Latar Belakang Kasus
Kesejahteraan pekerja merupakan salah satu indikator fundamental dalam menilai keberhasilan pembangunan ekonomi suatu wilayah. Di Indonesia, sebagai negara dengan jumlah tenaga kerja yang besar dan kondisi geografis yang luas, tingkat kesejahteraan pekerja antarprovinsi menunjukkan variasi yang signifikan. Faktor-faktor seperti upah minimum provinsi (UMP), rata-rata pengeluaran per kapita, garis kemiskinan, dan upah pekerja per jam menjadi parameter penting dalam mengukur disparitas kesejahteraan ini. Namun, kompleksitas data multidimensi tersebut seringkali menyulitkan dalam identifikasi pola dan pengelompokan provinsi berdasarkan kemiripan karakteristik kesejahteraannya.
Permasalahan ketimpangan kesejahteraan pekerja antarprovinsi memerlukan analisis yang komprehensif untuk memahami struktur dan pola sebarannya. Pendekatan analisis multivariat diperlukan untuk menyederhanakan kompleksitas data tanpa kehilangan informasi esensial. Multidimensional Scaling (MDS) hadir sebagai teknik statistik yang tepat untuk memetakan objek-objek (dalam hal ini provinsi) dalam ruang dimensi rendah berdasarkan kemiripan atau ketidakmiripannya. Melalui MDS, hubungan kompleks antarprovinsi dapat direpresentasikan secara visual dalam bentuk peta persepsi yang mudah diinterpretasi.
Projek ini menggunakan data dari Kaggle yang mencakup empat variabel kunci kesejahteraan pekerja tahun 2022 di 35 provinsi Indonesia. Penerapan MDS diharapkan dapat mengungkap pola spasial kesejahteraan pekerja, mengidentifikasi provinsi-provinsi dengan karakteristik serupa, serta memberikan gambaran menyeluruh tentang kesenjangan kesejahteraan pekerja di tingkat regional. Hasil analisis ini dapat menjadi dasar empiris bagi pemangku kebijakan dalam merumuskan strategi yang tepat sasaran untuk meningkatkan kesejahteraan pekerja, khususnya di provinsi-provinsi yang tertinggal.
Data
X1: Garis Kemiskinan Per Kapita (Rupiah) X2: Rata-rata Pengeluaran Per Kapita (Rupiah) X3: Upah Minimum Provinsi - UMP (Rupiah) X4: Rata-rata Upah Pekerja Per Jam (Rupiah)
## Warning: package 'readxl' was built under R version 4.3.3Data <- read_excel(path="C:/Users/LENOVO/OneDrive/Dokumen/SEMESTER 5/Data Praktikum Anmul.xlsx")
Data## # A tibble: 35 × 5
## Provinsi X1 X2 X3 X4
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 ACEH 617293 1180132 3166460 16772
## 2 SUMATERA UTARA 592025 1216496 2522610 15131
## 3 SUMATERA BARAT 654194 1342985 2512539 15887
## 4 RIAU 648832 1425170 2938564 18626
## 5 JAMBI 585950 1261836 2698941 16042
## 6 SUMATERA SELATAN 513524 1148812 3144446 15978
## 7 BENGKULU 625652 1196483 2238094 16501
## 8 LAMPUNG 545992 1074987 2440486 13218
## 9 KEP. BANGKA BELITUNG 853226 1654280 3264884 18132
## 10 KEP. RIAU 730462 1831700 3050172 23528
## # ℹ 25 more rows## # A tibble: 6 × 5
## Provinsi X1 X2 X3 X4
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 ACEH 617293 1180132 3166460 16772
## 2 SUMATERA UTARA 592025 1216496 2522610 15131
## 3 SUMATERA BARAT 654194 1342985 2512539 15887
## 4 RIAU 648832 1425170 2938564 18626
## 5 JAMBI 585950 1261836 2698941 16042
## 6 SUMATERA SELATAN 513524 1148812 3144446 15978Latar Belakang Metode
Multidimensional Scaling (MDS) dipilih sebagai metode analisis untuk menyederhanakan data multidimensi ke dalam ruang dimensi rendah (biasanya 2D atau 3D) sambil mempertahankan struktur jarak asli antar objek. MDS mampu memvisualisasikan kemiripan atau ketidakmiripan antar provinsi berdasarkan variabel-variabel kesejahteraan pekerja.
Tinjauan Pustaka Metode
MDS merupakan salah satu teknik analisis yang digunakan untuk memperoleh peta spasial yang menggambarkan tingkat kemiripan beberapa objek (Nasution & Jana, 2021). Jenis Multidimensional Scaling (MDS) berdasarkan skala data terbagi menjadi dua bentuk utama, yaitu MDS metrik untuk skala data interval atau rasio dan MDS non-metrik untuk skala data nominal atau ordinal. Kedua pendekatan ini berbeda dalam cara mengolah data jarak atau ketidakmiripan serta asumsi yang digunakan dalam proses pemetaan.
Tujuan Projek
- Menganalisis jarak kemiripan antarprovinsi berdasarkan variabel kesejahteraan pekerja.
- Memvisualisasikan koordinat provinsi dalam plot MDS.
- Menilai kualitas representasi data melalui nilai stress.
Source Code
- Library yang Digunakan
- Menghitung Matriks Jarak Euclidean
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## 29 30 31 32 33 34 35
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## 21 356331.30 566497.3 416938.0 322030.0 303706.1 645097.6 229841.98
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## 23 764967.40 968164.2 747865.7 721618.0 399746.6 653601.3 596638.88
## 24 603642.72 795359.8 578940.4 534415.1 239412.9 573067.6 461078.09
## 25 519060.87 692000.1 728038.7 470000.3 348582.8 395846.2 593912.85
## 26 431774.31 341022.3 270105.5 473807.7 900479.4 1233584.3 418080.80
## 27 365505.60 521596.7 601435.1 327288.5 419672.1 561079.5 487260.01
## 28 95393.71 159009.8 263287.1 189168.1 655037.9 947849.6 240247.55
## 29 0.00 223342.9 299981.6 126389.8 572367.8 855360.2 222107.22
## 30 223342.90 0.0 331019.9 277874.3 770317.0 1042635.2 390701.89
## 31 299981.56 331019.9 0.0 277743.6 645122.9 984645.0 236277.06
## 32 126389.85 277874.3 277743.6 0.0 493281.8 781905.2 239547.79
## 33 572367.84 770317.0 645122.9 493281.8 0.0 364046.8 515574.14
## 34 855360.21 1042635.2 984645.0 781905.2 364046.8 0.0 852630.19
## 35 222107.22 390701.9 236277.1 239547.8 515574.1 852630.2 0.00- Menghitung MDS Klasik dengan Double Centering
A <- dist_matrix^2
I <- diag(35)
J <- matrix(rep(1,35), nrow=35, ncol=35)
V <- I - (1/35)*J
aa <- V %*% A
BB <- aa %*% V
B <- (-1/2) * BB- Analisis Eigen
## [1] 1.231227e+13 1.865856e+12 2.064105e+11 1.089575e+08 4.128256e-03
## [6] 3.051860e-03 1.070481e-03 5.365851e-04 5.035559e-04 2.793620e-04
## [11] 1.944216e-04 1.921833e-04 1.552509e-04 1.414038e-04 1.355895e-04
## [16] 1.299385e-04 7.315597e-05 5.377245e-05 2.812382e-05 2.596323e-05
## [21] 3.853769e-06 -7.958207e-06 -4.054028e-05 -4.430919e-05 -4.569153e-05
## [26] -7.953138e-05 -1.433973e-04 -1.678611e-04 -2.569204e-04 -5.461265e-04
## [31] -6.361232e-04 -6.734685e-04 -8.962485e-04 -1.051814e-03 -4.418685e-03## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.100414320 0.217530706 -0.149902850 -0.07697915 0.000000000
## [2,] -0.066752481 0.021307507 -0.095941926 -0.10682281 0.710258477
## [3,] -0.054556455 -0.075112958 -0.157741307 -0.13451850 0.019397694
## [4,] 0.066246670 -0.011397869 -0.086940060 -0.05041468 -0.018329306
## [5,] -0.015712971 0.040887495 -0.052091561 -0.10352078 -0.245245486
## [6,] 0.088195702 0.249616352 0.052725332 -0.13138136 -0.134354424
## [7,] -0.142931079 -0.049260986 -0.187623661 0.11653962 -0.147573869
## [8,] -0.104347787 0.099594487 -0.079794248 -0.15219759 0.093091920
## [9,] 0.182195935 -0.107035187 -0.383456934 -0.35582354 -0.173904556
## [10,] 0.139845526 -0.261847026 -0.029500328 0.04891606 -0.012412815
## [11,] 0.632668038 -0.288567513 0.317534197 -0.06700698 0.016092119
## [12,] -0.227541942 -0.291879023 0.244136841 0.23583064 -0.217966730
## [13,] -0.267859090 -0.089593498 0.099392942 -0.10261502 -0.180075998
## [14,] -0.221115076 -0.332262448 0.117056493 -0.18854637 0.085112567
## [15,] -0.241936758 -0.100422856 0.077133928 0.08361213 -0.270523975
## [16,] -0.030951589 -0.250718474 0.114857019 0.38950414 0.228055818
## [17,] -0.047479564 -0.115884800 0.194372247 -0.14328796 -0.008230583
## [18,] -0.158943103 -0.011234842 0.080134403 -0.31570696 -0.079638408
## [19,] -0.248555169 0.106712288 -0.084031213 0.10371512 0.207116096
## [20,] -0.089668876 -0.006692896 -0.003772523 0.01268942 -0.038009963
## [21,] 0.061792012 -0.016269186 0.058145635 0.04411098 0.089739294
## [22,] 0.053900046 0.002693166 0.046166436 -0.03104894 0.037312942
## [23,] 0.128078137 -0.255495151 -0.129938352 -0.02811961 0.167284018
## [24,] 0.106474974 -0.111266610 -0.330481013 -0.01675428 -0.051075841
## [25,] 0.139302196 0.247408113 0.232863119 -0.02932091 -0.115920546
## [26,] -0.116252868 0.078332587 -0.100284970 0.10991573 0.044923275
## [27,] 0.090434651 0.274865131 0.242707555 -0.01838060 0.043961003
## [28,] -0.032730308 0.168772071 0.190833064 0.15081338 0.063709535
## [29,] -0.005672237 0.172404863 0.205897086 -0.21020933 -0.011007866
## [30,] -0.057215145 0.263357215 0.114313694 0.02739385 0.068512229
## [31,] -0.043496676 0.064912780 -0.290221174 0.09727219 -0.081129579
## [32,] 0.012516160 0.180299855 -0.032879625 0.18037779 -0.019335082
## [33,] 0.139542059 0.034918905 -0.191909229 0.39721188 -0.097927716
## [34,] 0.234565857 0.136913145 -0.094841135 0.29443187 -0.096470957
## [35,] -0.002453113 0.014414655 0.093082117 -0.02967942 0.015684963
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.000000000 0.384851761 0.000000000 0.0000000000 0.0000000000
## [2,] 0.420741109 -0.386422523 -0.010330719 0.0612036902 0.0056251762
## [3,] -0.242341444 -0.252886693 0.172072384 0.1371780283 -0.0783223242
## [4,] 0.206816175 0.047008190 -0.056956376 0.0274027754 -0.0324873007
## [5,] 0.169586177 -0.057787052 0.133159190 -0.1517664822 -0.0724779729
## [6,] -0.076913244 -0.165238166 0.027723969 0.0120572705 -0.0270704559
## [7,] -0.396951401 -0.107836884 0.006669811 0.0230201734 -0.0159569323
## [8,] -0.102257230 0.014989242 0.071048159 -0.1548474231 -0.0136536695
## [9,] 0.130368075 -0.143982566 -0.216692928 -0.0605217807 -0.0655641267
## [10,] 0.192288230 0.107194430 -0.254170925 -0.1162014900 -0.0704674848
## [11,] -0.093606129 -0.227822411 0.152501544 0.0894805018 0.0428646007
## [12,] 0.229343515 -0.124014957 0.285816959 -0.2117015564 0.1658530272
## [13,] 0.201291055 -0.209399503 -0.266814736 -0.1054907255 -0.0481989797
## [14,] -0.192773795 0.015711319 -0.384557016 0.1274424409 0.2147717337
## [15,] 0.202020566 -0.194823060 0.025308462 0.4288752020 -0.1975016444
## [16,] -0.166137669 0.048366751 -0.203031001 0.0085312306 -0.0008302361
## [17,] 0.014625280 -0.018501356 -0.003257082 -0.2553182265 -0.0542435887
## [18,] -0.149496994 -0.197067865 0.092586591 -0.2006387060 -0.0429215229
## [19,] -0.153508176 -0.147623491 0.391453004 0.0454335040 0.0095025048
## [20,] 0.020957510 -0.012610329 -0.145693140 -0.1199070673 -0.2442218179
## [21,] -0.100082187 0.047108274 -0.194591121 -0.0003998328 -0.2402002314
## [22,] -0.110548605 -0.071181030 -0.099842916 -0.0735512767 0.4612923270
## [23,] -0.205554625 -0.028565299 0.155573471 -0.2570490125 -0.4830136431
## [24,] -0.071414104 -0.165215499 -0.028035907 -0.1582369586 0.4417658004
## [25,] -0.100762046 -0.377743218 -0.084677056 -0.0706421864 -0.0550879724
## [26,] -0.160333066 -0.116922806 -0.188755934 0.0206133127 0.0116815247
## [27,] -0.134036974 -0.058651341 -0.150693679 0.2203714178 0.0131675683
## [28,] -0.056144496 -0.058672698 -0.134050888 -0.2410680512 -0.0732634281
## [29,] 0.015227267 -0.049603478 -0.097656210 0.2385985194 0.0234650755
## [30,] 0.045138760 0.008569188 -0.045837616 -0.4534486016 0.1675979831
## [31,] -0.007283762 -0.156548631 -0.158409670 0.0648060994 0.0259523326
## [32,] 0.031210228 -0.068898503 -0.228133472 -0.0615192159 -0.1926963954
## [33,] -0.073417715 -0.326016691 -0.123851488 -0.0419420419 -0.0082263085
## [34,] 0.270697512 -0.078864321 0.066058632 -0.0046151237 0.0442017383
## [35,] -0.047419118 -0.077123549 -0.134834074 -0.2117122622 -0.1401472815
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000000 0.000000000 0.000000000 0.0000000000 0.00000000
## [2,] 0.024395917 0.021144245 -0.058744021 -0.0004768872 0.01782817
## [3,] -0.070182467 0.063875668 0.312655990 0.2322237189 0.04566223
## [4,] 0.051198119 0.178782177 -0.248756859 -0.2193097902 0.14190531
## [5,] -0.632825962 -0.015671628 0.181663652 0.1172694053 -0.03794858
## [6,] -0.056899391 0.133978770 -0.287868840 -0.1188247793 -0.34235537
## [7,] 0.045534161 0.186695998 -0.225823567 0.0505326209 0.09538565
## [8,] -0.125349748 0.003772482 -0.033761785 0.0098234779 -0.02107847
## [9,] -0.125030652 0.041399590 -0.144747225 -0.1724762040 0.06668450
## [10,] -0.069481806 -0.013223722 -0.044976606 0.3118949840 -0.14799033
## [11,] -0.049436448 -0.033977570 0.065519669 -0.1119505170 -0.19243011
## [12,] 0.256483839 0.007770051 -0.029047907 0.0021486916 0.09532579
## [13,] -0.003836894 0.037375913 0.081000727 0.3320324177 0.09918558
## [14,] 0.034875459 -0.146180450 0.162254448 -0.0134243652 -0.38469980
## [15,] -0.259313464 -0.141326488 0.087749027 -0.3783860927 0.08012702
## [16,] -0.462337802 0.011772425 -0.403387610 -0.0648447962 0.14398275
## [17,] -0.025519094 0.452220686 -0.005944064 -0.0643690659 0.08350437
## [18,] -0.005854750 -0.186329755 -0.436551301 0.1542509510 -0.24063846
## [19,] -0.108132829 -0.014325303 -0.053063541 -0.0002069387 -0.20080518
## [20,] 0.175514324 -0.278261769 -0.151151210 -0.3300938753 -0.08178002
## [21,] -0.017430053 -0.202209623 -0.033525841 0.2905883000 0.10275649
## [22,] -0.187397940 0.090090415 -0.036911366 -0.1181410442 0.23254661
## [23,] -0.010957266 -0.059403067 0.167783998 -0.0659321949 0.20479593
## [24,] 0.054359890 -0.090297487 0.131553979 -0.0899672519 0.18077749
## [25,] 0.163496401 -0.180808435 -0.115359964 0.0917301209 0.39123188
## [26,] -0.068203330 0.249314724 0.043997495 -0.0422064864 0.02271432
## [27,] -0.090017849 -0.204589083 0.044426860 0.0850078871 0.20628878
## [28,] -0.078770410 0.274789306 0.165284208 0.0072056365 -0.07978009
## [29,] 0.001013602 0.298984511 0.062811358 0.0335407148 -0.01580318
## [30,] -0.199854144 -0.357433328 0.176729562 -0.2050031051 -0.07635703
## [31,] 0.085841599 -0.130340896 -0.025344817 0.0898682494 0.01014490
## [32,] 0.087160670 0.096044716 0.198231999 -0.1424136808 -0.11678647
## [33,] 0.064596359 0.028338041 0.127408322 -0.0499650691 -0.30127339
## [34,] -0.061871798 0.043512128 -0.183482231 0.3114669220 -0.15780886
## [35,] 0.095741502 0.169243049 0.060973751 -0.1839912179 -0.05180416
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.000000000 0.0000000000 0.00000000 0.000000000 0.000000000
## [2,] -0.009073969 0.0003171732 0.08232705 0.000528828 0.011556716
## [3,] 0.128537004 -0.0058885138 0.02546009 0.025009471 -0.013836888
## [4,] 0.174014286 -0.0194521122 0.06475553 -0.013467621 -0.199004380
## [5,] -0.043960496 -0.0678335562 -0.04878162 0.012940025 0.083322514
## [6,] 0.085940627 0.0650625148 -0.09879685 0.035054599 -0.035816276
## [7,] 0.201498806 0.0130357044 0.06113948 -0.003220364 -0.099644414
## [8,] 0.057073078 -0.0366632793 0.09483465 -0.037479205 0.165745601
## [9,] 0.158897288 0.0270572174 0.29514683 -0.061391135 -0.002218565
## [10,] 0.039274786 -0.0062968708 -0.33326696 0.063289286 0.058436609
## [11,] -0.036107039 0.0070870323 -0.05192479 0.020018761 -0.023564550
## [12,] 0.166527436 -0.0665511645 0.18021643 0.012298563 -0.198822663
## [13,] 0.087183588 -0.1044326176 -0.07995356 0.041652155 0.064055730
## [14,] 0.052713140 0.0475270165 0.08906493 -0.084733190 0.001862315
## [15,] -0.132153858 0.0759667733 -0.04006060 0.072043864 -0.065794090
## [16,] -0.009721602 0.0397458227 0.01744208 -0.185633959 -0.039120205
## [17,] 0.288019345 0.2626607978 -0.17210556 -0.210667751 0.329440542
## [18,] -0.245459838 -0.1189586199 0.11419165 -0.035165678 -0.223646092
## [19,] 0.210616662 -0.0053569219 -0.34322369 0.058114067 0.078573128
## [20,] 0.047761579 0.0561248837 -0.39264741 0.167377449 0.262515256
## [21,] 0.133114527 -0.0322655971 -0.05716431 0.102243902 -0.201135280
## [22,] 0.118124200 -0.1681154097 -0.17179859 0.406092978 -0.103554103
## [23,] 0.016795399 0.0048559675 -0.04819370 0.045810159 -0.276370043
## [24,] -0.184131738 0.0380556822 -0.28056740 -0.122229062 -0.050605391
## [25,] -0.200310053 0.0394754101 -0.10729237 -0.239529511 0.206152741
## [26,] -0.400014066 -0.3408478835 -0.02326578 -0.019982349 0.086567443
## [27,] 0.386328398 -0.0530717696 0.22191301 0.140163818 0.131721753
## [28,] -0.331327782 0.4935027739 0.21689104 0.175434211 -0.102764378
## [29,] 0.085060067 0.0624815274 -0.30312739 -0.114347472 -0.465624707
## [30,] 0.200576319 0.0572819383 0.04103676 -0.145066592 -0.239973561
## [31,] 0.032998234 0.5151501327 -0.11115780 0.224951504 -0.194494351
## [32,] 0.097682737 -0.3464116049 -0.14479341 -0.358573008 -0.264112615
## [33,] 0.206766195 -0.0180339284 0.21336602 -0.084545918 0.179875562
## [34,] 0.014696356 -0.0752591926 -0.04037718 0.115298128 -0.065962140
## [35,] -0.015456873 -0.2893494342 0.05547220 0.572835542 0.025111462
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.000000000 0.000000000 0.0000000000 0.000000000 0.000000000
## [2,] 0.162258905 -0.030850101 0.0117860459 0.011121455 0.053160139
## [3,] 0.355261828 -0.192097317 0.1958936483 0.053483796 -0.117626996
## [4,] -0.262002520 -0.279394559 0.0204257953 0.111542987 -0.122925762
## [5,] -0.008754180 -0.002994742 0.0936137424 -0.147427529 0.080498366
## [6,] 0.170581911 0.051169738 -0.0926352958 0.224539490 0.179627820
## [7,] 0.180864256 -0.229563264 0.0321070252 0.142585725 -0.053727343
## [8,] -0.070472842 0.268295522 -0.0726320749 -0.054065192 0.115085794
## [9,] -0.190987544 0.034509294 -0.0244481454 0.018706216 -0.058173611
## [10,] -0.141499459 -0.263104860 0.0890882131 0.016682003 -0.014115654
## [11,] -0.177346856 -0.063168978 0.0345886161 0.044848870 -0.005062722
## [12,] -0.072437986 -0.035259199 0.0002767005 -0.162268195 0.123483744
## [13,] -0.151739658 0.240668549 -0.0670089688 0.134921938 0.013024507
## [14,] 0.015942719 -0.093775672 0.1090427516 0.052314205 -0.042101019
## [15,] 0.096594483 -0.088155303 -0.1565309312 0.181940053 0.001799512
## [16,] 0.084751848 0.126139439 0.0328372244 -0.109105421 0.033455273
## [17,] 0.137933249 -0.170253013 -0.0833715498 -0.033879782 0.033859808
## [18,] 0.009118124 -0.044719144 0.0220481290 -0.153061122 0.138505931
## [19,] -0.528970257 -0.057238416 -0.0658302562 0.154734085 -0.036465014
## [20,] 0.212962267 0.016173004 0.0592324326 -0.249176376 0.046725747
## [21,] 0.004158575 0.033127466 -0.5194956761 0.314582658 -0.053748231
## [22,] 0.045553654 0.305494475 0.2744891327 0.151905605 -0.053478617
## [23,] -0.021301323 0.104863435 0.0476010732 -0.158945737 0.053426453
## [24,] 0.086050295 -0.124066212 -0.4258693887 -0.003170302 0.389842717
## [25,] -0.070609465 0.017113176 0.1722566972 0.129694225 -0.250781880
## [26,] -0.225776925 -0.339305309 -0.0782236803 -0.267880610 -0.169714316
## [27,] -0.128144312 -0.280278546 -0.0429697817 -0.301548261 0.445500937
## [28,] -0.101514769 -0.034937560 -0.0168167416 0.171551534 0.201096683
## [29,] 0.032860370 0.185033843 -0.1992836079 -0.450078788 -0.183357876
## [30,] 0.085717108 -0.264572847 -0.0487117849 0.030997532 -0.374335566
## [31,] -0.187531894 -0.013305823 0.2911986388 -0.195450422 0.021694666
## [32,] -0.027034569 0.039594481 0.3450725938 0.213494287 0.401723189
## [33,] -0.036885487 0.313708687 -0.2126393625 -0.193344405 -0.189829748
## [34,] 0.302587616 -0.162658211 0.0229495283 -0.050632233 -0.032198959
## [35,] 0.069407596 -0.096663456 -0.1094345514 -0.011465449 -0.061047640
## [,26] [,27] [,28] [,29] [,30]
## [1,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.011593405 -0.018447518 -0.043979250 0.039723028 0.091888446
## [3,] 0.016925293 -0.118455085 0.183178823 -0.125359029 0.061140699
## [4,] -0.065457582 -0.080369624 0.025114673 -0.186172179 0.034235692
## [5,] 0.133002420 -0.032047695 0.071333732 0.108883411 0.381104891
## [6,] 0.100238890 0.277339775 -0.442424762 -0.004103478 0.224199180
## [7,] -0.119157346 0.015232817 -0.011292451 -0.162534226 0.096014153
## [8,] -0.846888277 0.006314820 0.003340963 -0.047989465 0.064645709
## [9,] 0.094270415 -0.093337525 0.120173315 -0.087086986 0.099114157
## [10,] -0.182221274 0.027474988 0.101535235 -0.174355244 -0.145610273
## [11,] -0.134811697 -0.050681167 -0.035271839 0.042089062 0.051740685
## [12,] -0.078535656 -0.081441537 -0.051330168 0.037673193 0.340892116
## [13,] 0.111540665 0.200994111 -0.238890853 -0.231789080 -0.155661662
## [14,] -0.070401688 0.072019015 -0.089107860 -0.042285388 0.168324448
## [15,] -0.223229374 -0.025185059 -0.015978939 0.045232209 -0.301466221
## [16,] 0.081053164 0.218617658 0.163527141 -0.017224517 0.072691368
## [17,] 0.007486334 -0.117433997 -0.036485806 0.379140536 -0.246673718
## [18,] 0.081736405 -0.211641535 0.176936481 0.121183999 -0.371526487
## [19,] 0.110579595 0.018804819 0.152809913 -0.102065899 -0.014221842
## [20,] 0.041463681 -0.339295396 0.016165336 -0.256228828 0.231189444
## [21,] -0.018876400 -0.342831098 0.002644175 0.324246782 0.251481291
## [22,] 0.009994822 -0.338357383 -0.134904132 0.027410240 -0.155964205
## [23,] 0.026880076 0.144772023 -0.377775839 -0.135442650 -0.160083805
## [24,] 0.014437715 0.132522592 0.110051629 -0.087178341 -0.015666050
## [25,] -0.073834752 0.140509104 0.121566484 -0.030581995 0.138788183
## [26,] -0.052432920 -0.178754722 -0.392485325 0.133844256 0.098946264
## [27,] 0.044844504 0.003371278 -0.066525280 -0.104199687 -0.116089998
## [28,] 0.016047357 -0.233250626 0.102747153 -0.329268111 0.037685881
## [29,] -0.058673383 0.019058053 0.169373420 -0.154488712 0.072337320
## [30,] -0.039387609 0.085553612 -0.091766481 -0.025125959 -0.115289194
## [31,] -0.106308493 0.142573069 -0.055835458 0.462543566 0.039954277
## [32,] -0.054654004 -0.081853180 0.156047623 0.155489210 -0.003278752
## [33,] 0.082792589 -0.123365465 0.060281198 -0.007919405 -0.185917634
## [34,] -0.191264801 -0.014273180 -0.099766943 -0.115011517 -0.115748973
## [35,] -0.025429368 0.432928924 0.388621209 0.167482719 0.032975067
## [,31] [,32] [,33] [,34] [,35]
## [1,] 0.0000000000 0.8752655733 0.000000000 0.000000000 0.000000000
## [2,] 0.0421064783 0.1464448761 0.118557301 -0.088592375 -0.200125102
## [3,] 0.2563046937 0.0972739290 -0.079572134 0.091163785 0.463342144
## [4,] 0.0494762053 -0.0447605343 -0.293865752 -0.550513539 0.282701834
## [5,] -0.0986062327 -0.0009764407 -0.005233972 -0.345871304 -0.184698433
## [6,] 0.1086009741 -0.0020257651 0.235859977 -0.016058425 0.272076703
## [7,] 0.0744287053 0.0541722650 0.087970331 -0.094905423 -0.630439505
## [8,] 0.0771752405 -0.0464235219 -0.057141323 -0.011502197 0.087002840
## [9,] -0.1520258460 -0.0279594910 0.091592145 0.495701865 0.001499022
## [10,] 0.1422913230 0.0011501010 0.557438163 -0.040789890 0.066860013
## [11,] 0.2404869351 0.1477978394 -0.240529968 0.075316126 -0.215269385
## [12,] -0.0153930181 0.2157280616 0.186337810 0.132328918 0.134419941
## [13,] 0.2640369650 0.1530667546 -0.374341257 0.064012947 -0.102650652
## [14,] -0.4521576482 0.1045018111 -0.095436910 -0.138501718 0.044758880
## [15,] -0.0650389140 0.1589414215 0.124790834 0.024638227 -0.002352487
## [16,] 0.1072639309 0.0985232555 -0.115510680 0.127005537 0.184238285
## [17,] -0.1378046524 0.0630702030 -0.075096856 0.022172129 0.018057859
## [18,] 0.0314608072 0.0936350349 -0.017984265 -0.114516975 0.026873909
## [19,] -0.2095343206 0.0616336862 -0.053663299 0.168236995 0.021487735
## [20,] 0.0854806029 0.0179652509 -0.173382917 0.052569221 -0.033617532
## [21,] -0.0409236978 -0.0099211438 -0.025351605 -0.008116187 0.053725588
## [22,] -0.1003590808 0.0296210911 0.134149850 -0.043570873 0.041939859
## [23,] -0.2837767341 0.0366378103 0.065096847 -0.093637123 0.041673975
## [24,] -0.0242114349 0.0300091675 -0.069732756 -0.081443616 0.056365111
## [25,] -0.2687018398 0.1259253135 0.134090998 -0.093008554 0.077630155
## [26,] 0.0824531835 0.0377712503 -0.005698087 0.148564662 0.073436775
## [27,] -0.0337131541 -0.0129478841 0.060734899 -0.006373125 0.013297860
## [28,] -0.0431876822 0.0335551658 0.008501871 0.046186718 0.009641284
## [29,] -0.0524235955 -0.0036114391 0.068696880 0.044663271 -0.062630658
## [30,] 0.1665086749 -0.0406690555 -0.011031265 0.125904829 -0.054295994
## [31,] 0.1208058828 0.0165414162 -0.120282244 0.001911544 0.014766746
## [32,] 0.0001924451 -0.0057185687 -0.050981598 0.074184543 -0.033010250
## [33,] 0.0227902120 0.1207284282 0.136109081 -0.295759750 0.062100202
## [34,] -0.4592456628 -0.0166090752 -0.325832418 0.188077046 0.026796634
## [35,] -0.0565578523 0.0439414169 -0.041454727 0.005571649 0.012948961- Menghitung Cumulative Variance
## [1] 0.8559314 0.9856431 0.9999924 1.0000000 1.0000000 1.0000000 1.0000000
## [8] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## [15] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## [22] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## [29] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000- Menghitung Titik Koordinat 2 Dimensi
## [,1] [,2]
## 1 352342.234 297138.956
## 2 -234226.733 29105.273
## 3 -191432.289 -102601.542
## 4 232451.903 -15569.071
## 5 -55134.996 55850.816
## 6 309468.517 340966.770
## 7 -501528.624 -67288.698
## 8 -366144.313 136042.412
## 9 639304.461 -146206.135
## 10 490701.775 -357673.421
## 11 2219958.961 -394172.626
## 12 -798418.352 -398696.027
## 13 -939886.561 -122381.428
## 14 -775867.223 -453858.302
## 15 -848928.098 -137173.934
## 16 -108605.546 -342472.228
## 17 -166600.298 -158294.381
## 18 -557712.962 -15346.382
## 19 -872151.336 145765.066
## 20 -314637.712 -9142.250
## 21 216821.022 -22223.111
## 22 189129.028 3678.766
## 23 449411.367 -348996.993
## 24 373608.367 -151986.103
## 25 488795.294 337950.397
## 26 -407917.868 106999.437
## 27 317324.728 375455.675
## 28 -114846.866 230536.451
## 29 -19903.224 235498.712
## 30 -200761.324 359736.285
## 31 -152624.803 88668.473
## 32 43917.759 246282.981
## 33 489636.945 47697.941
## 34 823064.460 187018.327
## 35 -8607.691 19689.890- Menghitung Nilai Stress
disparities <- matrix(0, nrow=35, ncol=35)
for (i in 1:35) {
for (j in 1:35) {
disparities[i,j] <- sqrt(sum((fit[i,] - fit[j,])^2))
}
}
stress <- sqrt(sum((dist_matrix - disparities)^2) / sum(dist_matrix^2))
stress## [1] 0.02133579- Visualisasi
plot(fit, type='n', xlab = "Dimensi 1", ylab = "Dimensi 2")
text(fit, labels = Data$'Provinsi')
text(fit, labels = 1:nrow(data)) #Objek dinyatakan dengan angka
Hasil dan Pembahasan
Nilai Eigen
Berdasarkan hasil analisis nilai eigen dan kumulatif keragaman yang dilakukan, dapat disimpulkan bahwa data dapat disederhanakan ke dalam ruang dimensi yang lebih rendah tanpa kehilangan informasi yang signifikan. Dimensi pertama mampu menjelaskan sekitar 85.6% dari total keragaman data. Ketika ditambahkan dimensi kedua, persentase kumulatif keragaman yang terjelaskan meningkat menjadi 98.6%. Hal ini menunjukkan bahwa kedua dimensi utama tersebut telah menangkap hampir seluruh variasi yang ada dalam data. Sehingga visualisasi data akan dilakukan dalam ruang dua dimensi.
Titik Koordinat 2 Dimensi
Setiap objek dalam analisis ini direpresentasikan melalui dua nilai koordinat yang masing-masing mencerminkan dimensi 1 dan dimensi 2. Koordinat ini menggambarkan posisi relatif setiap objek berdasarkan tingkat kemiripannya. Objek-objek dengan nilai koordinat yang saling berdekatan mengindikasikan hubungan yang dekat dalam data asli, sebaliknya objek-objek yang terpisah jauh dalam koordinat merepresentasikan hubungan yang memang tidak mirip sesuai dengan matriks jarak awal.
Koordinat Posisi Pada Plot
Plot MDS menunjukkan tiga kluster utama: 1. Kluster Kesejahteraan Tinggi: Papua, Papua Barat, DKI Jakarta 2. Kluster Kesejahteraan Rendah: Sulawesi Barat, NTT, Maluku 3. Kluster Transisi: Jawa Tengah, Sumatra Barat, Kalimantan Timur
Nilai Stress
Berdasarkan hasil perhitungan yang dilakukan, diperoleh nilai stress sebesar 0.02133579 atau 2.13%. Apabila mengacu pada kriteria kualitas pemetaan, nilai stress tersebut termasuk dalam kategori < 2,5%, yang berarti kualitas representasi model MDS ini dinilai Sempurna.
Kesimpulan
MDS berhasil memetakan 35 provinsi ke dalam ruang dua dimensi dengan akurasi sempurna (stress = 2.13%). Teridentifikasi tiga kluster provinsi berdasarkan karakteristik kesejahteraan pekerja, dengan disparitas yang signifikan antara provinsi di Indonesia bagian timur dan barat.
Saran
Perlu penelitian lanjutan dengan menambahkan variabel-variabel lain yang mempengaruhi kesejahteraan pekerja, serta analisis faktor yang mendasari terbentuknya dimensi-dimensi dalam MDS.
Daftar Pustaka
Nasution, N. B., & Jana, P. (2021). Analisis Multidimensional Scaling Untuk Pemetaan Aplikasi Pembelajaran Daring. Statmat: Jurnal Statistika Dan Matematika, 3(1), 71-81.
Rezky, A. (2022). Pekerja Sejahtera Dataset [Data set]. Kaggle. https://www.kaggle.com/datasets/rezkyyayang/pekerjasejahtera?select=gk.csv