -0.091529983 -0.110034210 0.007564645 0.007036417 0.0612367026
## [25,] 0.110012308 0.069627702 0.002514852 -0.392793936 0.1691688411
## [26,] -0.347336606 0.003807554 -0.395731139 -0.102718962 0.1363789410
## [27,] -0.076354122 -0.115423713 -0.094498406 -0.141172616 -0.2683543247
## [28,] 0.060832666 0.096107910 -0.133339160 0.262353289 0.1148188677
## [29,] 0.184670665 0.050740221 -0.079059597 0.112484891 -0.2984371875
## [,26] [,27] [,28] [,29]
## [1,] 0.44875146 -0.145084663 0.270407766 -0.179743471
## [2,] 0.18410280 0.278999107 0.062897051 -0.027214576
## [3,] -0.07395073 0.100420543 0.140849211 -0.306901899
## [4,] -0.07097515 -0.247362919 0.015947978 -0.065442730
## [5,] -0.22026667 -0.231373071 -0.060753703 -0.133331442
## [6,] -0.26904878 0.038148569 -0.252074370 -0.276220471
## [7,] 0.17783098 0.091749602 0.020627542 -0.010330333
## [8,] 0.12030529 -0.192346108 -0.164728254 -0.079647217
## [9,] -0.09047952 -0.243454937 0.109537857 -0.130276658
## [10,] 0.42739807 -0.047215051 -0.418746903 -0.118962149
## [11,] -0.01372705 0.035502257 -0.273675436 -0.145668089
## [12,] -0.08341270 -0.067465215 -0.216789515 -0.187667897
## [13,] 0.06478457 0.076392474 0.136769450 -0.200144601
## [14,] -0.17955228 0.080355870 -0.075343539 -0.175207695
## [15,] -0.16307454 0.143408956 -0.039145947 -0.164129440
## [16,] 0.06505140 -0.238334737 0.155564025 -0.134597605
## [17,] -0.20756915 -0.197187788 0.038395612 -0.175372582
## [18,] 0.08491631 -0.145944862 -0.038804614 -0.030109304
## [19,] 0.32858169 0.001858185 -0.494642643 -0.214375092
## [20,] 0.08238133 0.016464734 0.007335517 -0.008215207
## [21,] -0.19085127 -0.080042686 -0.012778869 -0.219999170
## [22,] 0.08652092 0.299837420 0.152986784 -0.142275397
## [23,] -0.10162952 0.204780631 0.019497445 -0.155442359
## [24,] -0.08573464 0.157909772 0.037291213 -0.170754750
## [25,] 0.03190272 0.040428684 0.085587895 -0.203247546
## [26,] -0.03224720 0.134209585 -0.192022391 -0.133457093
## [27,] -0.05350380 -0.398337956 0.060125673 -0.285370947
## [28,] 0.30020756 -0.169139875 0.319992514 -0.261192020
## [29,] 0.01658621 0.376688112 0.159456611 -0.395165487Dengan jumlah dimensi 2 didapatkan nilai eigen value positif pertama dari matriks B yaitu ; \[ \lambda1 : 5.277866e+08 \] \[ \lambda2 : 3.308936e+07 \]
2.4 Titik Koordinat Objek 2 Dimensi
Menentukan koordinat titik dari 29 objek:
fit <- cmdscale(MJ,k=2)
fit## [,1] [,2]
## 1 32.708094 -13.96412581
## 2 -8.392857 6.90406182
## 3 40.026760 -6.90570697
## 4 24.640646 -0.04430309
## 5 31.318987 3.15168699
## 6 38.950367 5.87399662
## 7 1.634721 7.48988099
## 8 24.941575 12.56800960
## 9 30.725678 -6.16114692
## 10 -21.711244 -14.70684299
## 11 -24.935783 -8.62261878
## 12 -27.965961 -5.73316834
## 13 -28.511377 3.81463798
## 14 -27.308543 -2.10759547
## 15 -26.582828 -1.15234626
## 16 30.779620 -8.87216098
## 17 34.176417 -2.44498867
## 18 17.245550 8.09307407
## 19 34.256325 16.31096547
## 20 5.322321 2.27683169
## 21 -29.836996 -0.16128325
## 22 -24.579605 5.24363433
## 23 -25.937713 0.62603943
## 24 -26.938884 1.15693488
## 25 -28.800503 2.40558754
## 26 -24.199162 -6.50491721
## 27 -32.814328 1.56090800
## 28 -31.142037 7.57287665
## 29 42.930759 -7.667921352.5 Visualisasi Objek dalam 2 Dimensi
plot(fit,pch=16,xlim=c(-35,55),ylim=c(-20,20),main="Plot 2 Dimensi",xlab="Dimensi 1",ylab="Dimensi 2",col="orange")
text.default(fit,pos=4,labels=data$`Kab/Kota`,cex=0.7)
abline(h=0,col="black")
abline(v=0,col="black")
Dari koordinat titik 29 objek didapatkan plot 2 dimensi yang dapat menentukan kemiripan kota/kabupaten di Papua sesuai dengan karakteristik IPM.
2.6 Jarak Objek dari Koordinat yang Terbentuk
MJt<-dist(fit)
MJt## 1 2 3 4 5 6 7
## 2 46.095222
## 3 10.167800 50.350463
## 4 16.088666 33.756364 16.846702
## 5 17.172090 39.888731 13.303251 7.403687
## 6 20.797045 47.354428 12.824954 15.485295 8.102403
## 7 37.760150 10.044676 41.002215 24.208191 29.999593 37.350616
## 8 27.645488 33.812197 24.633076 12.615902 11.372709 15.525980 23.853655
## 9 8.050867 41.242690 9.330836 8.628059 9.331714 14.577043 32.134629
## 10 54.424406 25.385244 62.228923 48.615715 55.956523 64.057802 32.213796
## 11 57.890831 22.688019 64.985228 50.313118 57.473763 65.510243 31.074175
## 12 61.229810 23.298197 68.002831 52.913309 59.947024 67.915545 32.419892
## 13 63.748789 20.354345 69.371479 53.291922 59.834036 67.493168 30.369304
## 14 61.176581 20.952640 67.506037 51.990148 58.862954 66.737912 30.493017
## 15 60.659337 19.894239 66.857598 51.235457 58.061561 65.908793 29.511322
## 16 5.444917 42.229992 9.453917 10.752585 12.035939 16.858537 33.423668
## 17 11.612342 43.583803 7.356937 9.833322 6.283923 9.591460 34.024456
## 18 26.937155 25.665963 27.275391 10.995651 14.915728 21.817960 15.622478
## 19 30.314653 43.674278 23.923039 18.972509 13.483122 11.443965 33.793203
## 20 31.839429 14.474715 35.898706 19.457269 26.011382 33.819891 6.385474
## 21 64.050033 22.578091 70.188544 54.477768 61.245653 69.051617 32.388413
## 22 60.422004 16.271688 65.738793 49.503489 55.937722 63.533099 26.310388
## 23 60.433465 18.634257 66.393065 50.582802 57.312378 65.099954 28.413931
## 24 61.533799 19.416090 67.449267 51.593516 58.292011 66.057883 29.266996
## 25 63.649628 20.897567 69.454247 53.497275 60.124120 67.839592 30.856975
## 26 57.394038 20.727759 64.227173 49.265265 56.351707 64.351383 29.381012
## 27 67.336577 24.999151 73.331492 57.477394 64.153041 71.894187 34.955539
## 28 67.384581 22.759009 72.626628 56.300347 62.617301 70.112989 32.776863
## 29 12.006043 53.352191 3.002362 19.815342 15.871269 14.114782 43.990019
## 8 9 10 11 12 13 14
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 19.601968
## 10 54.040754 53.128709
## 11 54.192191 55.715861 6.885887
## 12 55.983395 58.693200 10.938388 4.186992
## 13 54.164930 60.071166 19.730359 12.941029 9.563372
## 14 54.271984 58.175615 13.786617 6.933651 3.684695 6.043150
## 15 53.319905 57.526976 14.403358 7.649688 4.785080 5.328249 1.199652
## 16 22.220794 2.711551 52.814149 55.715962 58.829386 60.633136 58.480715
## 17 17.625902 5.071235 57.216988 59.434126 62.229312 62.999543 61.485886
## 18 8.902463 19.618784 45.138321 45.372671 47.278385 45.956516 45.706902
## 19 10.038639 22.747776 63.988071 64.229193 66.011792 63.999551 64.261002
## 20 22.154536 26.768079 31.925834 32.161326 34.238427 33.868628 32.924103
## 21 56.238126 60.859148 16.661367 9.778348 5.877642 4.191088 3.190800
## 22 50.059902 56.468960 20.155621 13.870827 11.487280 4.183403 7.841408
## 23 52.261962 57.068432 15.904727 9.302771 6.674827 4.097671 3.058093
## 24 53.120567 58.127068 16.702924 9.982589 6.966234 3.088061 3.285393
## 25 54.694477 60.139465 18.522767 11.685778 8.181431 1.438408 4.753395
## 26 52.712319 54.925916 8.570958 2.242158 3.845045 11.184293 5.385600
## 27 58.795414 64.007520 19.695639 12.875391 8.758437 4.857437 6.616010
## 28 56.305620 63.373793 24.193507 17.343923 13.679850 4.587453 10.411878
## 29 27.075887 12.297738 65.024111 67.873257 70.923115 72.359021 70.459044
## 15 16 17 18 19 20 21
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16 57.879582
## 17 60.772994 7.269579
## 18 44.792907 21.702310 19.942543
## 19 63.295891 25.421985 18.756124 18.891803
## 20 32.088905 27.791619 29.237893 13.266200 32.157946
## 21 3.401737 61.239314 64.054136 47.800633 66.176195 35.243751
## 22 6.702348 57.130548 59.256941 41.922105 59.867791 30.048746 7.540112
## 23 1.891779 57.507145 60.192524 43.824090 62.204013 31.303592 3.977974
## 24 2.336569 58.583346 61.221351 44.725543 63.043621 32.280637 3.183827
## 25 4.192491 60.638096 63.163443 46.395976 64.571845 34.123068 2.768238
## 26 5.859341 55.029722 58.516589 43.940477 62.750366 30.799953 8.486864
## 27 6.796569 64.444078 67.110410 50.484261 68.673406 38.143369 3.439542
## 28 9.844587 64.068174 66.082206 48.390383 65.979542 36.846947 7.843492
## 29 69.818275 12.210666 10.193995 30.135344 25.499663 38.901063 73.153918
## 22 23 24 25 26 27 28
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23 4.813174
## 24 4.718825 1.133222
## 25 5.086305 3.370810 2.241598
## 26 11.754710 7.339830 8.136956 10.028432
## 27 9.020706 6.939871 5.889316 4.101740 11.801637
## 28 6.963540 8.680065 7.670124 5.673064 15.696745 6.240218
## 29 68.733962 69.366103 70.424747 72.435141 67.139994 76.305239 75.624474Berdasarkan matriks MJ topi menunjukkan kabupaten Mamberamo Tengah dan Kabupaten Yalimo memiliki jarak terdekat diantara kabupaten/kota lainnya sebesar 1,133222 yang berarti 2 kabupaten tersebut memiliki karakteristik IPM yang mirip. Kabupaten Intan Jaya dan kota Jayapura memiliki jarak terjauh diantara kabupaten/kota lainnya sebesar 76,305239 yang berarti 2 kabupaten tersebut memiliki karakteristik IPM yang sangat berbeda dari kabupaten/kota lainnya.
2.7 Menghitung Nilai STRESS dan Koefisien Determinasi
a<-sum((MJ-MJt)^2)## Warning in MJ - MJt: longer object length is not a multiple of shorter object
## lengthb<-sum((MJ-(sum(MJ)/29))^2)
STRESS<-sqrt(a/b)
cat("STRESS :",STRESS)## STRESS : 0.0350977RSQ<-1-(a/b)
cat("R Square :",RSQ)## R Square : 0.9987682Nilai STRESS yang diperoleh sebesar 0,03509 atau 3,5% yang menunjukkan bahwa model penskalaan yang diperoleh termasuk kriteria sangat baik.
Nilai R Square yang diperoleh dalam analisis Multidimensional Scaling menunjukkan bahwa model penskalaan sangat mewakili data karena bernilai 0,9987 atau 99,87%.
3 PEMBAHASAN
Berdasarkan hasil yang diperoleh, peta geometri 2 dimensi yang terbentuk dapat diterima karena nilai STRESS sebesar 3,5% yang termasuk kriteria sangat baik dan nilai R Square sebesar 99,87% yang berarti sangat akurat. Dari plot 2 dimensi secara keseluruhan terdapat beberapa kelompok kabupaten/kota yang memiliki kemiripan karakteristik IPM ditinjau dari AMH, AHH dan Kemiskinan. Hal tersebut digambarkan dari kedekatan titik atau posisi kabupaten/kota. Berikut beberapa kelompok yang berdekatan :
Kabupaten Deiyai, Kabupaten Lanny Jaya, Kabupaten Yahukimo, Kabupaten Puncak Jaya, Kabupaten Intan Jaya, Kabupaten Yalimo, Kabupaten Memberamo Tengah, Kabupaten Nduga, Kabupaten Tolikara, dan Pegunungan Bintang.
Kabupaten Asmat, Kabupaten Dogiyai, dan Kabupaten Mappi.
Kabupaten Jayawijaya dan Kabupaten Paniai.
Kabupaten Keerom, Kabupaten Mimika, Kabupaten Sarmi, Kabupaten Merauke, Kabupaten Jayapura dan Kota Jayapura.
Kabupaten Biak Numfor, Kabupaten Yapen Waropen, dan Kabupaten Nabire.
Kabupaten Supiori, Kabupaten Puncak Jaya, Kabupaten Waropen, dan Kabupaten Mamberamo Raya.
Kabupaten Boven Digoel.
PENUTUP
Kesimpulan
Berdasarkan plot 2 dimensi terdapat 7 kelompok kabupaten/kota yang memiliki kemiripan karakteristik IPM dengan tingkatan AMH, AHH, dan Kemiskinan yang berbeda. Peta geometri 2 dimensi yang terbentuk memiliki standar kelayakan yang tinggi karena nilai STRESS bernilai 3,5% yang termasuk kategori sempurna dan nilai determinasi sebesar 99,87% yang berarti sangat akurat.
Saran
Peningkatan AHH dan AMH serta penurunan presentase kemiskinan dapat disesuaikan dengan kelompok yang telah didapatkan.
Daftar Pustaka
Hardle, W., and Simar, L. 2003. Applied Multivariate Statistical Analysis. First Edition. MD TECH. https://drive.google.com/file/d/1Kx2j_oDE2njOFCqp2-845n5QjN99oA6/view?usp=drivesdk.
Eka, S., Setiawan, D., Mubarok, R., Ernawati, & Otok, B. 2017. Analisis Multidimensional Scaling pada Kabupaten di Papua Berdasarkan Faktor-Faktor yang Mempengaruhi Indeks Pembangunan Manusia (IPM) Tahun 2013.https://www.researchgate.net/publication/316988151_Analisis_Multi_Dimensional_Scaling_pada_Kabupaten_di_Papua_Berdasarkan_Faktor-Faktor_yang_Mempengaruhi_Indeks_Pembangunan_Manusia_IPM_Tahun_2013.
Claudius, H. 2023. Pertemuan Kelima : Multi-Dimensional Scaling [Slide Powerpoint].
Irmawati. 2017. Penerapan Analisis Multidimensional Scaling pada Pemetaan Karakteristik Kemiskinan di Provinsi Sulawesi Selatan. http://repostori.uin-alauddin.ac.id/6760/1/Irmawati.pdf.