PEMETAAN DISPARITAS AKSES FAKTOR LINGKUNGAN DASAR PENENTU KUALITAS KESEHATAN MASYARAKAT DI PROVINSI JAWA TENGAH TAHUN 2024 MENGGUNAKAN PENDEKATAN MULTIDIMENSIONAL SCALING (MDS)
Umiatun Hayati
2025-12-02
BAB I STUDI KASUS
Kualitas kesehatan masyarakat merupakan indikator holistik yang melampaui sekadar ketiadaan penyakit, melainkan mencakup kesejahteraan fisik, mental, dan sosial (WHO, 1948), yang secara intrinsik ditentukan oleh kondisi lingkungan dasar. Dalam konteks Provinsi Jawa Tengah, studi ini berfokus pada empat faktor lingkungan kritis yang bersumber dari Badan Pusat Statistik (BPS) Jawa Tengah seperti empat variabel berikut:
- X1: Persentase rumah tangga dengan akses terhadap air minum yang layak
- X2: Persentase rumah tangga dengan akses terhadap sanitasi yang layak
- X3: Persentase rumah tangga yang menempati rumah layak huni
- X4: Persentase rumah tangga yang menggunakan energi utama untuk memasak bersih (gas elpiji/listrik)
Keempat indikator ini merupakan prasyarat utama untuk kesehatan, di mana ketersediaan air bersih dan sanitasi (X1 dan X2) sangat vital dalam memutus mata rantai penyakit berbasis lingkungan seperti diare dan stunting (Kementerian Kesehatan RI, 2018). Sementara itu, kondisi rumah layak huni (X3) berkorelasi langsung dengan pencegahan penyakit pernapasan, dan penggunaan energi bersih (X4) merupakan upaya mitigasi terhadap polusi udara dalam ruangan yang menyebabkan penyakit paru kronis (WHO, 2016). Akses terhadap faktor-faktor lingkungan ini diukur secara valid dan resmi melalui data Survei Sosial Ekonomi Nasional (Susenas) BPS, menjadikannya dasar yang kuat untuk perumusan kebijakan.
Meskipun Jawa Tengah memiliki capaian agregat provinsi, permasalahan utamanya terletak pada disparitas spasial atau ketidaksetaraan akses antar 35 Kabupaten/Kota. Perbedaan kondisi geografis, tingkat urbanisasi, dan alokasi sumber daya diyakini menciptakan ketidakmerataan akses terhadap X1 hingga X4 (Firman, 2017). Tantangan ini menuntut adanya pengukuran derajat kesamaan atau ketidakmiripan kondisi lingkungan antar wilayah secara simultan. Dengan menganalisis keempat indikator ini secara bersamaan untuk setiap wilayah, kita dapat mengukur jarak ketidaksamaan multivariat.
Studi kasus mengenai disparitas akses faktor lingkungan dasar di Jawa Tengah didukung kuat oleh penelitian empiris sebelumnya. Relevansi variabel X1 dan X2 telah dibuktikan dalam penelitian yang menunjukkan dampak signifikan faktor lingkungan terhadap status kesehatan spesifik, seperti temuan Utami & Hidayat (2020) mengenai pengaruh air bersih dan sanitasi terhadap status gizi balita. Peran X3 juga dikuatkan oleh studi Setiawan, dkk (2019) yang mengaitkan kualitas perumahan dengan angka kejadian penyakit pernapasan, sementara dampak variabel X4 terhadap kesehatan paru-paru telah diuraikan oleh Wulandari & Suryani (2018) yang fokus pada bahaya polusi udara dalam ruangan. Secara metodologis, pendekatan untuk mengukur derajat ketidakmiripan antardaerah telah memiliki pereseden yang kuat di Indonesia, khususnya di wilayah sekitar Jawa Tengah. Ahadin, dkk. (2021) telah berhasil menerapkan Multidimensional Scaling (MDS) untuk mengelompokkan kabupaten/kota di Jawa Tengah berdasarkan tingkat kesejahteraan, memberikan validasi empiris atas penggunaan teknik ini di wilayah studi. Pendekatan serupa juga diterapkan oleh Santoso, dkk. (2022) dalam pemetaan disparitas pembangunan kesehatan di Jawa Timur. Oleh karena itu, untuk visualisasi dan mengukur jarak ketidaksamaan multivariat antara setiap kabupaten/kota di Jawa Tengah berdasarkan seluruh indikator kesehatan lingkungan (X1, X2, X3, dan X4) secara simultan, diperlukan teknik Multidimensional Scaling (MDS). MDS adalah teknik statistik multivariat yang bertujuan memetakan objek (Kabupaten/Kota) dari ruang dimensi tinggi (empat variabel lingkungan) ke dalam ruang dimensi rendah, di mana jarak antar titik pada peta dimensi rendah mencerminkan sedekat mungkin jarak ketidakmiripan aslinya (Kruskal & Wish, 1978; Hair et. al., 2019). Teknik ini sangat efektif dalam mengidentifikasi clustering atau pengelompokkan alami antar wilayah berdasarkan kondisi lingkungan dasar mereka, memungkinkan perumusan kebijakan kesehatan lingkungan yang lebih merata dan efektif sesuai dengan derajat kesamaan kondisi yang diukur (Santoso et al., 2022). Dengan MDS, pemerintah daerah dapat memvisualisasikan posisi relatif tiap kabupaten/kota dan memprioritaskan intervensi secara tepat sasaran.
BAB II SOURCE CODE
2.1 Library
library(readxl)
library(MASS)
knitr::opts_chunk$set(echo = FALSE)2.2 Data
Data <- read_excel("D:/data mds/Data MDS Analisis Multivariat I.xlsx")
head(Data,35)## # A tibble: 35 × 5
## `Kabupaten/Kota` Persentase Rumah Tangga denga…¹ Persentase Rumah Tan…²
## <chr> <dbl> <dbl>
## 1 Kabupaten Cilacap 93.3 83.2
## 2 Kabupaten Banyumas 94.3 83.2
## 3 Kabupaten Purbalingga 88.2 82.0
## 4 Kabupaten Banjarnegara 91.8 52.4
## 5 Kabupaten Kebumen 87.3 93.4
## 6 Kabupaten Purworejo 90.0 84.6
## 7 Kabupaten Wonosobo 95.2 63.8
## 8 Kabupaten Magelang 93.3 83.8
## 9 Kabupaten Boyolali 94.8 88.3
## 10 Kabupaten Klaten 99.5 97.9
## # ℹ 25 more rows
## # ℹ abbreviated names:
## # ¹`Persentase Rumah Tangga dengan Akses terhadap Air Minum yang Layak`,
## # ²`Persentase Rumah Tangga dengan Akses terhadap Sanitasi yang Layak`
## # ℹ 2 more variables:
## # `Persentase Rumah Tangga yang Menempati Rumah Layak Huni` <dbl>,
## # `Persentase Rumah Tangga yang Menggunakan Energi Utama untuk Memasak Bersih (Gas/Listrik)` <dbl>datamds <- Data[,-1]
knitr::opts_chunk$set(echo = FALSE)2.3 Menghitung Jarak
dist_matrix <- as.matrix(dist(datamds))
dist_matrix## 1 2 3 4 5 6 7
## 1 0.000000 7.159085 5.866669 36.31986 18.046532 21.292569 31.67673
## 2 7.159085 0.000000 7.769447 40.52527 15.317043 21.930663 36.19992
## 3 5.866669 7.769447 0.000000 36.87579 15.986673 20.296229 32.74508
## 4 36.319855 40.525269 36.875790 0.00000 52.013250 45.027567 22.69421
## 5 18.046532 15.317043 15.986673 52.01325 0.000000 17.965472 43.23952
## 6 21.292569 21.930663 20.296229 45.02757 17.965472 0.000000 29.90767
## 7 31.676733 36.199916 32.745076 22.69421 43.239520 29.907673 0.00000
## 8 19.519380 20.921465 19.625662 42.54416 19.602584 4.401625 27.02854
## 9 13.155843 9.421927 13.249174 46.86813 9.287265 16.234854 38.07042
## 10 37.749906 31.604112 37.114410 70.39598 25.525617 36.420677 61.97302
## 11 35.502611 29.321953 34.911001 68.32562 23.677075 35.061299 60.25959
## 12 35.027449 31.841509 34.565384 64.60214 22.336963 21.750372 49.79664
## 13 37.273479 31.570377 36.747814 69.93003 24.321207 33.697028 60.08031
## 14 24.454120 19.282440 24.656143 58.76761 13.898694 25.355423 49.91243
## 15 13.354632 16.454291 13.913662 45.15524 18.169037 27.589170 41.26160
## 16 11.754446 17.253304 16.375414 40.38086 22.734201 24.301718 33.03182
## 17 19.438750 14.892397 19.644531 54.68990 9.652652 22.733475 46.40902
## 18 27.212155 21.334969 27.139937 61.42774 17.246863 30.601430 54.32117
## 19 35.188554 28.775020 34.629737 67.72458 24.370892 36.211443 60.54203
## 20 17.375437 19.772210 16.789830 23.59543 32.462220 32.871485 29.90464
## 21 24.848074 18.880606 24.466822 59.18214 15.755244 30.462480 53.26224
## 22 16.076872 11.436184 17.067613 47.66420 14.244111 18.442204 38.72670
## 23 15.231205 18.175151 17.031259 27.29348 28.296567 20.709580 18.85441
## 24 9.955029 7.480916 11.644303 40.98949 15.522993 16.708821 32.79605
## 25 18.781022 22.070621 20.118504 19.53009 34.333201 28.832636 19.55468
## 26 17.429487 10.371138 16.887279 47.39071 16.943167 25.197553 42.75910
## 27 8.087299 1.379819 8.552087 41.90247 14.369214 21.967287 37.31369
## 28 21.017448 14.100092 20.845971 52.69528 17.355766 28.339453 47.82061
## 29 16.160724 9.187573 15.359661 48.45375 14.245073 25.416988 44.05492
## 30 21.338943 14.687784 21.713058 53.54015 17.899922 28.962869 48.42148
## 31 15.929818 9.344870 16.936343 47.42610 17.856758 26.802026 43.14937
## 32 29.485885 23.375284 29.319130 63.22591 19.571753 32.680350 56.36106
## 33 19.361679 15.960141 21.516547 53.67562 19.873392 32.885369 49.88697
## 34 24.982712 18.193224 24.798433 56.87389 19.179463 30.875515 51.61966
## 35 29.719186 23.069753 29.404044 61.98063 21.714260 34.137435 56.31073
## 8 9 10 11 12 13 14
## 1 19.519380 13.155843 37.749906 35.502611 35.02745 37.273479 24.454120
## 2 20.921465 9.421927 31.604112 29.321953 31.84151 31.570377 19.282440
## 3 19.625662 13.249174 37.114410 34.911001 34.56538 36.747814 24.656143
## 4 42.544157 46.868131 70.395976 68.325618 64.60214 69.930027 58.767609
## 5 19.602584 9.287265 25.525617 23.677075 22.33696 24.321207 13.898694
## 6 4.401625 16.234854 36.420677 35.061299 21.75037 33.697028 25.355423
## 7 27.028537 38.070416 61.973015 60.259588 49.79664 60.080315 49.912433
## 8 0.000000 16.066543 37.835978 36.364826 23.75670 35.207221 25.985477
## 9 16.066543 0.000000 25.868278 23.835683 22.60891 24.712131 12.603182
## 10 37.835978 25.868278 0.000000 2.422107 22.58528 4.663732 14.310800
## 11 36.364826 23.835683 2.422107 0.000000 22.55437 5.629085 12.317719
## 12 23.756704 22.608910 22.585283 22.554374 0.00000 18.203005 19.007257
## 13 35.207221 24.712131 4.663732 5.629085 18.20301 0.000000 13.377048
## 14 25.985477 12.603182 14.310800 12.317719 19.00726 13.377048 0.000000
## 15 26.925026 19.258676 39.886486 37.664211 38.61937 39.612258 26.868588
## 16 21.659931 19.043645 42.587869 40.464189 37.24845 41.474235 28.333425
## 17 23.143142 8.542166 19.574407 17.460298 21.48744 18.819559 5.737857
## 18 31.312276 16.730344 11.699462 9.360545 23.59013 12.753188 5.900153
## 19 37.361374 24.119277 4.465031 2.786557 24.91128 8.314018 12.998935
## 20 31.247256 28.071541 49.991333 47.751611 49.11873 50.315721 38.865077
## 21 31.145212 15.683144 15.024200 12.644311 26.20220 16.431318 7.947100
## 22 17.742548 5.738658 24.067181 22.116686 21.91835 22.947706 11.852451
## 23 17.596619 21.403649 45.151405 43.222732 37.93464 43.987878 33.068487
## 24 15.069930 6.857740 30.812822 28.768264 26.94971 29.821918 18.060581
## 25 26.106831 27.967735 51.246005 49.185825 46.32310 50.690214 39.519337
## 26 25.066631 11.316545 23.572518 21.381296 28.46650 24.219389 14.626832
## 27 21.108420 8.587701 30.363086 28.071640 30.99652 30.351899 18.004166
## 28 28.424688 13.274106 19.093756 16.781880 27.74156 20.313865 11.267897
## 29 25.485537 10.304378 23.448134 21.122244 28.83898 24.202773 13.446687
## 30 28.850555 13.557924 18.763664 16.430140 27.69881 19.948150 10.480902
## 31 26.039357 11.502604 24.811020 22.502327 30.14887 25.520178 14.480287
## 32 33.465558 19.044679 9.751123 7.387544 24.50653 11.606326 8.057903
## 33 32.023635 17.336061 27.520153 25.215142 34.60557 28.480316 16.772495
## 34 31.208622 16.202855 15.367612 13.062806 27.18477 17.138573 10.354202
## 35 34.795071 20.134393 11.152838 8.929871 27.16938 13.870753 11.150982
## 15 16 17 18 19 20 21 22
## 1 13.35463 11.75445 19.438750 27.212155 35.188554 17.37544 24.848074 16.076872
## 2 16.45429 17.25330 14.892397 21.334969 28.775020 19.77221 18.880606 11.436184
## 3 13.91366 16.37541 19.644531 27.139937 34.629737 16.78983 24.466822 17.067613
## 4 45.15524 40.38086 54.689903 61.427742 67.724582 23.59543 59.182142 47.664204
## 5 18.16904 22.73420 9.652652 17.246863 24.370892 32.46222 15.755244 14.244111
## 6 27.58917 24.30172 22.733475 30.601430 36.211443 32.87148 30.462480 18.442204
## 7 41.26160 33.03182 46.409021 54.321165 60.542034 29.90464 53.262240 38.726696
## 8 26.92503 21.65993 23.143142 31.312276 37.361374 31.24726 31.145212 17.742548
## 9 19.25868 19.04364 8.542166 16.730344 24.119277 28.07154 15.683144 5.738658
## 10 39.88649 42.58787 19.574407 11.699462 4.465031 49.99133 15.024200 24.067181
## 11 37.66421 40.46419 17.460298 9.360545 2.786557 47.75161 12.644311 22.116686
## 12 38.61937 37.24845 21.487443 23.590134 24.911285 49.11873 26.202202 21.918353
## 13 39.61226 41.47424 18.819559 12.753188 8.314018 50.31572 16.431318 22.947706
## 14 26.86859 28.33343 5.737857 5.900153 12.998935 38.86508 7.947100 11.852451
## 15 0.00000 13.28633 21.186326 28.788911 37.518290 26.12632 25.887785 23.973506
## 16 13.28633 0.00000 23.311941 31.825663 40.548126 26.02488 30.130705 21.898041
## 17 21.18633 23.31194 0.000000 9.428160 17.827392 34.57345 8.838179 10.080823
## 18 28.78891 31.82566 9.428160 0.000000 9.030399 40.36958 4.140942 15.879742
## 19 37.51829 40.54813 17.827392 9.030399 0.000000 46.83695 11.868593 22.249533
## 20 26.12632 26.02488 34.573452 40.369580 46.836950 0.00000 37.480659 29.557168
## 21 25.88778 30.13071 8.838179 4.140942 11.868593 37.48066 0.000000 15.726850
## 22 23.97351 21.89804 10.080823 15.879742 22.249533 29.55717 15.726850 0.000000
## 23 27.74001 20.76042 29.595753 36.748200 43.108114 17.83087 35.441518 21.478114
## 24 20.51413 17.16680 14.553082 21.765794 28.731925 23.42888 20.624990 7.094082
## 25 30.50629 24.97635 35.761602 42.346870 48.674084 12.22688 40.439985 28.243849
## 26 25.01131 26.42620 13.200644 15.197269 20.448968 26.67607 13.437626 9.636078
## 27 16.35479 17.57779 13.587560 20.006344 27.538942 21.06612 17.538449 10.728159
## 28 26.21170 28.48006 11.194378 10.177293 15.581008 31.51793 8.511986 11.507124
## 29 21.57043 24.68579 10.846142 13.700620 20.240887 26.84265 11.025960 10.630776
## 30 26.17706 27.99073 10.654168 9.293046 15.234185 32.52086 7.955684 11.520273
## 31 22.87999 23.55020 12.422790 14.947913 21.467981 26.63405 13.028027 9.812049
## 32 31.23133 34.35012 12.037898 2.658458 6.603249 42.07080 5.748374 17.793145
## 33 18.62022 21.67557 13.711200 16.086746 24.289634 32.50590 13.671920 18.191899
## 34 29.16390 31.72210 12.142319 7.499620 11.583687 35.68771 6.867452 14.185144
## 35 32.70667 35.78074 14.525667 6.370071 6.933087 40.68413 7.432442 18.226327
## 23 24 25 26 27 28 29
## 1 15.231205 9.955029 18.781022 17.429487 8.087299 21.017448 16.160724
## 2 18.175151 7.480916 22.070621 10.371138 1.379819 14.100092 9.187573
## 3 17.031259 11.644303 20.118504 16.887279 8.552087 20.845971 15.359661
## 4 27.293477 40.989493 19.530092 47.390713 41.902469 52.695284 48.453750
## 5 28.296567 15.522993 34.333201 16.943167 14.369214 17.355766 14.245073
## 6 20.709580 16.708821 28.832636 25.197553 21.967287 28.339453 25.416988
## 7 18.854405 32.796052 19.554677 42.759104 37.313695 47.820607 44.054920
## 8 17.596619 15.069930 26.106831 25.066631 21.108420 28.424688 25.485537
## 9 21.403649 6.857740 27.967735 11.316545 8.587701 13.274106 10.304378
## 10 45.151405 30.812822 51.246005 23.572518 30.363086 19.093756 23.448134
## 11 43.222732 28.768264 49.185825 21.381296 28.071640 16.781880 21.122244
## 12 37.934636 26.949705 46.323098 28.466503 30.996519 27.741559 28.838984
## 13 43.987878 29.821918 50.690214 24.219389 30.351899 20.313865 24.202773
## 14 33.068487 18.060581 39.519337 14.626832 18.004166 11.267897 13.446687
## 15 27.740011 20.514127 30.506291 25.011313 16.354785 26.211698 21.570433
## 16 20.760419 17.166799 24.976353 26.426195 17.577787 28.480065 24.685789
## 17 29.595753 14.553082 35.761602 13.200644 13.587560 11.194378 10.846142
## 18 36.748200 21.765794 42.346870 15.197269 20.006344 10.177293 13.700620
## 19 43.108114 28.731925 48.674084 20.448968 27.538942 15.581008 20.240887
## 20 17.830866 23.428884 12.226880 26.676068 21.066120 31.517933 26.842653
## 21 35.441518 20.624990 40.439985 13.437626 17.538449 8.511986 11.025960
## 22 21.478114 7.094082 28.243849 9.636078 10.728159 11.507124 10.630776
## 23 0.000000 15.143388 9.038916 24.374105 19.312908 29.413036 25.803252
## 24 15.143388 0.000000 21.720704 11.950314 7.600566 15.750775 12.523985
## 25 9.038916 21.720704 0.000000 28.628493 23.416618 33.869209 29.932294
## 26 24.374105 11.950314 28.628493 0.000000 9.650813 5.728988 4.442139
## 27 19.312908 7.600566 23.416618 9.650813 0.000000 13.026485 8.100160
## 28 29.413036 15.750775 33.869209 5.728988 13.026485 0.000000 5.683740
## 29 25.803252 12.523985 29.932294 4.442139 8.100160 5.683740 0.000000
## 30 29.980769 16.058857 34.586418 7.309343 13.572454 2.274335 6.983960
## 31 24.457618 11.616234 28.543246 5.222040 8.510870 6.313193 5.396712
## 32 38.678886 23.849470 44.151967 16.398085 22.072304 11.124743 15.283841
## 33 32.212293 19.499703 35.876948 17.164929 14.975386 14.729212 14.106389
## 34 33.335655 19.391526 38.002180 9.704334 17.056134 4.240873 9.589260
## 35 38.219843 24.015449 43.094362 14.692617 21.872074 9.335443 14.346268
## 30 31 32 33 34 35
## 1 21.338943 15.929818 29.485885 19.36168 24.982712 29.719186
## 2 14.687784 9.344870 23.375284 15.96014 18.193224 23.069753
## 3 21.713058 16.936343 29.319130 21.51655 24.798433 29.404044
## 4 53.540148 47.426096 63.225908 53.67562 56.873885 61.980633
## 5 17.899922 17.856758 19.571753 19.87339 19.179463 21.714260
## 6 28.962869 26.802026 32.680350 32.88537 30.875515 34.137435
## 7 48.421484 43.149374 56.361059 49.88697 51.619662 56.310725
## 8 28.850555 26.039357 33.465558 32.02364 31.208622 34.795071
## 9 13.557924 11.502604 19.044679 17.33606 16.202855 20.134393
## 10 18.763664 24.811020 9.751123 27.52015 15.367612 11.152838
## 11 16.430140 22.502327 7.387544 25.21514 13.062806 8.929871
## 12 27.698807 30.148872 24.506526 34.60557 27.184766 27.169384
## 13 19.948150 25.520178 11.606326 28.48032 17.138573 13.870753
## 14 10.480902 14.480287 8.057903 16.77250 10.354202 11.150982
## 15 26.177064 22.879989 31.231334 18.62022 29.163897 32.706669
## 16 27.990725 23.550204 34.350124 21.67557 31.722104 35.780735
## 17 10.654168 12.422790 12.037898 13.71120 12.142319 14.525667
## 18 9.293046 14.947913 2.658458 16.08675 7.499620 6.370071
## 19 15.234185 21.467981 6.603249 24.28963 11.583687 6.933087
## 20 32.520856 26.634048 42.070805 32.50590 35.687705 40.684132
## 21 7.955684 13.028027 5.748374 13.67192 6.867452 7.432442
## 22 11.520273 9.812049 17.793145 18.19190 14.185144 18.226327
## 23 29.980769 24.457618 38.678886 32.21229 33.335655 38.219843
## 24 16.058857 11.616234 23.849470 19.49970 19.391526 24.015449
## 25 34.586418 28.543246 44.151967 35.87695 38.002180 43.094362
## 26 7.309343 5.222040 16.398085 17.16493 9.704334 14.692617
## 27 13.572454 8.510870 22.072304 14.97539 17.056134 21.872074
## 28 2.274335 6.313193 11.124743 14.72921 4.240873 9.335443
## 29 6.983960 5.396712 15.283841 14.10639 9.589260 14.346268
## 30 0.000000 6.323116 10.332526 13.34832 4.079828 8.921026
## 31 6.323116 0.000000 16.418669 12.82300 10.181012 15.200582
## 32 10.332526 16.418669 0.000000 17.88771 7.620807 4.668126
## 33 13.348322 12.822999 17.887705 0.00000 16.086905 18.783892
## 34 4.079828 10.181012 7.620807 16.08690 0.000000 5.128674
## 35 8.921026 15.200582 4.668126 18.78389 5.128674 0.000000knitr::opts_chunk$set(echo = FALSE)2.4 Mencari Nilai Eigen
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
eigen_result <- eigen(B)
eigen_result## eigen() decomposition
## $values
## [1] 9.539935e+03 1.955325e+03 1.039309e+03 2.861340e+02 4.582953e-13
## [6] 3.186432e-13 1.717025e-13 1.705783e-13 1.591931e-13 1.528205e-13
## [11] 1.137275e-13 8.411095e-14 7.991109e-14 4.123126e-14 3.759258e-14
## [16] 2.031698e-14 5.341296e-15 -1.167416e-14 -1.208535e-14 -2.979636e-14
## [21] -5.884407e-14 -6.632939e-14 -9.104860e-14 -9.192980e-14 -1.008422e-13
## [26] -1.079787e-13 -2.070162e-13 -3.224767e-13 -4.459823e-13 -5.073524e-13
## [31] -5.481097e-13 -9.197147e-13 -1.190282e-12 -1.299842e-12 -2.214020e-12
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.118039123 -0.07582044 -0.152008294 1.323229e-02 0.829394449
## [2,] -0.059104999 -0.10065033 -0.028477253 -4.742660e-02 0.196032356
## [3,] -0.111077406 -0.06548711 -0.125973747 -3.265884e-01 0.016450260
## [4,] -0.462491071 -0.13684320 0.260737285 -8.760014e-02 0.023780856
## [5,] 0.029716888 0.09706572 -0.236773030 -4.109801e-01 -0.015203387
## [6,] -0.083256509 0.38622584 -0.070899833 -2.344875e-01 -0.040602926
## [7,] -0.371594499 0.31486373 0.132190474 1.772414e-01 0.226401000
## [8,] -0.105728925 0.36017338 -0.066703624 -1.961308e-02 0.013506319
## [9,] -0.004941140 0.07302494 -0.067485020 -1.937889e-02 -0.004003782
## [10,] 0.251315008 0.06251161 0.134163871 -4.773657e-02 0.040795253
## [11,] 0.230974053 0.03495011 0.113908578 -4.255916e-02 0.137822578
## [12,] 0.129595789 0.48579958 0.003431773 -5.464042e-06 0.165381506
## [13,] 0.238646634 0.15978476 0.101897243 -5.950048e-04 0.175215918
## [14,] 0.122114281 0.06061281 -0.059113584 1.055002e-01 -0.023497259
## [15,] -0.080542947 -0.14122136 -0.526991478 -1.776923e-01 0.050173645
## [16,] -0.133382663 -0.01131803 -0.425484333 4.314927e-01 0.021078888
## [17,] 0.075275811 0.02840582 -0.149144112 3.210089e-02 -0.055347609
## [18,] 0.157193777 -0.04335238 -0.029982482 4.476123e-02 0.006280604
## [19,] 0.227858843 -0.02374412 0.143659919 -3.501966e-02 0.288008436
## [20,] -0.236695098 -0.26201940 0.105725884 -3.146506e-01 0.038230797
## [21,] 0.133857180 -0.10421992 -0.061094239 -6.898092e-02 0.024394073
## [22,] 0.009286398 0.07608412 0.067901567 1.848352e-01 0.012681010
## [23,] -0.208987873 0.08540501 0.147684328 1.896570e-01 -0.095348679
## [24,] -0.060419139 0.04741568 0.026819165 1.386015e-01 0.002754467
## [25,] -0.269228530 -0.06045798 0.204239771 1.028447e-01 -0.005312436
## [26,] 0.021641021 -0.09744711 0.179845671 -7.617262e-02 0.051312619
## [27,] -0.045499618 -0.09771241 -0.039272134 -4.761310e-02 0.073095525
## [28,] 0.075003586 -0.12307507 0.128541494 -5.599622e-04 0.050686526
## [29,] 0.028722846 -0.12349188 0.053722026 -1.460044e-01 0.019202263
## [30,] 0.081935578 -0.12608836 0.099853312 1.153020e-01 0.028296353
## [31,] 0.018080836 -0.14387953 0.092872163 1.533325e-01 0.049213172
## [32,] 0.178458306 -0.05748992 0.017613719 3.935239e-02 0.033283412
## [33,] 0.052798577 -0.24351871 -0.251399520 3.433948e-01 -0.011696528
## [34,] 0.118067558 -0.12030274 0.139680578 2.227130e-02 0.155971176
## [35,] 0.170446571 -0.11418311 0.136313862 9.744518e-03 0.013239261
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.0000000000 0.000000000 0.00000000 0.0000000000 0.00000000
## [2,] 0.0072024361 0.063729813 -0.04523615 0.0069812350 -0.02305323
## [3,] 0.0967490618 0.101562237 0.12959322 0.0319372675 0.36601590
## [4,] -0.1432474421 0.056513727 -0.07226684 0.1036298913 0.02896457
## [5,] -0.0736351741 0.062930481 -0.19487933 0.1502662172 -0.05712028
## [6,] 0.0357057573 -0.017837619 -0.13874511 -0.0643831297 -0.06872758
## [7,] -0.0476597482 -0.043662145 -0.22443295 -0.0205473370 0.05557511
## [8,] -0.1880291970 0.178056316 0.18353162 -0.0392319411 -0.12598655
## [9,] -0.0008146576 0.372145022 -0.38074393 -0.2742991905 -0.10620001
## [10,] 0.2069369265 0.040100242 -0.09151897 -0.1269809909 0.16715489
## [11,] -0.1876683018 -0.022589912 0.21320904 0.1464538342 -0.22332996
## [12,] 0.0594547436 0.004993540 0.19530981 -0.1159028308 0.37705369
## [13,] 0.1061797833 -0.032888989 -0.24394104 -0.1389095498 -0.18458287
## [14,] -0.2421974663 0.167868182 -0.05106672 -0.1636972756 0.01504913
## [15,] -0.0074462111 -0.144139988 -0.08518133 -0.0783930413 0.04868265
## [16,] 0.2268058048 -0.003089225 0.07137408 0.1052520777 -0.24094610
## [17,] -0.2734301008 0.131696484 -0.22139862 -0.1910838173 -0.03734609
## [18,] 0.0090664542 0.155713544 -0.07211735 0.2880957980 0.14867728
## [19,] -0.1342531257 0.021604055 0.05697857 0.1023456005 0.02553677
## [20,] 0.0386944061 0.159010047 0.11412836 -0.0888297179 -0.09023369
## [21,] -0.1363884425 -0.275044873 0.05934163 -0.1904788473 -0.11052147
## [22,] 0.2566606703 0.187378005 0.07564117 0.0110571694 -0.19445173
## [23,] -0.1111895152 0.326339565 0.01512120 0.1594899177 0.08450965
## [24,] 0.2260024879 -0.336073505 0.02976357 0.1398463985 0.05491173
## [25,] -0.0829503538 -0.336895351 -0.31050751 -0.2113839274 0.06719779
## [26,] 0.1412823395 -0.031016192 0.12875318 -0.2009105710 0.30408954
## [27,] 0.2757192755 0.357268067 0.02109908 0.1748814930 -0.08766966
## [28,] -0.3316796560 0.185051398 0.07377182 0.0095773560 -0.01216994
## [29,] 0.2712919800 0.091574753 -0.12795571 -0.2437538268 -0.14281548
## [30,] 0.2771319749 0.165886896 0.01127316 -0.3443221867 0.10890418
## [31,] 0.0846618611 0.139500772 0.01303601 -0.0363208613 -0.02905607
## [32,] 0.0518707247 0.029377977 -0.48039739 0.4574532345 0.30415915
## [33,] -0.2671367912 0.098654301 -0.01748889 -0.1987536565 0.36271511
## [34,] -0.1891048388 -0.035938061 0.04325967 0.0007018276 -0.15832774
## [35,] 0.0140029063 -0.112768136 -0.27182311 0.0829680984 -0.17940535
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] -0.031434470 -0.059174222 0.018596714 0.058309442 0.034530348
## [3,] -0.095965539 0.023345686 -0.061003282 0.308944865 0.334631060
## [4,] 0.148540420 0.160804765 0.174967184 0.029624347 -0.101929236
## [5,] 0.116681646 -0.195704631 0.457157176 -0.058475506 -0.226094330
## [6,] -0.046244789 -0.181005226 -0.022610682 -0.049443398 -0.143391467
## [7,] 0.017869505 -0.154787466 -0.052552802 -0.138314668 0.010421056
## [8,] -0.003299134 0.328554951 0.015811479 -0.114465094 -0.019605536
## [9,] -0.068208323 0.132131844 0.164483196 0.278519035 0.029993632
## [10,] 0.014385677 0.214734778 -0.038354935 -0.115436739 0.035208708
## [11,] 0.076702770 0.383393319 -0.189875985 -0.045544331 -0.032872924
## [12,] 0.069369050 -0.077858016 -0.078123022 -0.042579882 -0.024045492
## [13,] -0.156082633 0.344988383 0.083334047 0.223801897 0.040068246
## [14,] -0.185062868 -0.279808136 -0.061770272 0.095749293 0.089399363
## [15,] -0.139390238 0.245866894 -0.103132616 0.124430251 -0.087723513
## [16,] 0.240075410 -0.069219955 0.135948947 -0.084037765 0.207369930
## [17,] 0.371965521 0.163720652 -0.058698590 -0.236939724 0.134481693
## [18,] 0.314979982 0.123299780 0.169359128 0.159306863 -0.111316980
## [19,] 0.156613482 -0.254695617 -0.008628062 -0.010195751 -0.151770256
## [20,] 0.164470045 0.054995195 -0.289713411 -0.120570270 -0.154304775
## [21,] 0.033158360 -0.034313521 -0.029974979 0.041286053 -0.366780322
## [22,] -0.033018869 -0.079441554 -0.056438593 0.196129502 -0.426479729
## [23,] 0.140294610 0.051945357 -0.073412773 0.341265776 -0.104391372
## [24,] -0.091700791 0.214499791 0.298014741 0.149852401 -0.260164020
## [25,] -0.121973069 0.081069371 -0.101551497 0.013215858 -0.002417601
## [26,] 0.138115851 0.003058757 0.383695376 -0.031766209 0.087534862
## [27,] -0.384632136 -0.044416656 -0.159723631 -0.108371769 -0.046657954
## [28,] -0.396343754 -0.017979456 0.294214036 -0.188871957 -0.117383284
## [29,] 0.283352507 -0.061372629 -0.043822819 -0.161788046 -0.064267508
## [30,] 0.105306844 -0.018763233 -0.023266400 0.028219395 -0.146508704
## [31,] -0.168041289 0.114401851 0.308920353 -0.380506174 0.183441861
## [32,] 0.007323018 0.110945057 -0.215221679 -0.198191312 -0.058961321
## [33,] -0.030094057 -0.005283383 -0.047013002 0.009890634 -0.306004750
## [34,] 0.144847366 -0.078463053 0.075849553 0.371771109 0.268643212
## [35,] -0.021312807 -0.277983912 -0.077684993 0.111326002 0.125310616
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.00000000 0.000000000 0.00000000 0.000000e+00 0.000000000
## [2,] 0.08817537 0.004071534 -0.04208785 -1.080437e-02 -0.023325027
## [3,] 0.10909443 -0.213309930 -0.05013823 2.968308e-01 -0.046495896
## [4,] 0.21611701 -0.157183220 -0.04077158 -1.235090e-03 -0.035694263
## [5,] 0.04233653 -0.254488638 0.13116397 -1.006363e-03 -0.154482729
## [6,] 0.02591133 0.263313904 0.04277685 -1.713563e-01 -0.022369897
## [7,] -0.23466941 0.110823058 -0.02022239 4.672694e-05 0.022210231
## [8,] -0.08377976 -0.239387700 -0.09863663 1.346650e-03 -0.072259822
## [9,] -0.10279970 -0.015382501 0.01185390 -6.514874e-02 0.204599994
## [10,] -0.16008126 -0.072728471 0.04479033 -7.360518e-02 -0.083768409
## [11,] -0.18714806 -0.193087122 0.03200440 5.807409e-02 -0.106794522
## [12,] 0.12536208 0.091794403 -0.03915623 1.411576e-01 0.221063080
## [13,] 0.52820358 0.165710587 0.02091841 4.152496e-02 -0.071344773
## [14,] -0.01588569 -0.353705266 -0.17898709 1.093482e-01 0.084882082
## [15,] -0.35792056 0.064913841 -0.06311970 7.981633e-02 0.063139707
## [16,] 0.12289850 -0.077498773 0.19182056 5.579403e-02 0.051058639
## [17,] 0.09865560 -0.050455583 -0.05093971 -9.713546e-02 -0.141579402
## [18,] -0.25714195 0.353918336 -0.30877058 -1.096406e-03 0.198520739
## [19,] 0.04268038 -0.256703738 -0.03325212 -3.941309e-02 0.015559420
## [20,] 0.23930986 0.213377634 0.08956421 4.410602e-02 0.193642664
## [21,] 0.05460157 -0.128976806 -0.24134440 -2.056052e-01 0.362058907
## [22,] -0.07929784 0.015021415 -0.13973113 3.283000e-01 -0.452010132
## [23,] -0.01087779 -0.097533833 -0.02417405 -3.265387e-02 0.218534183
## [24,] 0.04779782 -0.186780765 0.03315805 1.995730e-02 0.179832722
## [25,] -0.17812953 -0.149683706 -0.05513469 4.811142e-02 -0.140031831
## [26,] -0.11301218 0.035142638 -0.15702552 -2.416241e-01 -0.306301500
## [27,] -0.04011004 -0.071542148 -0.18050164 -4.973523e-01 -0.092592624
## [28,] -0.15074969 0.242411350 0.35036864 3.197478e-01 0.097272598
## [29,] -0.14286641 -0.010267139 -0.15523408 4.193828e-01 -0.001496653
## [30,] -0.13629058 -0.250026313 0.49304628 -1.277337e-01 0.199661498
## [31,] 0.05018486 -0.035154547 -0.36672079 1.052447e-01 0.249744826
## [32,] 0.03137453 -0.107029018 0.18765294 5.615487e-02 0.004115593
## [33,] 0.25144181 0.130986070 -0.06800014 -3.002940e-02 -0.267572058
## [34,] -0.19029553 0.171594332 0.17808798 -1.723572e-01 -0.113359775
## [35,] 0.04784853 -0.046281328 -0.21009651 1.204024e-01 0.083910046
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.000000000 0.00000000 0.000000000 0.000000000 0.000000000
## [2,] 0.091903633 -0.11440520 -0.003957855 -0.261633037 0.043131986
## [3,] -0.112191210 0.01055355 0.260096765 0.231431418 0.165745917
## [4,] 0.010426418 -0.14065242 -0.046271486 -0.267045872 -0.056200466
## [5,] -0.059865349 0.08014523 0.002327399 0.233765876 0.148307243
## [6,] 0.050596955 0.03203347 -0.138471657 0.126532055 -0.018515206
## [7,] -0.007335903 0.04533141 0.040965726 0.191304982 0.065375404
## [8,] -0.208782326 -0.23444178 -0.072454581 -0.294259550 0.156550475
## [9,] 0.133170201 -0.21424690 -0.003666309 0.087749457 -0.097315949
## [10,] -0.106730100 -0.32797243 0.142821197 0.114181240 0.077106988
## [11,] 0.066708752 0.12325474 -0.168370546 0.434291626 -0.142500268
## [12,] 0.090979555 -0.14307975 0.087381194 0.019203666 -0.056695131
## [13,] -0.148399781 0.28160063 -0.122873883 -0.011126807 -0.006132069
## [14,] -0.228372543 -0.14475574 -0.374231792 -0.016735649 -0.326005004
## [15,] 0.152091159 0.14488511 -0.160752075 -0.143415372 0.011624926
## [16,] -0.204614868 -0.13166209 -0.087027808 0.235608300 -0.042940922
## [17,] 0.067288943 0.03908738 0.469349389 0.021465084 -0.073107283
## [18,] -0.520144972 0.08934757 0.038157229 -0.079574171 -0.025238400
## [19,] -0.032891620 0.26343578 0.099720983 -0.160030447 -0.090186027
## [20,] -0.220240781 -0.24396614 -0.163648831 0.259546505 -0.054756423
## [21,] 0.031718576 -0.20129331 0.072886186 0.155883621 0.293781335
## [22,] 0.026147974 -0.15241573 0.047980027 0.010522614 0.285245510
## [23,] 0.291024107 0.28008808 -0.041131976 0.245754634 0.033685532
## [24,] 0.100200185 -0.20172161 0.244650441 0.061072532 -0.409429307
## [25,] -0.338513094 0.12867273 0.089314069 0.168291362 0.035593842
## [26,] 0.039309908 -0.03562120 -0.368670868 0.172785200 -0.132603919
## [27,] -0.065643899 0.02822928 0.261429317 0.073068704 -0.217955325
## [28,] -0.095533051 -0.04536518 0.185605360 0.079485959 -0.105082597
## [29,] 0.228600394 0.06720294 0.041973439 -0.078783310 -0.350461899
## [30,] -0.165001168 0.21625934 -0.036902826 -0.144751306 0.217036197
## [31,] 0.212310769 0.10315194 -0.083972740 0.112444447 0.374183637
## [32,] 0.151545764 -0.22809194 -0.258953491 -0.036199681 0.097189028
## [33,] 0.048618462 -0.04367288 0.001794754 0.135203497 -0.039906646
## [34,] 0.197601309 -0.31196516 0.054788826 0.006905694 0.112323537
## [35,] -0.091885634 -0.14021039 0.067604289 0.095156035 0.067897419
## [,26] [,27] [,28] [,29] [,30]
## [1,] 0.00000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.01848713 0.111466078 -0.002821092 0.106446102 0.233688632
## [3,] 0.04831193 -0.002762534 0.152011392 0.059219103 0.136496189
## [4,] -0.05794530 0.019431856 -0.084180500 -0.374273262 -0.217182693
## [5,] -0.20600679 0.104568533 -0.073846469 -0.008948815 -0.164054483
## [6,] -0.22965699 -0.033415715 0.033982989 -0.011168197 0.279777195
## [7,] 0.07552990 0.070278261 -0.019167509 0.257724621 -0.021097867
## [8,] 0.02465804 0.319903137 0.107250553 0.282071808 0.048553902
## [9,] 0.21537064 -0.320249929 0.335218493 0.088626382 -0.248896698
## [10,] -0.20472371 0.120304471 -0.057352117 -0.048826644 0.254179643
## [11,] -0.04474568 -0.034834485 0.060000221 -0.012744096 -0.247627694
## [12,] -0.02277766 0.003763632 -0.162647798 -0.343918505 -0.348308728
## [13,] 0.01949260 0.146231259 -0.069193446 -0.074558404 0.103768649
## [14,] -0.18721104 -0.115075796 -0.235252682 -0.105915190 0.191468028
## [15,] 0.03224834 0.004335761 -0.362722275 -0.072870649 -0.004683925
## [16,] 0.10790814 0.069094192 0.083070763 -0.225831869 0.105282043
## [17,] 0.15098811 -0.171266979 -0.379215079 -0.024601959 0.153093552
## [18,] -0.10243516 -0.026448654 0.039937081 -0.030828357 -0.004675737
## [19,] 0.07330891 -0.280434592 0.158476487 0.117518644 0.176871932
## [20,] -0.05368330 -0.173387423 -0.183010327 0.216025108 0.056017603
## [21,] 0.24285758 0.148988691 0.177879818 -0.249607767 0.179438013
## [22,] 0.10893719 -0.267945252 -0.178997181 -0.096814109 0.051518533
## [23,] 0.01966934 0.285878817 -0.155269879 -0.044118504 0.284848991
## [24,] -0.14675628 -0.099321859 -0.167395940 0.311998987 0.111825679
## [25,] -0.12635702 -0.065401598 0.115130077 -0.238533688 0.030882300
## [26,] 0.41255924 0.073629294 -0.123845886 0.023133983 0.086856705
## [27,] -0.03016201 0.149894726 -0.032120175 -0.197973340 -0.095312177
## [28,] 0.22478369 0.150975956 -0.061286953 -0.146717033 0.153518623
## [29,] -0.14195099 0.347391617 0.262969314 -0.095362517 0.074777084
## [30,] -0.08188602 0.072175529 -0.166598361 0.073672351 -0.135233721
## [31,] -0.31674726 -0.193015768 -0.083438892 0.044198080 0.019543180
## [32,] 0.11492969 -0.015872048 0.071800382 -0.076454009 0.110867695
## [33,] -0.25332178 0.191010668 0.178922252 0.204852645 -0.166918661
## [34,] -0.38479777 0.045910461 -0.047735456 -0.116859436 0.045546860
## [35,] 0.17024214 0.359038768 -0.332399805 0.260822854 -0.331438861
## [,31] [,32] [,33] [,34] [,35]
## [1,] 0.000000000 0.00000000 -0.518788261 0.000000000 0.000000000
## [2,] -0.080296870 -0.15394456 0.348692198 0.133824911 0.760444370
## [3,] 0.117774487 0.11645182 0.089724535 -0.271078248 -0.009721373
## [4,] -0.233846722 0.13974110 0.084616180 -0.329313312 -0.045716787
## [5,] 0.019835738 0.02703942 0.013640112 0.305015460 0.037453931
## [6,] -0.017951598 -0.22064421 -0.087622595 -0.596450544 0.086279739
## [7,] 0.001588737 0.47788307 0.366270003 0.037106881 -0.059980376
## [8,] 0.201478627 -0.22119941 0.012054419 -0.014913214 -0.183823025
## [9,] -0.097539697 -0.11508387 0.003330079 0.016454854 0.007153040
## [10,] -0.631966773 0.07460121 -0.041625826 0.094589341 -0.076006200
## [11,] -0.039737242 0.04990050 0.128216414 -0.211685202 0.297358291
## [12,] 0.081718732 -0.22408124 0.162906274 0.128082652 0.048026520
## [13,] 0.069050560 0.14415940 0.172597238 0.071632976 -0.124682683
## [14,] 0.068135177 0.24215419 -0.054196839 0.011745745 0.045897532
## [15,] -0.134846612 -0.08046254 0.269058182 -0.031318831 -0.195294994
## [16,] -0.105023236 -0.14406923 0.201376972 -0.095632189 -0.055839484
## [17,] 0.170452585 0.02918136 -0.065244966 -0.091605709 0.079292639
## [18,] 0.074521831 0.06140572 -0.009462514 -0.068057655 0.118624270
## [19,] -0.198677263 -0.25960791 0.369082637 -0.072159892 -0.331536900
## [20,] 0.068061316 -0.11976209 0.114265033 0.196695992 -0.114387736
## [21,] 0.114493850 0.20649834 0.039916052 -0.054310870 0.013204269
## [22,] 0.067645301 0.01951190 -0.008140389 -0.031171299 0.007898349
## [23,] -0.104077473 -0.18567638 -0.155801542 0.173147220 -0.032938239
## [24,] 0.162339853 -0.01864651 0.006897929 -0.064743265 0.011837979
## [25,] 0.137854025 -0.42927568 0.004379585 0.162270581 0.069359637
## [26,] 0.118523667 -0.10070371 0.036713291 -0.037363041 -0.030456225
## [27,] 0.160758736 -0.01087118 0.151784498 0.008678506 -0.064862109
## [28,] 0.010937433 -0.06429362 0.044277387 -0.095074794 -0.020148113
## [29,] 0.155868444 0.04298133 0.022746991 -0.003551575 -0.074126574
## [30,] 0.163402904 0.06076450 0.018706067 -0.230696616 0.114399160
## [31,] 0.065785690 -0.09585106 0.072290565 -0.080576040 -0.032121342
## [32,] 0.279309172 -0.02533721 0.016851225 -0.042150458 -0.056856008
## [33,] -0.055916920 -0.02625907 0.087297801 -0.103460416 -0.031945454
## [34,] 0.285543358 -0.02651520 0.199712570 0.011351880 -0.193870363
## [35,] -0.131574072 -0.24226777 -0.040620188 -0.244444690 -0.034801137eigenvalues <- eigen_result$values
eigenvalues## [1] 9.539935e+03 1.955325e+03 1.039309e+03 2.861340e+02 4.582953e-13
## [6] 3.186432e-13 1.717025e-13 1.705783e-13 1.591931e-13 1.528205e-13
## [11] 1.137275e-13 8.411095e-14 7.991109e-14 4.123126e-14 3.759258e-14
## [16] 2.031698e-14 5.341296e-15 -1.167416e-14 -1.208535e-14 -2.979636e-14
## [21] -5.884407e-14 -6.632939e-14 -9.104860e-14 -9.192980e-14 -1.008422e-13
## [26] -1.079787e-13 -2.070162e-13 -3.224767e-13 -4.459823e-13 -5.073524e-13
## [31] -5.481097e-13 -9.197147e-13 -1.190282e-12 -1.299842e-12 -2.214020e-12eigenvectors <- eigen_result$vectors
eigenvectors## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.118039123 -0.07582044 -0.152008294 1.323229e-02 0.829394449
## [2,] -0.059104999 -0.10065033 -0.028477253 -4.742660e-02 0.196032356
## [3,] -0.111077406 -0.06548711 -0.125973747 -3.265884e-01 0.016450260
## [4,] -0.462491071 -0.13684320 0.260737285 -8.760014e-02 0.023780856
## [5,] 0.029716888 0.09706572 -0.236773030 -4.109801e-01 -0.015203387
## [6,] -0.083256509 0.38622584 -0.070899833 -2.344875e-01 -0.040602926
## [7,] -0.371594499 0.31486373 0.132190474 1.772414e-01 0.226401000
## [8,] -0.105728925 0.36017338 -0.066703624 -1.961308e-02 0.013506319
## [9,] -0.004941140 0.07302494 -0.067485020 -1.937889e-02 -0.004003782
## [10,] 0.251315008 0.06251161 0.134163871 -4.773657e-02 0.040795253
## [11,] 0.230974053 0.03495011 0.113908578 -4.255916e-02 0.137822578
## [12,] 0.129595789 0.48579958 0.003431773 -5.464042e-06 0.165381506
## [13,] 0.238646634 0.15978476 0.101897243 -5.950048e-04 0.175215918
## [14,] 0.122114281 0.06061281 -0.059113584 1.055002e-01 -0.023497259
## [15,] -0.080542947 -0.14122136 -0.526991478 -1.776923e-01 0.050173645
## [16,] -0.133382663 -0.01131803 -0.425484333 4.314927e-01 0.021078888
## [17,] 0.075275811 0.02840582 -0.149144112 3.210089e-02 -0.055347609
## [18,] 0.157193777 -0.04335238 -0.029982482 4.476123e-02 0.006280604
## [19,] 0.227858843 -0.02374412 0.143659919 -3.501966e-02 0.288008436
## [20,] -0.236695098 -0.26201940 0.105725884 -3.146506e-01 0.038230797
## [21,] 0.133857180 -0.10421992 -0.061094239 -6.898092e-02 0.024394073
## [22,] 0.009286398 0.07608412 0.067901567 1.848352e-01 0.012681010
## [23,] -0.208987873 0.08540501 0.147684328 1.896570e-01 -0.095348679
## [24,] -0.060419139 0.04741568 0.026819165 1.386015e-01 0.002754467
## [25,] -0.269228530 -0.06045798 0.204239771 1.028447e-01 -0.005312436
## [26,] 0.021641021 -0.09744711 0.179845671 -7.617262e-02 0.051312619
## [27,] -0.045499618 -0.09771241 -0.039272134 -4.761310e-02 0.073095525
## [28,] 0.075003586 -0.12307507 0.128541494 -5.599622e-04 0.050686526
## [29,] 0.028722846 -0.12349188 0.053722026 -1.460044e-01 0.019202263
## [30,] 0.081935578 -0.12608836 0.099853312 1.153020e-01 0.028296353
## [31,] 0.018080836 -0.14387953 0.092872163 1.533325e-01 0.049213172
## [32,] 0.178458306 -0.05748992 0.017613719 3.935239e-02 0.033283412
## [33,] 0.052798577 -0.24351871 -0.251399520 3.433948e-01 -0.011696528
## [34,] 0.118067558 -0.12030274 0.139680578 2.227130e-02 0.155971176
## [35,] 0.170446571 -0.11418311 0.136313862 9.744518e-03 0.013239261
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.0000000000 0.000000000 0.00000000 0.0000000000 0.00000000
## [2,] 0.0072024361 0.063729813 -0.04523615 0.0069812350 -0.02305323
## [3,] 0.0967490618 0.101562237 0.12959322 0.0319372675 0.36601590
## [4,] -0.1432474421 0.056513727 -0.07226684 0.1036298913 0.02896457
## [5,] -0.0736351741 0.062930481 -0.19487933 0.1502662172 -0.05712028
## [6,] 0.0357057573 -0.017837619 -0.13874511 -0.0643831297 -0.06872758
## [7,] -0.0476597482 -0.043662145 -0.22443295 -0.0205473370 0.05557511
## [8,] -0.1880291970 0.178056316 0.18353162 -0.0392319411 -0.12598655
## [9,] -0.0008146576 0.372145022 -0.38074393 -0.2742991905 -0.10620001
## [10,] 0.2069369265 0.040100242 -0.09151897 -0.1269809909 0.16715489
## [11,] -0.1876683018 -0.022589912 0.21320904 0.1464538342 -0.22332996
## [12,] 0.0594547436 0.004993540 0.19530981 -0.1159028308 0.37705369
## [13,] 0.1061797833 -0.032888989 -0.24394104 -0.1389095498 -0.18458287
## [14,] -0.2421974663 0.167868182 -0.05106672 -0.1636972756 0.01504913
## [15,] -0.0074462111 -0.144139988 -0.08518133 -0.0783930413 0.04868265
## [16,] 0.2268058048 -0.003089225 0.07137408 0.1052520777 -0.24094610
## [17,] -0.2734301008 0.131696484 -0.22139862 -0.1910838173 -0.03734609
## [18,] 0.0090664542 0.155713544 -0.07211735 0.2880957980 0.14867728
## [19,] -0.1342531257 0.021604055 0.05697857 0.1023456005 0.02553677
## [20,] 0.0386944061 0.159010047 0.11412836 -0.0888297179 -0.09023369
## [21,] -0.1363884425 -0.275044873 0.05934163 -0.1904788473 -0.11052147
## [22,] 0.2566606703 0.187378005 0.07564117 0.0110571694 -0.19445173
## [23,] -0.1111895152 0.326339565 0.01512120 0.1594899177 0.08450965
## [24,] 0.2260024879 -0.336073505 0.02976357 0.1398463985 0.05491173
## [25,] -0.0829503538 -0.336895351 -0.31050751 -0.2113839274 0.06719779
## [26,] 0.1412823395 -0.031016192 0.12875318 -0.2009105710 0.30408954
## [27,] 0.2757192755 0.357268067 0.02109908 0.1748814930 -0.08766966
## [28,] -0.3316796560 0.185051398 0.07377182 0.0095773560 -0.01216994
## [29,] 0.2712919800 0.091574753 -0.12795571 -0.2437538268 -0.14281548
## [30,] 0.2771319749 0.165886896 0.01127316 -0.3443221867 0.10890418
## [31,] 0.0846618611 0.139500772 0.01303601 -0.0363208613 -0.02905607
## [32,] 0.0518707247 0.029377977 -0.48039739 0.4574532345 0.30415915
## [33,] -0.2671367912 0.098654301 -0.01748889 -0.1987536565 0.36271511
## [34,] -0.1891048388 -0.035938061 0.04325967 0.0007018276 -0.15832774
## [35,] 0.0140029063 -0.112768136 -0.27182311 0.0829680984 -0.17940535
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] -0.031434470 -0.059174222 0.018596714 0.058309442 0.034530348
## [3,] -0.095965539 0.023345686 -0.061003282 0.308944865 0.334631060
## [4,] 0.148540420 0.160804765 0.174967184 0.029624347 -0.101929236
## [5,] 0.116681646 -0.195704631 0.457157176 -0.058475506 -0.226094330
## [6,] -0.046244789 -0.181005226 -0.022610682 -0.049443398 -0.143391467
## [7,] 0.017869505 -0.154787466 -0.052552802 -0.138314668 0.010421056
## [8,] -0.003299134 0.328554951 0.015811479 -0.114465094 -0.019605536
## [9,] -0.068208323 0.132131844 0.164483196 0.278519035 0.029993632
## [10,] 0.014385677 0.214734778 -0.038354935 -0.115436739 0.035208708
## [11,] 0.076702770 0.383393319 -0.189875985 -0.045544331 -0.032872924
## [12,] 0.069369050 -0.077858016 -0.078123022 -0.042579882 -0.024045492
## [13,] -0.156082633 0.344988383 0.083334047 0.223801897 0.040068246
## [14,] -0.185062868 -0.279808136 -0.061770272 0.095749293 0.089399363
## [15,] -0.139390238 0.245866894 -0.103132616 0.124430251 -0.087723513
## [16,] 0.240075410 -0.069219955 0.135948947 -0.084037765 0.207369930
## [17,] 0.371965521 0.163720652 -0.058698590 -0.236939724 0.134481693
## [18,] 0.314979982 0.123299780 0.169359128 0.159306863 -0.111316980
## [19,] 0.156613482 -0.254695617 -0.008628062 -0.010195751 -0.151770256
## [20,] 0.164470045 0.054995195 -0.289713411 -0.120570270 -0.154304775
## [21,] 0.033158360 -0.034313521 -0.029974979 0.041286053 -0.366780322
## [22,] -0.033018869 -0.079441554 -0.056438593 0.196129502 -0.426479729
## [23,] 0.140294610 0.051945357 -0.073412773 0.341265776 -0.104391372
## [24,] -0.091700791 0.214499791 0.298014741 0.149852401 -0.260164020
## [25,] -0.121973069 0.081069371 -0.101551497 0.013215858 -0.002417601
## [26,] 0.138115851 0.003058757 0.383695376 -0.031766209 0.087534862
## [27,] -0.384632136 -0.044416656 -0.159723631 -0.108371769 -0.046657954
## [28,] -0.396343754 -0.017979456 0.294214036 -0.188871957 -0.117383284
## [29,] 0.283352507 -0.061372629 -0.043822819 -0.161788046 -0.064267508
## [30,] 0.105306844 -0.018763233 -0.023266400 0.028219395 -0.146508704
## [31,] -0.168041289 0.114401851 0.308920353 -0.380506174 0.183441861
## [32,] 0.007323018 0.110945057 -0.215221679 -0.198191312 -0.058961321
## [33,] -0.030094057 -0.005283383 -0.047013002 0.009890634 -0.306004750
## [34,] 0.144847366 -0.078463053 0.075849553 0.371771109 0.268643212
## [35,] -0.021312807 -0.277983912 -0.077684993 0.111326002 0.125310616
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.00000000 0.000000000 0.00000000 0.000000e+00 0.000000000
## [2,] 0.08817537 0.004071534 -0.04208785 -1.080437e-02 -0.023325027
## [3,] 0.10909443 -0.213309930 -0.05013823 2.968308e-01 -0.046495896
## [4,] 0.21611701 -0.157183220 -0.04077158 -1.235090e-03 -0.035694263
## [5,] 0.04233653 -0.254488638 0.13116397 -1.006363e-03 -0.154482729
## [6,] 0.02591133 0.263313904 0.04277685 -1.713563e-01 -0.022369897
## [7,] -0.23466941 0.110823058 -0.02022239 4.672694e-05 0.022210231
## [8,] -0.08377976 -0.239387700 -0.09863663 1.346650e-03 -0.072259822
## [9,] -0.10279970 -0.015382501 0.01185390 -6.514874e-02 0.204599994
## [10,] -0.16008126 -0.072728471 0.04479033 -7.360518e-02 -0.083768409
## [11,] -0.18714806 -0.193087122 0.03200440 5.807409e-02 -0.106794522
## [12,] 0.12536208 0.091794403 -0.03915623 1.411576e-01 0.221063080
## [13,] 0.52820358 0.165710587 0.02091841 4.152496e-02 -0.071344773
## [14,] -0.01588569 -0.353705266 -0.17898709 1.093482e-01 0.084882082
## [15,] -0.35792056 0.064913841 -0.06311970 7.981633e-02 0.063139707
## [16,] 0.12289850 -0.077498773 0.19182056 5.579403e-02 0.051058639
## [17,] 0.09865560 -0.050455583 -0.05093971 -9.713546e-02 -0.141579402
## [18,] -0.25714195 0.353918336 -0.30877058 -1.096406e-03 0.198520739
## [19,] 0.04268038 -0.256703738 -0.03325212 -3.941309e-02 0.015559420
## [20,] 0.23930986 0.213377634 0.08956421 4.410602e-02 0.193642664
## [21,] 0.05460157 -0.128976806 -0.24134440 -2.056052e-01 0.362058907
## [22,] -0.07929784 0.015021415 -0.13973113 3.283000e-01 -0.452010132
## [23,] -0.01087779 -0.097533833 -0.02417405 -3.265387e-02 0.218534183
## [24,] 0.04779782 -0.186780765 0.03315805 1.995730e-02 0.179832722
## [25,] -0.17812953 -0.149683706 -0.05513469 4.811142e-02 -0.140031831
## [26,] -0.11301218 0.035142638 -0.15702552 -2.416241e-01 -0.306301500
## [27,] -0.04011004 -0.071542148 -0.18050164 -4.973523e-01 -0.092592624
## [28,] -0.15074969 0.242411350 0.35036864 3.197478e-01 0.097272598
## [29,] -0.14286641 -0.010267139 -0.15523408 4.193828e-01 -0.001496653
## [30,] -0.13629058 -0.250026313 0.49304628 -1.277337e-01 0.199661498
## [31,] 0.05018486 -0.035154547 -0.36672079 1.052447e-01 0.249744826
## [32,] 0.03137453 -0.107029018 0.18765294 5.615487e-02 0.004115593
## [33,] 0.25144181 0.130986070 -0.06800014 -3.002940e-02 -0.267572058
## [34,] -0.19029553 0.171594332 0.17808798 -1.723572e-01 -0.113359775
## [35,] 0.04784853 -0.046281328 -0.21009651 1.204024e-01 0.083910046
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.000000000 0.00000000 0.000000000 0.000000000 0.000000000
## [2,] 0.091903633 -0.11440520 -0.003957855 -0.261633037 0.043131986
## [3,] -0.112191210 0.01055355 0.260096765 0.231431418 0.165745917
## [4,] 0.010426418 -0.14065242 -0.046271486 -0.267045872 -0.056200466
## [5,] -0.059865349 0.08014523 0.002327399 0.233765876 0.148307243
## [6,] 0.050596955 0.03203347 -0.138471657 0.126532055 -0.018515206
## [7,] -0.007335903 0.04533141 0.040965726 0.191304982 0.065375404
## [8,] -0.208782326 -0.23444178 -0.072454581 -0.294259550 0.156550475
## [9,] 0.133170201 -0.21424690 -0.003666309 0.087749457 -0.097315949
## [10,] -0.106730100 -0.32797243 0.142821197 0.114181240 0.077106988
## [11,] 0.066708752 0.12325474 -0.168370546 0.434291626 -0.142500268
## [12,] 0.090979555 -0.14307975 0.087381194 0.019203666 -0.056695131
## [13,] -0.148399781 0.28160063 -0.122873883 -0.011126807 -0.006132069
## [14,] -0.228372543 -0.14475574 -0.374231792 -0.016735649 -0.326005004
## [15,] 0.152091159 0.14488511 -0.160752075 -0.143415372 0.011624926
## [16,] -0.204614868 -0.13166209 -0.087027808 0.235608300 -0.042940922
## [17,] 0.067288943 0.03908738 0.469349389 0.021465084 -0.073107283
## [18,] -0.520144972 0.08934757 0.038157229 -0.079574171 -0.025238400
## [19,] -0.032891620 0.26343578 0.099720983 -0.160030447 -0.090186027
## [20,] -0.220240781 -0.24396614 -0.163648831 0.259546505 -0.054756423
## [21,] 0.031718576 -0.20129331 0.072886186 0.155883621 0.293781335
## [22,] 0.026147974 -0.15241573 0.047980027 0.010522614 0.285245510
## [23,] 0.291024107 0.28008808 -0.041131976 0.245754634 0.033685532
## [24,] 0.100200185 -0.20172161 0.244650441 0.061072532 -0.409429307
## [25,] -0.338513094 0.12867273 0.089314069 0.168291362 0.035593842
## [26,] 0.039309908 -0.03562120 -0.368670868 0.172785200 -0.132603919
## [27,] -0.065643899 0.02822928 0.261429317 0.073068704 -0.217955325
## [28,] -0.095533051 -0.04536518 0.185605360 0.079485959 -0.105082597
## [29,] 0.228600394 0.06720294 0.041973439 -0.078783310 -0.350461899
## [30,] -0.165001168 0.21625934 -0.036902826 -0.144751306 0.217036197
## [31,] 0.212310769 0.10315194 -0.083972740 0.112444447 0.374183637
## [32,] 0.151545764 -0.22809194 -0.258953491 -0.036199681 0.097189028
## [33,] 0.048618462 -0.04367288 0.001794754 0.135203497 -0.039906646
## [34,] 0.197601309 -0.31196516 0.054788826 0.006905694 0.112323537
## [35,] -0.091885634 -0.14021039 0.067604289 0.095156035 0.067897419
## [,26] [,27] [,28] [,29] [,30]
## [1,] 0.00000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.01848713 0.111466078 -0.002821092 0.106446102 0.233688632
## [3,] 0.04831193 -0.002762534 0.152011392 0.059219103 0.136496189
## [4,] -0.05794530 0.019431856 -0.084180500 -0.374273262 -0.217182693
## [5,] -0.20600679 0.104568533 -0.073846469 -0.008948815 -0.164054483
## [6,] -0.22965699 -0.033415715 0.033982989 -0.011168197 0.279777195
## [7,] 0.07552990 0.070278261 -0.019167509 0.257724621 -0.021097867
## [8,] 0.02465804 0.319903137 0.107250553 0.282071808 0.048553902
## [9,] 0.21537064 -0.320249929 0.335218493 0.088626382 -0.248896698
## [10,] -0.20472371 0.120304471 -0.057352117 -0.048826644 0.254179643
## [11,] -0.04474568 -0.034834485 0.060000221 -0.012744096 -0.247627694
## [12,] -0.02277766 0.003763632 -0.162647798 -0.343918505 -0.348308728
## [13,] 0.01949260 0.146231259 -0.069193446 -0.074558404 0.103768649
## [14,] -0.18721104 -0.115075796 -0.235252682 -0.105915190 0.191468028
## [15,] 0.03224834 0.004335761 -0.362722275 -0.072870649 -0.004683925
## [16,] 0.10790814 0.069094192 0.083070763 -0.225831869 0.105282043
## [17,] 0.15098811 -0.171266979 -0.379215079 -0.024601959 0.153093552
## [18,] -0.10243516 -0.026448654 0.039937081 -0.030828357 -0.004675737
## [19,] 0.07330891 -0.280434592 0.158476487 0.117518644 0.176871932
## [20,] -0.05368330 -0.173387423 -0.183010327 0.216025108 0.056017603
## [21,] 0.24285758 0.148988691 0.177879818 -0.249607767 0.179438013
## [22,] 0.10893719 -0.267945252 -0.178997181 -0.096814109 0.051518533
## [23,] 0.01966934 0.285878817 -0.155269879 -0.044118504 0.284848991
## [24,] -0.14675628 -0.099321859 -0.167395940 0.311998987 0.111825679
## [25,] -0.12635702 -0.065401598 0.115130077 -0.238533688 0.030882300
## [26,] 0.41255924 0.073629294 -0.123845886 0.023133983 0.086856705
## [27,] -0.03016201 0.149894726 -0.032120175 -0.197973340 -0.095312177
## [28,] 0.22478369 0.150975956 -0.061286953 -0.146717033 0.153518623
## [29,] -0.14195099 0.347391617 0.262969314 -0.095362517 0.074777084
## [30,] -0.08188602 0.072175529 -0.166598361 0.073672351 -0.135233721
## [31,] -0.31674726 -0.193015768 -0.083438892 0.044198080 0.019543180
## [32,] 0.11492969 -0.015872048 0.071800382 -0.076454009 0.110867695
## [33,] -0.25332178 0.191010668 0.178922252 0.204852645 -0.166918661
## [34,] -0.38479777 0.045910461 -0.047735456 -0.116859436 0.045546860
## [35,] 0.17024214 0.359038768 -0.332399805 0.260822854 -0.331438861
## [,31] [,32] [,33] [,34] [,35]
## [1,] 0.000000000 0.00000000 -0.518788261 0.000000000 0.000000000
## [2,] -0.080296870 -0.15394456 0.348692198 0.133824911 0.760444370
## [3,] 0.117774487 0.11645182 0.089724535 -0.271078248 -0.009721373
## [4,] -0.233846722 0.13974110 0.084616180 -0.329313312 -0.045716787
## [5,] 0.019835738 0.02703942 0.013640112 0.305015460 0.037453931
## [6,] -0.017951598 -0.22064421 -0.087622595 -0.596450544 0.086279739
## [7,] 0.001588737 0.47788307 0.366270003 0.037106881 -0.059980376
## [8,] 0.201478627 -0.22119941 0.012054419 -0.014913214 -0.183823025
## [9,] -0.097539697 -0.11508387 0.003330079 0.016454854 0.007153040
## [10,] -0.631966773 0.07460121 -0.041625826 0.094589341 -0.076006200
## [11,] -0.039737242 0.04990050 0.128216414 -0.211685202 0.297358291
## [12,] 0.081718732 -0.22408124 0.162906274 0.128082652 0.048026520
## [13,] 0.069050560 0.14415940 0.172597238 0.071632976 -0.124682683
## [14,] 0.068135177 0.24215419 -0.054196839 0.011745745 0.045897532
## [15,] -0.134846612 -0.08046254 0.269058182 -0.031318831 -0.195294994
## [16,] -0.105023236 -0.14406923 0.201376972 -0.095632189 -0.055839484
## [17,] 0.170452585 0.02918136 -0.065244966 -0.091605709 0.079292639
## [18,] 0.074521831 0.06140572 -0.009462514 -0.068057655 0.118624270
## [19,] -0.198677263 -0.25960791 0.369082637 -0.072159892 -0.331536900
## [20,] 0.068061316 -0.11976209 0.114265033 0.196695992 -0.114387736
## [21,] 0.114493850 0.20649834 0.039916052 -0.054310870 0.013204269
## [22,] 0.067645301 0.01951190 -0.008140389 -0.031171299 0.007898349
## [23,] -0.104077473 -0.18567638 -0.155801542 0.173147220 -0.032938239
## [24,] 0.162339853 -0.01864651 0.006897929 -0.064743265 0.011837979
## [25,] 0.137854025 -0.42927568 0.004379585 0.162270581 0.069359637
## [26,] 0.118523667 -0.10070371 0.036713291 -0.037363041 -0.030456225
## [27,] 0.160758736 -0.01087118 0.151784498 0.008678506 -0.064862109
## [28,] 0.010937433 -0.06429362 0.044277387 -0.095074794 -0.020148113
## [29,] 0.155868444 0.04298133 0.022746991 -0.003551575 -0.074126574
## [30,] 0.163402904 0.06076450 0.018706067 -0.230696616 0.114399160
## [31,] 0.065785690 -0.09585106 0.072290565 -0.080576040 -0.032121342
## [32,] 0.279309172 -0.02533721 0.016851225 -0.042150458 -0.056856008
## [33,] -0.055916920 -0.02625907 0.087297801 -0.103460416 -0.031945454
## [34,] 0.285543358 -0.02651520 0.199712570 0.011351880 -0.193870363
## [35,] -0.131574072 -0.24226777 -0.040620188 -0.244444690 -0.034801137knitr::opts_chunk$set(echo = FALSE)2.5 Menghitung Nilai Kumulatif Variasi
cumulative_variance <- cumsum(eigenvalues) / sum(eigenvalues)
print(cumulative_variance)## [1] 0.7441039 0.8966170 0.9776819 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 1.0000000knitr::opts_chunk$set(echo = FALSE)2.6 Menentukan Titik Koordinat Objek
fit <- cmdscale(dist_matrix, k=2)
fit## [,1] [,2]
## 1 -11.5291867 -3.3527082
## 2 -5.7729382 -4.4506626
## 3 -10.8492177 -2.8957781
## 4 -45.1727001 -6.0510769
## 5 2.9025254 4.2921543
## 6 -8.1318788 17.0785417
## 7 -36.2945966 13.9229766
## 8 -10.3268178 15.9265265
## 9 -0.4826139 3.2290937
## 10 24.5465873 2.7642042
## 11 22.5598336 1.5454608
## 12 12.6579562 21.4815987
## 13 23.3092345 7.0655311
## 14 11.9272179 2.6802412
## 15 -7.8668381 -6.2446753
## 16 -13.0278300 -0.5004725
## 17 7.3523833 1.2560788
## 18 15.3535231 -1.9170015
## 19 22.2555630 -1.0499424
## 20 -23.1186229 -11.5862506
## 21 13.0741773 -4.6085062
## 22 0.9070265 3.3643681
## 23 -20.4123865 3.7765289
## 24 -5.9012937 2.0966768
## 25 -26.2962475 -2.6733948
## 26 2.1137346 -4.3090192
## 27 -4.4440655 -4.3207506
## 28 7.3257944 -5.4422632
## 29 2.8054347 -5.4606942
## 30 8.0028600 -5.5755080
## 31 1.7660020 -6.3622168
## 32 17.4304847 -2.5421501
## 33 5.1569737 -10.7681673
## 34 11.5319640 -5.3196735
## 35 16.6479578 -5.0490691knitr::opts_chunk$set(echo = FALSE)2.7 Menghitung Disparities
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))
}
}
disparities## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.0000000 5.860026 0.8192331 33.75155 16.331511 20.71178 30.19561
## [2,] 5.8600256 0.000000 5.3090752 39.43225 12.316676 21.65805 35.62530
## [3,] 0.8192331 5.309075 0.0000000 34.46821 15.516985 20.15831 30.50144
## [4,] 33.7515508 39.432253 34.4682078 0.00000 49.175296 43.66923 21.85826
## [5,] 16.3315106 12.316676 15.5169846 49.17530 0.000000 16.88934 40.36294
## [6,] 20.7117762 21.658053 20.1583080 43.66923 16.889339 0.00000 28.33895
## [7,] 30.1956091 35.625303 30.5014395 21.85826 40.362942 28.33895 0.00000
## [8,] 19.3166917 20.879838 18.8295526 41.19770 17.617438 2.47889 26.04496
## [9,] 12.8587280 9.325566 12.0407860 45.64346 3.548136 15.82146 37.37455
## [10,] 36.5906831 31.166134 35.8454797 70.27438 21.697927 35.67608 61.85603
## [11,] 34.4391255 28.960308 33.7029571 68.15720 19.848277 34.39851 60.14189
## [12,] 34.6664200 31.814777 33.8650812 64.05024 19.764752 21.25098 49.53267
## [13,] 36.3628286 31.279314 35.5812807 69.72676 20.594305 32.99703 59.99701
## [14,] 24.2198141 19.082592 23.4490514 57.76363 9.167515 24.69167 49.51507
## [15,] 4.6665053 2.757335 4.4843841 37.30636 15.066651 23.32472 34.85501
## [16,] 3.2219839 8.260597 3.2378759 32.62057 16.635669 18.24807 27.37478
## [17,] 19.4359102 14.312266 18.6691241 53.03092 5.386928 22.13849 45.44787
## [18,] 26.9210204 21.277848 26.2210151 60.66724 13.913337 30.20587 54.02252
## [19,] 33.8631369 28.234054 33.1562002 67.61348 20.076804 35.38416 60.43434
## [20,] 14.2164078 18.756049 15.0353788 22.73808 30.483174 32.34614 28.71109
## [21,] 24.6353922 18.847776 23.9846256 58.26474 13.516074 30.33191 52.73226
## [22,] 14.1343027 10.280887 13.3191107 47.03182 2.200637 16.42499 38.67098
## [23,] 11.3902265 16.792859 11.6607837 26.63935 23.320613 18.10399 18.84662
## [24,] 7.8338353 6.548597 7.0289798 40.10772 9.073442 15.14701 32.61310
## [25,] 14.7826774 20.600119 15.4486304 19.17627 30.018115 26.83437 19.37541
## [26,] 13.6763969 7.887945 13.0397616 47.31851 8.637267 23.71498 42.51594
## [27,] 7.1509474 1.335208 6.5617469 40.76537 11.320536 21.71473 36.70545
## [28,] 18.9704125 13.136212 18.3525380 52.50202 10.692249 27.31531 47.72579
## [29,] 14.4887879 8.637630 13.8934635 47.98177 9.753332 25.05278 43.64103
## [30,] 19.6581201 13.821646 19.0415805 53.17769 11.107843 27.81251 48.39892
## [31,] 13.6315511 7.777510 13.0828119 46.93973 10.714817 25.44479 43.12886
## [32,] 28.9710126 23.281779 28.2819133 62.70145 16.055196 32.22431 56.19150
## [33,] 18.2597093 12.624335 17.8373955 50.55024 15.228126 30.85503 48.24816
## [34,] 23.1448834 17.326708 22.5120538 56.70938 12.917215 29.80515 51.55249
## [35,] 28.2281617 22.428880 27.5813583 61.82878 16.619127 33.22155 56.23924
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 19.31669 12.858728 36.590683 34.439126 34.66642 36.362829 24.219814
## [2,] 20.87984 9.325566 31.166134 28.960308 31.81478 31.279314 19.082592
## [3,] 18.82955 12.040786 35.845480 33.702957 33.86508 35.581281 23.449051
## [4,] 41.19770 45.643459 70.274378 68.157197 64.05024 69.726758 57.763626
## [5,] 17.61744 3.548136 21.697927 19.848277 19.76475 20.594305 9.167515
## [6,] 2.47889 15.821456 35.676076 34.398515 21.25098 32.997030 24.691667
## [7,] 26.04496 37.374553 61.856025 60.141889 49.53267 59.997010 49.515073
## [8,] 0.00000 16.066523 37.274671 35.893549 23.64654 34.783635 25.897996
## [9,] 16.06652 0.000000 25.033518 23.103874 22.49063 24.099176 12.421963
## [10,] 37.27467 25.033518 0.000000 2.330778 22.17387 4.475763 12.619649
## [11,] 35.89355 23.103874 2.330778 0.000000 22.25976 5.570707 10.693000
## [12,] 23.64654 22.490632 22.173868 22.259757 0.00000 17.924083 18.815553
## [13,] 34.78363 24.099176 4.475763 5.570707 17.92408 0.000000 12.197585
## [14,] 25.89800 12.421963 12.619649 10.693000 18.81555 12.197585 0.000000
## [15,] 22.30726 12.011622 33.642088 31.408097 34.49657 33.898512 21.713102
## [16,] 16.64758 13.087861 37.715977 35.646425 33.80786 37.116393 25.156934
## [17,] 22.97338 8.079602 17.260217 15.210203 20.90982 16.981485 4.791383
## [18,] 31.27094 16.651292 10.316303 7.994971 23.55336 11.999135 5.733603
## [19,] 36.73979 23.137304 4.449327 2.613178 24.49050 8.183589 10.981302
## [20,] 30.34111 27.053342 49.778588 47.528552 48.71803 50.034337 37.838390
## [21,] 31.13349 15.659328 13.637194 11.307033 26.09342 15.525448 7.378439
## [22,] 16.85251 1.396209 23.647178 21.729070 21.59441 22.705892 11.041406
## [23,] 15.79054 19.937290 44.970369 43.030098 37.51156 43.845156 32.358181
## [24,] 14.52068 5.535744 30.455197 28.466465 26.83693 29.630128 17.838060
## [25,] 24.51489 26.479861 51.132781 49.037898 45.83551 50.552453 38.596564
## [26,] 23.75383 7.972714 23.521551 21.267767 27.86282 24.054721 12.047996
## [27,] 21.08457 8.526033 29.843836 27.633729 30.95546 29.998218 17.805415
## [28,] 27.71714 11.668919 19.076211 16.760198 27.44679 20.295696 9.335319
## [29,] 25.09720 9.291054 23.244928 20.960021 28.68727 24.027320 12.226273
## [30,] 28.25446 12.228012 18.526892 16.205360 27.45463 19.851473 9.141005
## [31,] 25.35793 9.851371 24.540714 22.246681 29.89837 25.385336 13.602072
## [32,] 33.34006 18.819839 8.876729 6.558871 24.49321 11.263536 7.586786
## [33,] 30.86024 15.090668 23.644919 21.318653 33.11060 25.446913 15.056424
## [34,] 30.48290 14.745559 15.320884 12.990149 26.82491 17.090857 8.009673
## [35,] 34.17037 19.025889 11.110157 8.856529 26.82902 13.825200 9.056910
## [,15] [,16] [,17] [,18] [,19] [,20] [,21]
## [1,] 4.666505 3.221984 19.435910 26.921020 33.863137 14.216408 24.635392
## [2,] 2.757335 8.260597 14.312266 21.277848 28.234054 18.756049 18.847776
## [3,] 4.484384 3.237876 18.669124 26.221015 33.156200 15.035379 23.984626
## [4,] 37.306364 32.620575 53.030924 60.667242 67.613475 22.738084 58.264738
## [5,] 15.066651 16.635669 5.386928 13.913337 20.076804 30.483174 13.516074
## [6,] 23.324723 18.248071 22.138489 30.205873 35.384157 32.346141 30.331912
## [7,] 34.855009 27.374775 45.447873 54.022525 60.434340 28.711095 52.732264
## [8,] 22.307256 16.647575 22.973380 31.270935 36.739788 30.341114 31.133489
## [9,] 12.011622 13.087861 8.079602 16.651292 23.137304 27.053342 15.659328
## [10,] 33.642088 37.715977 17.260217 10.316303 4.449327 49.778588 13.637194
## [11,] 31.408097 35.646425 15.210203 7.994971 2.613178 47.528552 11.307033
## [12,] 34.496572 33.807855 20.909824 23.553356 24.490496 48.718028 26.093425
## [13,] 33.898512 37.116393 16.981485 11.999135 8.183589 50.034337 15.525448
## [14,] 21.713102 25.156934 4.791383 5.733603 10.981302 37.838390 7.378439
## [15,] 0.000000 7.722157 16.967204 23.620202 30.567046 16.160116 21.004837
## [16,] 7.722157 0.000000 20.455771 28.416681 35.287671 14.990616 26.423299
## [17,] 16.967204 20.455771 0.000000 8.607362 15.080534 33.066715 8.193429
## [18,] 23.620202 28.416681 8.607362 0.000000 6.956288 39.668632 3.526984
## [19,] 30.567046 35.287671 15.080534 6.956288 0.000000 46.581440 9.846889
## [20,] 16.160116 14.990616 33.066715 39.668632 46.581440 0.000000 36.859296
## [21,] 21.004837 26.423299 8.193429 3.526984 9.846889 36.859296 0.000000
## [22,] 13.012087 14.460886 6.781409 15.381617 21.800141 28.297576 14.546693
## [23,] 16.056628 8.533722 27.878937 36.216247 42.940060 15.599318 34.520411
## [24,] 8.569803 7.585032 13.280307 21.630461 28.332134 21.992247 20.125307
## [25,] 18.772245 13.445166 33.877295 41.656638 48.578945 9.462362 39.417953
## [26,] 10.166543 15.613200 7.642889 13.454135 20.403795 26.260806 10.964534
## [27,] 3.926431 9.395506 13.048265 19.942982 26.899226 20.038128 17.520606
## [28,] 15.213808 20.944959 6.698395 8.767662 15.562470 31.058189 5.808533
## [29,] 10.701030 16.592048 8.111090 13.038876 19.943977 26.637928 10.304043
## [30,] 15.883800 21.634369 6.862485 8.210781 14.953939 31.696620 5.162688
## [31,] 9.633557 15.912810 9.447015 14.296177 21.167011 25.427054 11.443353
## [32,] 25.566839 30.526667 10.770082 2.169004 5.050551 41.545468 4.821539
## [33,] 13.787010 20.883310 12.223024 13.502324 19.667375 28.287429 10.031128
## [34,] 19.420843 25.028148 7.791625 5.116883 11.542364 35.212685 1.698288
## [35,] 24.543934 30.022360 11.232212 3.389013 6.887543 40.300319 3.600834
## [,22] [,23] [,24] [,25] [,26] [,27] [,28]
## [1,] 14.134303 11.390226 7.833835 14.782677 13.676397 7.150947 18.9704125
## [2,] 10.280887 16.792859 6.548597 20.600119 7.887945 1.335208 13.1362121
## [3,] 13.319111 11.660784 7.028980 15.448630 13.039762 6.561747 18.3525380
## [4,] 47.031817 26.639350 40.107721 19.176267 47.318513 40.765374 52.5020244
## [5,] 2.200637 23.320613 9.073442 30.018115 8.637267 11.320536 10.6922492
## [6,] 16.424992 18.103989 15.147006 26.834368 23.714982 21.714734 27.3153128
## [7,] 38.670984 18.846618 32.613099 19.375410 42.515945 36.705448 47.7257899
## [8,] 16.852510 15.790539 14.520675 24.514889 23.753835 21.084568 27.7171407
## [9,] 1.396209 19.937290 5.535744 26.479861 7.972714 8.526033 11.6689190
## [10,] 23.647178 44.970369 30.455197 51.132781 23.521551 29.843836 19.0762108
## [11,] 21.729070 43.030098 28.466465 49.037898 21.267767 27.633729 16.7601981
## [12,] 21.594406 37.511559 26.836933 45.835507 27.862817 30.955458 27.4467901
## [13,] 22.705892 43.845156 29.630128 50.552453 24.054721 29.998218 20.2956960
## [14,] 11.041406 32.358181 17.838060 38.596564 12.047996 17.805415 9.3353188
## [15,] 13.012087 16.056628 8.569803 18.772245 10.166543 3.926431 15.2138078
## [16,] 14.460886 8.533722 7.585032 13.445166 15.613200 9.395506 20.9449593
## [17,] 6.781409 27.878937 13.280307 33.877295 7.642889 13.048265 6.6983948
## [18,] 15.381617 36.216247 21.630461 41.656638 13.454135 19.942982 8.7676621
## [19,] 21.800141 42.940060 28.332134 48.578945 20.403795 26.899226 15.5624700
## [20,] 28.297576 15.599318 21.992247 9.462362 26.260806 20.038128 31.0581893
## [21,] 14.546693 34.520411 20.125307 39.417953 10.964534 17.520606 5.8085331
## [22,] 0.000000 21.323397 6.925335 27.865260 7.767691 9.364573 10.8975840
## [23,] 21.323397 0.000000 14.608002 8.730483 23.933287 17.904000 29.2299984
## [24,] 6.925335 14.608002 0.000000 20.945351 10.260293 6.580797 15.2246995
## [25,] 27.865260 8.730483 20.945351 0.000000 28.457026 21.914188 33.7358612
## [26,] 7.767691 23.933287 10.260293 28.457026 0.000000 6.557811 5.3338363
## [27,] 9.364573 17.904000 6.580797 21.914188 6.557811 0.000000 11.8231718
## [28,] 10.897584 29.229998 15.224699 33.735861 5.333836 11.823172 0.0000000
## [29,] 9.026942 24.987867 11.529136 29.234858 1.343430 7.338578 4.5203973
## [30,] 11.413686 29.914659 15.880425 34.421665 6.023769 12.510011 0.6900522
## [31,] 9.764440 24.385961 11.416668 28.303662 2.082436 6.537012 5.6353886
## [32,] 17.547411 38.366764 23.788455 43.726929 15.418322 21.946739 10.5126316
## [33,] 14.757731 29.416668 16.964359 32.478154 7.140161 11.564996 5.7505685
## [34,] 13.722313 33.214190 18.945203 37.920659 9.472300 16.007229 4.2079557
## [35,] 17.848329 38.096723 23.654396 43.009866 14.553052 21.104594 9.3304519
## [,29] [,30] [,31] [,32] [,33] [,34] [,35]
## [1,] 14.488788 19.6581201 13.631551 28.971013 18.259709 23.144883 28.228162
## [2,] 8.637630 13.8216458 7.777510 23.281779 12.624335 17.326708 22.428880
## [3,] 13.893463 19.0415805 13.082812 28.281913 17.837395 22.512054 27.581358
## [4,] 47.981767 53.1776866 46.939733 62.701446 50.550242 56.709381 61.828778
## [5,] 9.753332 11.1078428 10.714817 16.055196 15.228126 12.917215 16.619127
## [6,] 25.052784 27.8125109 25.444787 32.224307 30.855029 29.805146 33.221551
## [7,] 43.641026 48.3989210 43.128856 56.191501 48.248163 51.552492 56.239244
## [8,] 25.097196 28.2544611 25.357925 33.340064 30.860241 30.482903 34.170369
## [9,] 9.291054 12.2280120 9.851371 18.819839 15.090668 14.745559 19.025889
## [10,] 23.244928 18.5268916 24.540714 8.876729 23.644919 15.320884 11.110157
## [11,] 20.960021 16.2053596 22.246681 6.558871 21.318653 12.990149 8.856529
## [12,] 28.687268 27.4546342 29.898373 24.493214 33.110605 26.824915 26.829022
## [13,] 24.027320 19.8514727 25.385336 11.263536 25.446913 17.090857 13.825200
## [14,] 12.226273 9.1410054 13.602072 7.586786 15.056424 8.009673 9.056910
## [15,] 10.701030 15.8838000 9.633557 25.566839 13.787010 19.420843 24.543934
## [16,] 16.592048 21.6343686 15.912810 30.526667 20.883310 25.028148 30.022360
## [17,] 8.111090 6.8624848 9.447015 10.770082 12.223024 7.791625 11.232212
## [18,] 13.038876 8.2107806 14.296177 2.169004 13.502324 5.116883 3.389013
## [19,] 19.943977 14.9539388 21.167011 5.050551 19.667375 11.542364 6.887543
## [20,] 26.637928 31.6966200 25.427054 41.545468 28.287429 35.212685 40.300319
## [21,] 10.304043 5.1626884 11.443353 4.821539 10.031128 1.698288 3.600834
## [22,] 9.026942 11.4136864 9.764440 17.547411 14.757731 13.722313 17.848329
## [23,] 24.987867 29.9146590 24.385961 38.366764 29.416668 33.214190 38.096723
## [24,] 11.529136 15.8804253 11.416668 23.788455 16.964359 18.945203 23.654396
## [25,] 29.234858 34.4216652 28.303662 43.726929 32.478154 37.920659 43.009866
## [26,] 1.343430 6.0237689 2.082436 15.418322 7.140161 9.472300 14.553052
## [27,] 7.338578 12.5100108 6.537012 21.946739 11.564996 16.007229 21.104594
## [28,] 4.520397 0.6900522 5.635389 10.512632 5.750568 4.207956 9.330452
## [29,] 0.000000 5.1986933 1.375923 14.913416 5.805085 8.727669 13.848642
## [30,] 5.198693 0.0000000 6.286279 9.903604 5.921383 3.538365 8.661112
## [31,] 1.375923 6.2862793 0.000000 16.123552 5.559774 9.821452 14.939778
## [32,] 14.913416 9.9036038 16.123552 0.000000 14.775197 6.519753 2.626212
## [33,] 5.805085 5.9213833 5.559774 14.775197 0.000000 8.386095 12.835529
## [34,] 8.727669 3.5383650 9.821452 6.519753 8.386095 0.000000 5.123145
## [35,] 13.848642 8.6611116 14.939778 2.626212 12.835529 5.123145 0.000000knitr::opts_chunk$set(echo = FALSE)2.8 Menghitung Nilai Stress
stress <- sqrt(sum((dist_matrix - disparities)^2) / sum(dist_matrix^2))
cat("Nilai Stress:", stress, "\n")## Nilai Stress: 0.1219136knitr::opts_chunk$set(echo = FALSE)2.9 Visualisasi
plot(fit, type='n', main="Peta Persepsi (Multidimensional Scaling", xlab = "Dimensi 1", ylab = "Dimensi 2")
text(fit, labels = Data$'Kabupaten/Kota')
knitr::opts_chunk$set(echo = FALSE)BAB III HASIL DAN PEMBAHASAN
Proses analisis diawali dengan memuat data dan memilih variabel-variabel yang akan digunakan. Variabel kuantitatif ini yang nantinya akan mewakili karakteristik dari 35 objek kabupaten/kota yang ada di Provinsi Jawa Tengah pada tahun 2024.
Kemudian, data yang sudah dimuat digunakan untuk menghitung matriks ketidaksamaan (disimilarities) atau matriks jarak (dist_matrix). Perhitungan ini menggunakan matriks jarak Euclidean, di mana setiap elemen matriks 〖dist〗_ij mencerminkan tingkat perbedaan yang absolut antara Kabupaten/Kota i dan Kabupaten/Kota j. Matriks simetris berukuran 35 x 35 ini akan menjadi input yang fundamental dan akan merepresentasikan kedekatan antar objek pada ruang multidimensi awal.
Untuk menentukan jumlah dimensi terbaik (k) yang memadai, dilakukan perhitungan nilai eigen (λ) melalui metode Principal Coordinate Analysis (PCoA). Langkah ini melibatkan transformasi matriks jarak kuadrat ke dalam matriks double-centered (B), yang kemudian nilai eigen dan vektor eigennya dihitung. Tingkat representasi dimensi diukur melalui variasi kumulatif yang dijelaskan oleh dimensi-dimensi yang diurutkan. Hasil menunjukkan bahwa Dimensi 1 mampu menjelaskan 74,41% dari total variasi dan gabungan dari dua dimensi (Dimensi 1 dan Dimensi 2) secara kumulatif mampu menjelaskan 89,66% dari total variasi. Karena persentase yang dijelaskan sudah memenuhi kriteria kesesuaian yang baik, yaitu 0,8, sehingga solusi menggunakan 2 dimensi sudah sesuai untuk digunakan dan sudah optimal untuk visualisasi.
Setelah dimensi optimal ditetapkan, koordinat objek (fit) dihitung. Koordinat ini diperoleh dari hasil perkalian matriks vektor eigen dengan akar kuadrat matriks nilai eigen dari dua dimensi pertama. Koordinat ini memberikan posisi spesifik bagi setiap objek Kabupaten/Kota pada bidang 2 dimensi.
Selanjutnya, model MDS juga menghasilkan matriks disparitas (disparities), yaitu jarak yang diprediksi oleh model 2 dimensi yang disesuaikan secara monotonik untuk menjaga urutan kedekatan jarak aslinya. Matriks disparitas ini merupakan hasil output yang dioptimalkan untuk meminimalkan perbedaan dengan jarak aslinya.
Plot koordinat objek memvisualisasikan 35 Kabupaten/Kota pada ruang 2 dimensi berdasarkan koordinat fit yang telah dihitung. Secara interpretatif, objek yang berada berdekatan pada plot memiliki profil akses layanan dasar yang sangat mirip sehingga dapat disimpulkan memiliki tingkat kesejahteraan yang serupa, sedangkan objek yang berjauhan menunjukkan adanya perbedaan signifikan dalam indikator-indikator tersebut. Dimensi 1 pada sumbu horizontal dan Dimensi 2 pada sumbu vertikal dapat diinterpretasikan sebagai faktor laten utama yang memisahkan Kabupaten/Kota.
Berdasarkan output peta persepsi, daerah seperti Kota Semarang, Kota Surakarta, dan Kabupaten Klaten merupakan daerah dengan akses layanan dasar yang paling mirip dan relatif tinggi. Di sisi lain, daerah seperti Kabupaten Banjarnegara, Kabupaten Wonosobo, dan Kabupaten Wonogiri merupakan daerah dengan akses layanan dasar yang paling berbeda dan relatif rendah karena posisinya jauh dari objek lainnya. Sedangkan daerah lain seperti Kabupaten Temanggung, Kabupaten Batang, dan Kabupaten Grobogan merupakan daerah “transisi” atau memiliki profil akses layanan dasar yang moderat, terletak antara dua kelompok ekstrem tersebut.
Kualitas kesesuaian model (Goodness of fit) dievaluasi menggunakan nilai Stress Shepard yang membandingkan matriks jarak asli dan matriks disparitas hasil model. Perhitungan menghasilkan nilai stress sebesar 0,1219136. Menurut kriteria Kruskal, nilai stress ini diklasifikasikan sebagai cukup baik (fair), karena berada di bawah batas 0,15. Nilai stress yang relatif rendah ini mengindikasikan bahwa hanya sekitar 12,19% informasi kedekatan yang terdistorsi akibat reduksi dimensi ke 2 dimensi, sehingga plot yang dihasilkan merupakan representasi yang valid dan andal.
BAB IV KESIMPULAN
Penentuan dimensi optimal untuk analisis Multidimensional Scaling (MDS) menunjukkan bahwa reduksi dari data awal dengan empat variabel kuantitatif menghasilkan dua dimensi ruang representatif terbaik dan mampu menjelaskan 89,66% dari total variasi data awal. Berdasarkan peta persepsi yang dihasilkan, pengelompokkan Kabupaten/Kota berdasarkan kemiripan akses layanan dasar terbagi menjadi 3 kelompok utama, yaitu:
- Daerah seperti Kota Semarang, Kota Surakarta, dan Kabupaten Klaten merupakan daerah dengan akses layanan dasar yang paling mirip dan relatif tinggi.
- Daerah seperti Kabupaten Banjarnegara, Kabupaten Wonosobo, dan Kabupaten Wonogiri merupakan daerah dengan akses layanan dasar yang paling berbeda dan relatif rendah karena posisinya jauh dari objek lainnya.
- Daerah lain seperti Kabupaten Temanggung, Kabupaten Batang, dan Kabupaten Grobogan merupakan daerah “transisi” atau memiliki profil akses layanan dasar yang moderat, terletak antara dua kelompok ekstrem tersebut.
Kualitas model dua dimensi ini selanjutnya dievaluasi menggunakan nilai Stress Shepard. Perhitungan menghasilkan nilai stress sebesar 0,1219136 yang tergolong cukup baik menurut Kruskal. Nilai stress ini mengindikasikan bahwa distorsi informasi yang terjadi akibat proyeksi ke ruang 2 dimensi sangat kecil, hanya sekitar 12,189%. Oleh karena itu, koordinat objek dan peta persepsi yang dihasilkan merupakan representasi yang valid dan andal dari jarak atau ketidakmiripan asli antar Kabupaten/Kota.