Implementasi Multidimensional Scaling untuk Mengidentifikasi Pola Pengeluaran Masyarakat Indonesia Tahun 2024 Menggunakan RStudio
Naomi Andwinovli Sitorus
2025-11-28
1 PENDAHULUAN
1.1 Latar Belakang
Pembangunan ekonomi di Indonesia tidak dapat dilepaskan dari kondisi sosial ekonomi masyarakat yang tersebar pada berbagai wilayah dengan karakteristik yang berbeda. Setiap provinsi memiliki tingkat kemampuan ekonomi yang dipengaruhi oleh struktur industri, akses terhadap lapangan pekerjaan, kualitas sumber daya manusia, serta berbagai faktor demografis. Salah satu indikator penting dalam menilai kondisi tersebut adalah rata-rata penghasilan masyarakat. Indikator ini mencerminkan kapasitas individu dalam memenuhi kebutuhan dasar, meningkatkan kualitas hidup, dan berpartisipasi dalam kegiatan ekonomi produktif. Perbedaan tingkat penghasilan antardaerah pada akhirnya dapat menggambarkan ketimpangan kesejahteraan yang masih menjadi tantangan dalam pembangunan nasional.
Selain menggambarkan kesejahteraan individu, variasi penghasilan juga berkaitan dengan efektivitas kebijakan pemerintah dalam meningkatkan aktivitas ekonomi di berbagai wilayah. Provinsi dengan tingkat penghasilan yang lebih tinggi biasanya memiliki struktur ekonomi yang lebih beragam, peluang kerja yang lebih luas, serta akses terhadap pendidikan dan infrastruktur yang lebih baik. Sebaliknya, provinsi dengan rata-rata penghasilan lebih rendah cenderung menghadapi hambatan dalam meningkatkan produktivitas dan pertumbuhan ekonomi. Oleh karena itu, memahami pola perbedaan penghasilan antarprovinsi menjadi langkah penting dalam upaya merumuskan kebijakan pembangunan yang tepat sasaran dan berkeadilan.
Untuk menganalisis perbedaan tersebut secara komprehensif, diperlukan metode statistik yang mampu menggambarkan hubungan kemiripan atau ketidaksamaan antarprovinsi berdasarkan indikator penghasilan yang dimiliki. Multidimensional Scaling merupakan salah satu metode analisis multivariat yang digunakan untuk memetakan objek ke dalam ruang berdimensi rendah berdasarkan tingkat kemiripannya. Metode ini memungkinkan peneliti untuk melihat struktur pola data secara visual, termasuk pengelompokan provinsi dengan karakteristik penghasilan yang serupa serta jarak antarprovinsi yang mencerminkan tingkat perbedaan ekonomi.
Melalui pendekatan MDS, representasi visual yang dihasilkan dapat membantu peneliti mengidentifikasi provinsi yang memiliki kesenjangan penghasilan cukup besar serta melihat kelompok wilayah yang memiliki struktur ekonomi yang relatif sama. Informasi ini penting bagi pemerintah maupun pemangku kebijakan lainnya dalam merancang strategi pembangunan yang lebih terarah, termasuk pemerataan ekonomi dan optimalisasi sumber daya lokal.
Dengan demikian, penggunaan metode Multidimensional Scaling dalam menganalisis data rata-rata penghasilan per provinsi di Indonesia menjadi relevan untuk memahami pola kesenjangan ekonomi wilayah. Analisis ini diharapkan mampu memberikan gambaran yang lebih jelas mengenai hubungan antarprovinsi serta membantu mendukung upaya pemerataan pembangunan di Indonesia.
1.2 Rumusan Masalah
Berdasarkan latar belakang tersebut, maka rumusan masalah dalam penelitian ini adalah sebagai berikut. - Bagaimana pola kemiripan dan perbedaan rata-rata pengeluaran per kapita antarpovinsi di Indonesia pada tahun 2024 jika dianalisis menggunakan metode Multidimensional Scaling. - Provinsi mana saja yang memiliki karakteristik pengeluaran yang relatif serupa, dan provinsi mana yang menunjukkan perbedaan paling mencolok. - Bagaimana pemetaan dua dimensi yang dihasilkan oleh MDS mampu menggambarkan struktur hubungan antarprovinsi berdasarkan indikator pengeluaran makanan, bukan makanan, dan total pengeluaran.
1.3 Tujuan
Tujuan penelitian ini dirumuskan sebagai berikut. - Untuk menganalisis tingkat kemiripan dan ketidaksamaan rata-rata pengeluaran per kapita antarpovinsi di Indonesia menggunakan metode Multidimensional Scaling. - Untuk mengidentifikasi kelompok provinsi yang memiliki karakteristik pengeluaran yang serupa maupun berbeda secara signifikan. - Untuk menghasilkan pemetaan dua dimensi yang mampu memberikan visualisasi pola hubungan antarprovinsi berdasarkan komponen pengeluaran makanan, pengeluaran bukan makanan, dan total pengeluaran.
2 TINJAUAN PUSTAKA
2.1 Analisis Multivariat
Analisis multivariat merupakan cabang statistika yang mempelajari pengukuran, pemodelan, dan interpretasi beberapa variabel secara simultan. Berbeda dengan analisis univariat atau bivariat yang hanya mempertimbangkan satu atau dua variabel pada satu waktu, analisis multivariat menekankan pemahaman hubungan kompleks antar variabel dalam suatu sistem data yang memiliki dimensi tinggi. Pendekatan ini penting digunakan ketika variabel yang diamati saling berkaitan dan tidak dapat dianalisis secara terpisah tanpa mengurangi makna atau struktur informasinya.
Dalam analisis multivariat, tujuan utama adalah mereduksi dimensi data, mengidentifikasi pola hubungan, mengelompokkan objek, serta melakukan prediksi dengan mempertimbangkan interaksi antar variabel. Teknik-teknik yang umum digunakan meliputi analisis faktor, analisis komponen utama, analisis diskriminan, analisis klaster, dan Multidimensional Scaling. Melalui pendekatan ini, peneliti dapat memahami struktur internal data yang kompleks sehingga interpretasi menjadi lebih informatif dan representatif terhadap fenomena yang diteliti.
Analisis multivariat banyak digunakan dalam bidang ekonomi, ilmu sosial, psikologi, dan pemasaran, terutama ketika analisis perlu dilakukan terhadap unit pengamatan yang memiliki banyak karakteristik. Dengan memanfaatkan teknik reduksi dimensi dan pemetaan visual, peneliti dapat menyajikan temuan secara lebih mudah dipahami tanpa kehilangan informasi penting yang merepresentasikan hubungan antarvariabel.
2.2 Multidimensional Scaling
Multidimensional Scaling (MDS) merupakan metode analisis multivariat yang digunakan untuk memvisualisasikan tingkat kemiripan atau ketidaksamaan antar objek dalam suatu ruang berdimensi rendah, biasanya dua atau tiga dimensi. MDS bekerja dengan mengubah matriks jarak atau ketidaksamaan antar objek menjadi representasi koordinat pada suatu peta persepsi. Semakin dekat posisi dua objek pada peta tersebut, semakin mirip karakteristik keduanya berdasarkan variabel yang dianalisis.
Secara prinsip, MDS berusaha meminimalkan perbedaan antara jarak asli (berdasarkan data) dengan jarak hasil pemetaan dalam ruang representasi. Tingkat ketepatan pemetaan ini diukur melalui indeks yang disebut stress value. Nilai stress yang rendah menunjukkan bahwa peta hasil MDS mampu menggambarkan jarak asli dengan baik. Selain itu, koefisien determinasi atau R-square juga digunakan untuk menilai seberapa besar proporsi variasi jarak asli yang dapat dijelaskan oleh model MDS.
MDS terbagi menjadi dua jenis utama, yaitu metric MDS dan non-metric MDS. Metric MDS mempertahankan jarak absolut antar objek, sedangkan non-metric MDS mempertahankan urutan (ranking) jarak. Pemilihan jenis MDS bergantung pada karakteristik data dan tujuan penelitian. Dalam berbagai aplikasi, MDS digunakan untuk mengidentifikasi pengelompokan objek, visualisasi hubungan kompleks, serta interpretasi pola yang sulit diamati melalui tabel data biasa.
Metode ini banyak diterapkan dalam penelitian ekonomi, pemasaran, dan ilmu sosial karena kemampuannya menampilkan struktur data secara intuitif. Ketika data memiliki dimensi tinggi dan variabel lebih dari satu, MDS menjadi alat yang efektif untuk menyederhanakan informasi tanpa menghilangkan makna hubungan antar objek.
3 SOURCE CODE
3.1 Import Library
> library(readxl)
> library(MASS)3.2 Import Data
> data <- read.csv("C:/Users/nandw/Downloads/Rata-rata Pengeluaran per Kapita Sebulan Makanan dan Bukan Makanan di Daerah Perkotaan dan Perdesaan Menurut Provinsi (rupiah), 2024.csv")
> data <- data[, -4]3.3 Buang kolom Provinsi
> Data <- data[ , -1]3.4 Pastikan data numerik
> Data <- as.data.frame(sapply(Data, as.numeric))
> 3.5 Menghitung Jarak
> D <- as.matrix(dist(Data))
> D
1 2 3 4 5 6 7
1 0.000 65466.83 159690.79 221423.42 164704.93 36847.53 149275.15
2 65466.827 0.00 99346.29 159945.05 100214.81 37020.03 85444.23
3 159690.791 99346.29 0.00 61783.26 28734.53 136353.57 73796.76
4 221423.422 159945.05 61783.26 0.00 64535.00 196901.97 110486.31
5 164704.928 100214.81 28734.53 64535.00 0.00 136336.41 49785.96
6 36847.527 37020.03 136353.57 196901.97 136336.41 0.00 114798.66
7 149275.145 85444.23 73796.76 110486.31 49785.96 114798.66 0.00
8 65535.225 99211.97 197556.93 256471.41 193476.48 63750.39 161769.39
9 382329.680 322722.93 223519.15 163189.27 226782.18 359739.78 267628.30
10 664303.987 599648.82 507274.57 446409.70 499624.30 634957.84 524606.52
11 1207260.086 1142504.25 1050087.64 988975.48 1042562.81 1177603.26 1066176.60
12 298217.552 233126.25 146192.90 92527.91 133803.88 268100.89 158903.71
13 111259.992 88738.30 161485.79 210774.30 146665.86 79492.51 102273.78
14 469091.176 404235.47 331283.94 282187.13 312889.61 434742.46 320005.81
15 129836.262 75962.52 109656.71 152668.84 90037.53 93033.50 42526.89
16 387183.276 323582.10 228610.05 167306.26 223483.25 359814.09 255233.60
17 531923.257 466481.62 384721.39 329404.78 370271.58 499118.56 384747.02
18 9003.729 59766.69 151950.57 213726.60 157902.59 35637.18 144603.66
19 210769.188 258589.74 357132.21 415566.75 351902.80 222270.23 315560.66
20 110800.312 45630.16 69192.55 123812.45 60009.25 78642.32 40881.92
21 241160.458 179792.61 81473.87 19848.28 83647.25 216746.18 127923.39
22 206864.630 143337.48 51015.33 24759.47 43975.99 179848.45 86684.02
23 609520.675 544974.13 452270.80 391353.93 444881.46 580415.79 470615.02
24 303474.153 239534.14 146082.37 86365.13 139360.14 275661.40 172039.42
25 122294.373 60090.39 81951.17 129773.05 65466.85 87255.69 27820.04
26 89932.230 91975.99 180934.36 235384.60 170892.06 67767.57 131625.24
27 134909.114 105393.91 165200.87 209146.13 146692.81 101761.70 98686.30
28 143341.792 131255.25 202764.42 248785.82 185752.55 116747.71 138467.23
29 141968.035 118652.48 181748.50 225562.19 163262.23 110970.73 115077.43
30 143241.555 172581.96 266482.79 321702.77 257222.81 140121.40 216982.54
31 124717.864 98069.45 163566.02 209925.10 146601.03 92134.17 99940.28
32 178511.389 114337.13 80519.28 99358.10 51973.26 144059.93 29279.72
33 288146.807 224819.15 129696.51 69035.14 125030.63 261270.34 160889.81
34 302769.408 237849.78 149320.83 93887.28 138136.12 273090.97 164799.97
35 274583.322 209142.71 134325.92 94982.18 114966.12 242083.81 128641.21
36 137992.217 72540.23 48567.45 96687.40 32178.60 107081.66 28677.81
37 174641.142 152888.28 121567.86 151882.82 149977.69 177050.19 186310.38
38 436076.203 424810.73 376935.72 373298.33 404658.02 446109.62 449646.79
8 9 10 11 12 13 14
1 65535.22 382329.68 664303.99 1207260.1 298217.552 111259.99 469091.2
2 99211.97 322722.93 599648.82 1142504.3 233126.249 88738.30 404235.5
3 197556.93 223519.15 507274.57 1050087.6 146192.904 161485.79 331283.9
4 256471.41 163189.27 446409.70 988975.5 92527.911 210774.30 282187.1
5 193476.48 226782.18 499624.30 1042562.8 133803.879 146665.86 312889.6
6 63750.39 359739.78 634957.84 1177603.3 268100.892 79492.51 434742.5
7 161769.39 267628.30 524606.52 1066176.6 158903.713 102273.78 320005.8
8 0.00 419653.10 686370.17 1227675.9 320325.474 80409.26 474992.4
9 419653.10 0.00 306651.94 841599.8 130027.292 369891.37 232985.8
10 686370.17 306651.94 0.00 542984.7 366903.800 618918.77 248582.6
11 1227675.90 841599.79 542984.71 0.0 909513.430 1157606.47 765528.2
12 320325.47 130027.29 366903.80 909513.4 0.000 257786.74 189836.1
13 80409.26 369891.37 618918.77 1157606.5 257786.745 0.00 399267.1
14 474992.36 232985.79 248582.59 765528.2 189836.099 399267.13 0.0
15 127398.31 309945.88 561151.71 1101313.2 197996.810 60301.95 347931.8
16 415172.24 65910.89 279299.69 821673.1 98379.963 355557.44 167759.6
17 543781.63 238681.58 168528.12 688821.0 238590.724 470608.73 80536.2
18 73177.78 374208.57 657333.58 1200314.2 291607.584 113245.34 463968.6
19 159588.77 578605.20 836286.08 1374088.7 473979.567 217397.84 612126.6
20 133522.08 286667.79 556436.84 1098998.4 189538.011 92776.07 358605.3
21 276181.97 143477.53 427674.61 970013.5 80149.269 229129.66 269674.8
22 237451.56 183165.27 457854.52 1000827.0 95177.691 187982.47 281393.5
23 632375.35 252926.09 55078.45 597881.1 312494.340 565834.45 207055.0
24 331115.79 103594.75 361326.11 904260.3 29688.451 273394.01 204376.6
25 134582.04 290489.74 551975.76 1093758.7 185747.851 81221.12 347493.3
26 44303.56 397164.58 653391.88 1193066.9 289922.500 37444.92 436170.4
27 103888.05 364496.23 604796.53 1141766.0 247697.745 24497.05 380948.1
28 94720.70 404572.74 641489.47 1176633.9 287027.064 43282.11 413501.0
29 103419.41 380211.29 617118.55 1152906.6 262190.320 31516.22 390584.5
30 78586.67 483418.44 734271.41 1271444.6 373932.932 116186.74 509480.4
31 93520.80 367058.97 611189.33 1148924.3 252218.662 13875.44 389094.2
32 189476.00 248076.80 497179.65 1038199.9 133157.543 124781.17 290726.1
33 317962.10 108697.11 377625.19 920392.7 39687.458 262953.32 222204.2
34 325962.79 122548.30 361877.15 904659.2 7514.038 264206.53 189483.7
35 290007.48 171338.91 396756.54 937677.4 41526.742 222967.82 197931.7
36 162089.84 258832.46 527876.92 1070542.4 161029.677 115206.89 333069.5
37 236844.86 266628.21 572119.23 1107912.1 243213.342 240898.54 432907.8
38 501327.86 371544.37 638257.96 1116443.9 437990.711 513053.28 600836.9
15 16 17 18 19 20 21
1 129836.26 387183.28 531923.3 9003.729 210769.2 110800.31 241160.46
2 75962.52 323582.10 466481.6 59766.686 258589.7 45630.16 179792.61
3 109656.71 228610.05 384721.4 151950.574 357132.2 69192.55 81473.87
4 152668.84 167306.26 329404.8 213726.597 415566.7 123812.45 19848.28
5 90037.53 223483.25 370271.6 157902.585 351902.8 60009.25 83647.25
6 93033.50 359814.09 499118.6 35637.183 222270.2 78642.32 216746.18
7 42526.89 255233.60 384747.0 144603.656 315560.7 40881.92 127923.39
8 127398.31 415172.24 543781.6 73177.783 159588.8 133522.08 276181.97
9 309945.88 65910.89 238681.6 374208.575 578605.2 286667.79 143477.53
10 561151.71 279299.69 168528.1 657333.580 836286.1 556436.84 427674.61
11 1101313.24 821673.11 688821.0 1200314.248 1374088.7 1098998.37 970013.51
12 197996.81 98379.96 238590.7 291607.584 473979.6 189538.01 80149.27
13 60301.95 355557.44 470608.7 113245.343 217397.8 92776.07 229129.66
14 347931.76 167759.61 80536.2 463968.616 612126.6 358605.35 269674.85
15 0.00 295476.67 416417.0 127475.260 276142.9 49146.55 170372.01
16 295476.67 0.00 182166.9 379851.175 570793.4 282336.89 148400.32
17 416417.00 182166.91 0.0 526070.872 685911.8 421208.79 313792.54
18 127475.26 379851.17 526070.9 0.000 219770.9 105379.03 233416.74
19 276142.87 570793.42 685911.8 219770.860 0.0 291946.27 435170.73
20 49146.55 282336.89 421208.8 105379.030 291946.3 0.00 143293.59
21 170372.01 148400.32 313792.5 233416.739 435170.7 143293.59 0.00
22 129119.32 180376.06 333724.0 199651.626 395751.1 103962.16 41253.07
23 507657.17 224221.77 130541.6 602501.454 783230.1 501963.38 372600.61
24 213106.06 84200.68 244579.3 296295.194 487362.0 198145.99 69414.81
25 28958.04 281192.41 412559.1 118069.024 289948.8 21644.25 148440.70
26 92320.70 386818.25 506847.7 94518.768 184066.1 112278.25 254513.50
27 56676.20 346014.17 453730.6 136376.542 232323.4 99303.41 226545.78
28 96117.03 385400.38 487954.1 147191.531 198705.8 134930.13 266389.47
29 73229.97 360566.15 464406.6 144368.738 221628.7 115472.50 242842.32
30 176065.73 471542.14 583179.1 151319.202 102739.8 198350.03 340847.55
31 57418.31 350366.46 461276.8 126415.502 225308.8 96165.05 227767.66
32 64839.71 230776.31 355768.8 173730.745 340917.8 69091.38 114095.88
33 202705.16 99067.14 262845.7 280788.154 475208.2 184551.00 51417.04
34 204288.61 91580.58 235984.3 296036.852 480117.6 194637.83 80213.76
35 164448.31 137582.63 257340.4 268764.185 440235.9 163905.39 90824.96
36 61120.03 253552.57 394090.8 131982.032 320020.5 28787.04 115819.44
37 208972.65 298562.76 474281.4 165861.016 383582.6 159827.32 163234.67
38 478338.97 434057.18 609264.1 428163.993 631201.1 429566.57 371418.67
22 23 24 25 26 27 28
1 206864.63 609520.67 303474.15 122294.37 89932.23 134909.11 143341.79
2 143337.48 544974.13 239534.14 60090.39 91975.99 105393.91 131255.25
3 51015.33 452270.80 146082.37 81951.17 180934.36 165200.87 202764.42
4 24759.47 391353.93 86365.13 129773.05 235384.60 209146.13 248785.82
5 43975.99 444881.46 139360.14 65466.85 170892.06 146692.81 185752.55
6 179848.45 580415.79 275661.40 87255.69 67767.57 101761.70 116747.71
7 86684.02 470615.02 172039.42 27820.04 131625.24 98686.30 138467.23
8 237451.56 632375.35 331115.79 134582.04 44303.56 103888.05 94720.70
9 183165.27 252926.09 103594.75 290489.74 397164.58 364496.23 404572.74
10 457854.52 55078.45 361326.11 551975.76 653391.88 604796.53 641489.47
11 1000827.03 597881.10 904260.34 1093758.68 1193066.94 1141766.00 1176633.87
12 95177.69 312494.34 29688.45 185747.85 289922.50 247697.74 287027.06
13 187982.47 565834.45 273394.01 81221.12 37444.92 24497.05 43282.11
14 281393.50 207054.99 204376.65 347493.30 436170.37 380948.07 413501.00
15 129119.32 507657.17 213106.06 28958.04 92320.70 56676.20 96117.03
16 180376.06 224221.77 84200.68 281192.41 386818.25 346014.17 385400.38
17 333723.97 130541.60 244579.31 412559.14 506847.74 453730.63 487954.06
18 199651.63 602501.45 296295.19 118069.02 94518.77 136376.54 147191.53
19 395751.11 783230.06 487361.96 289948.79 184066.09 232323.41 198705.84
20 103962.16 501963.38 198145.99 21644.25 112278.25 99303.41 134930.13
21 41253.07 372600.61 69414.81 148440.70 254513.50 226545.78 266389.47
22 0.00 402954.11 96644.83 107565.85 214045.19 185337.34 225150.78
23 402954.11 0.00 306379.76 497874.66 599961.45 552251.18 589394.21
24 96644.83 306379.76 0.00 197472.15 303627.95 265447.80 305294.89
25 107565.85 497874.66 197472.15 0.00 106793.13 83251.84 121162.27
26 214045.19 599961.45 303627.95 106793.13 0.00 59896.20 54144.77
27 185337.34 552251.18 265447.80 83251.84 59896.20 0.00 40082.89
28 225150.78 589394.21 305294.89 121162.27 54144.77 40082.89 0.00
29 201665.68 564891.57 280604.00 99797.70 59306.67 16596.77 24848.00
30 300344.73 681481.72 388923.64 192943.16 86334.07 129725.86 96378.09
31 186515.09 558405.66 269051.05 81898.37 49761.72 10636.50 39264.33
32 74601.40 443439.46 149021.30 56910.83 156934.22 116647.17 156656.27
33 81483.70 322601.42 18311.68 185350.18 292005.04 256377.41 296407.06
34 98382.36 307334.36 23426.93 191433.94 296051.76 254434.26 293853.43
35 86601.60 343210.10 68756.27 156371.67 256752.41 210920.67 249557.57
36 75744.06 473350.99 169364.68 34168.48 138714.39 117051.03 155303.77
37 159348.29 517653.80 230556.14 180775.56 243002.66 254534.24 283882.44
38 393096.09 593034.88 411935.24 449506.36 513406.48 526362.09 555981.04
29 30 31 32 33 34 35
1 141968.03 143241.56 124717.86 178511.39 288146.81 302769.408 274583.32
2 118652.48 172581.96 98069.45 114337.13 224819.15 237849.785 209142.71
3 181748.50 266482.79 163566.02 80519.28 129696.51 149320.832 134325.92
4 225562.19 321702.77 209925.10 99358.10 69035.14 93887.277 94982.18
5 163262.23 257222.81 146601.03 51973.26 125030.63 138136.120 114966.12
6 110970.73 140121.40 92134.17 144059.93 261270.34 273090.968 242083.81
7 115077.43 216982.54 99940.28 29279.72 160889.81 164799.971 128641.21
8 103419.41 78586.67 93520.80 189476.00 317962.10 325962.793 290007.48
9 380211.29 483418.44 367058.97 248076.80 108697.11 122548.301 171338.91
10 617118.55 734271.41 611189.33 497179.65 377625.19 361877.152 396756.54
11 1152906.61 1271444.65 1148924.25 1038199.91 920392.67 904659.171 937677.38
12 262190.32 373932.93 252218.66 133157.54 39687.46 7514.038 41526.74
13 31516.22 116186.74 13875.44 124781.17 262953.32 264206.532 222967.82
14 390584.53 509480.42 389094.20 290726.12 222204.17 189483.692 197931.70
15 73229.97 176065.73 57418.31 64839.71 202705.16 204288.605 164448.31
16 360566.15 471542.14 350366.46 230776.31 99067.14 91580.581 137582.63
17 464406.62 583179.06 461276.78 355768.83 262845.70 235984.292 257340.40
18 144368.74 151319.20 126415.50 173730.74 280788.15 296036.852 268764.19
19 221628.73 102739.84 225308.84 340917.85 475208.21 480117.580 440235.92
20 115472.50 198350.03 96165.05 69091.38 184551.00 194637.835 163905.39
21 242842.32 340847.55 227767.66 114095.88 51417.04 80213.764 90824.96
22 201665.68 300344.73 186515.09 74601.40 81483.70 98382.355 86601.60
23 564891.57 681481.72 558405.66 443439.46 322601.42 307334.360 343210.10
24 280604.00 388923.64 269051.05 149021.30 18311.68 23426.926 68756.27
25 99797.70 192943.16 81898.37 56910.83 185350.18 191433.938 156371.67
26 59306.67 86334.07 49761.72 156934.22 292005.04 296051.763 256752.41
27 16596.77 129725.86 10636.50 116647.17 256377.41 254434.258 210920.67
28 24848.00 96378.09 39264.33 156656.27 296407.06 293853.429 249557.57
29 0.00 118915.34 20633.87 132169.40 271909.91 269026.688 224729.63
30 118915.34 0.00 123088.52 240831.73 377790.60 380304.960 339004.89
31 20633.87 123088.52 0.00 120030.07 259374.82 258823.355 216258.52
32 132169.40 240831.73 120030.07 0.00 139754.04 139475.040 100545.26
33 271909.91 377790.60 259374.82 139754.04 0.00 35925.023 71559.13
34 269026.69 380304.96 258823.36 139475.04 35925.02 0.000 49039.07
35 224729.63 339004.89 216258.52 100545.26 71559.13 49039.075 0.00
36 133638.87 225044.40 116040.41 48860.12 155880.25 166018.012 136814.28
37 269323.88 315354.01 248764.03 200462.10 212266.48 243443.107 245160.61
38 541363.64 579293.21 520843.02 456332.56 398326.56 433944.841 461147.36
36 37 38
1 137992.22 174641.1 436076.2
2 72540.23 152888.3 424810.7
3 48567.45 121567.9 376935.7
4 96687.40 151882.8 373298.3
5 32178.60 149977.7 404658.0
6 107081.66 177050.2 446109.6
7 28677.81 186310.4 449646.8
8 162089.84 236844.9 501327.9
9 258832.46 266628.2 371544.4
10 527876.92 572119.2 638258.0
11 1070542.43 1107912.1 1116443.9
12 161029.68 243213.3 437990.7
13 115206.89 240898.5 513053.3
14 333069.51 432907.8 600836.9
15 61120.03 208972.6 478339.0
16 253552.57 298562.8 434057.2
17 394090.76 474281.4 609264.1
18 131982.03 165861.0 428164.0
19 320020.48 383582.6 631201.1
20 28787.04 159827.3 429566.6
21 115819.44 163234.7 371418.7
22 75744.06 159348.3 393096.1
23 473350.99 517653.8 593034.9
24 169364.68 230556.1 411935.2
25 34168.48 180775.6 449506.4
26 138714.39 243002.7 513406.5
27 117051.03 254534.2 526362.1
28 155303.77 283882.4 555981.0
29 133638.87 269323.9 541363.6
30 225044.40 315354.0 579293.2
31 116040.41 248764.0 520843.0
32 48860.12 200462.1 456332.6
33 155880.25 212266.5 398326.6
34 166018.01 243443.1 433944.8
35 136814.28 245160.6 461147.4
36 0.00 157632.6 421818.2
37 157632.64 0.0 272162.3
38 421818.22 272162.3 0.03.6 Menghitung Eigen secara manual
> n <- nrow(Data)
> A <- D^2
> I <- diag(n)
> J <- matrix(1, n, n)> V <- I - (1/n)*J> aa <- V %*% A
> BB <- aa %*% V
> B <- (-1/2) * BB> eigen_result <- eigen(B)
> eigenvalues <- eigen_result$values
> eigenvectors <- eigen_result$vectors> eigenvalues
[1] 2.235670e+12 3.235232e+11 3.328804e-04 3.199061e-04 1.821462e-04
[6] 1.724790e-04 1.266828e-04 7.434840e-05 6.065175e-05 5.002769e-05
[11] 4.828613e-05 2.129603e-05 2.117812e-05 2.021574e-05 1.297957e-05
[16] 9.752181e-06 2.401228e-06 1.462427e-06 9.809272e-07 1.025535e-07
[21] -7.897566e-07 -1.425771e-06 -1.446314e-06 -3.583884e-06 -4.330417e-06
[26] -4.348951e-06 -1.078011e-05 -1.677824e-05 -2.458666e-05 -3.244065e-05
[31] -3.451826e-05 -3.958902e-05 -4.163962e-05 -6.992310e-05 -9.089616e-05
[36] -1.031816e-04 -1.058883e-04 -2.891005e-04
> eigenvectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.137188453 -0.065545124 0.000000000 0.000000000 0.000000000
[2,] -0.094548593 -0.039402678 0.614631555 -0.561404308 0.111594326
[3,] -0.030729415 -0.087999632 -0.146659349 -0.254948393 -0.016556975
[4,] 0.010569544 -0.091517133 -0.184438455 0.293145165 0.146563799
[5,] -0.027526538 -0.038187591 -0.109558688 0.013044395 -0.251927241
[6,] -0.118530451 -0.023223953 -0.148541711 0.038593264 -0.156923887
[7,] -0.045143189 0.036087501 -0.081024562 -0.154487392 -0.149438088
[8,] -0.153314267 0.041591726 -0.345926784 -0.210890320 -0.101529361
[9,] 0.115235762 -0.172827497 0.016273070 -0.076023974 0.135579905
[10,] 0.305697007 0.027129740 -0.252246127 -0.092450868 0.174643357
[11,] 0.667266552 0.116042025 0.050490383 -0.031648260 0.182425975
[12,] 0.060459854 0.004726381 0.050444987 0.022918209 0.037642848
[13,] -0.106939665 0.113171154 0.072394523 -0.017125069 0.040959907
[14,] 0.156867501 0.221897753 0.118873584 0.025340439 0.079976577
[15,] -0.069135894 0.076239296 0.083697425 0.014506191 -0.132015770
[16,] 0.121744651 -0.058218762 0.177267623 -0.028585406 -0.282317422
[17,] 0.207048301 0.170447429 -0.121281471 -0.390650836 -0.033054343
[18,] -0.132224190 -0.074504867 -0.029601835 -0.190395580 0.104036409
[19,] -0.251628546 0.150811052 0.002402631 0.152910685 0.663457038
[20,] -0.066182357 -0.009816459 -0.013821246 -0.051470207 -0.001865494
[21,] 0.023635905 -0.097672757 0.030796587 0.014633715 -0.018381868
[22,] 0.001112734 -0.055784011 0.010488714 -0.008918965 -0.154160164
[23,] 0.269446654 0.009924644 0.125260526 0.243284026 -0.171485472
[24,] 0.065634075 -0.045665915 0.013964101 0.049551056 -0.061669036
[25,] -0.063464242 0.027559760 -0.003561697 -0.074410489 -0.099255231
[26,] -0.130602287 0.091615294 0.203757061 0.059080993 -0.074989299
[27,] -0.096262214 0.145837173 -0.086461994 0.021758616 -0.111087731
[28,] -0.119265577 0.182022855 0.274024750 0.197136886 -0.009899218
[29,] -0.103545199 0.167857065 -0.014297038 -0.038955108 0.096070447
[30,] -0.182941468 0.155712999 -0.217019844 -0.152829651 -0.013585420
[31,] -0.101109340 0.132149952 0.162991397 0.231904955 -0.172499561
[32,] -0.026669180 0.053159571 0.074362474 0.075514101 -0.114199140
[33,] 0.055522974 -0.063831197 -0.033601916 -0.035503231 0.100230987
[34,] 0.063976894 -0.004709715 0.081861720 0.051428611 -0.106276360
[35,] 0.040568640 0.055678492 0.079241819 0.120191407 -0.066829035
[36,] -0.046998507 -0.014094931 0.131248124 0.122165113 0.167472992
[37,] -0.057437321 -0.289869324 -0.059787629 -0.008559912 0.105135778
[38,] -0.003400153 -0.746790316 0.092122367 0.056392317 0.042827423
[,6] [,7] [,8] [,9] [,10]
[1,] 0.693418827 0.000000000 0.0000000000 0.0000000000 0.000000000
[2,] -0.145170809 0.309609154 -0.1257577513 -0.0621040613 0.027518423
[3,] 0.006600160 -0.087466665 0.1000891783 -0.0794291216 0.187883735
[4,] -0.014398939 0.390182465 -0.4174659123 0.1731200950 0.100240206
[5,] -0.186339771 0.264785764 -0.2039680089 -0.0431732978 -0.092610716
[6,] 0.008243978 0.315168317 0.1044321451 -0.1157335755 0.124437571
[7,] -0.031814702 -0.225995380 -0.1293997629 -0.1340820662 0.275677179
[8,] 0.103834420 0.062168221 -0.1565622589 -0.0007107262 -0.175610355
[9,] 0.110558639 0.465535986 0.3376442166 0.1077414474 0.159158460
[10,] -0.493716395 -0.046435762 0.1826239760 0.0431937175 0.035503455
[11,] 0.237561365 0.010992336 -0.0137255811 -0.0619815947 0.002808037
[12,] -0.006560123 0.023575643 -0.0394920355 0.0492055766 -0.082580800
[13,] -0.026031499 0.037091419 -0.1062493358 -0.3074369031 -0.067368113
[14,] 0.120568375 0.043609506 -0.1564683134 0.1287273301 -0.192582122
[15,] 0.006880083 0.079288345 0.1659207423 -0.0611339291 0.067254587
[16,] -0.094376039 -0.142095993 0.1218905760 0.0386997561 0.054672631
[17,] 0.145188925 0.049247484 -0.2457209166 0.3392030925 -0.066541049
[18,] -0.096212133 -0.202033275 -0.0748961216 0.1546501750 -0.268544187
[19,] -0.132856129 -0.081867922 -0.1231196234 -0.0127491454 -0.024854476
[20,] -0.034622487 0.017325978 -0.1676286648 -0.0241046453 0.202852732
[21,] -0.026078987 0.031902325 -0.1322022643 -0.0019861364 0.070308961
[22,] -0.069201815 -0.087285324 -0.1833912667 0.0300733984 0.038578427
[23,] -0.073043273 0.165138584 -0.0354319548 -0.4332622818 -0.258149663
[24,] -0.101939408 -0.013667044 -0.1492196983 0.1688365080 0.154261493
[25,] 0.049863709 -0.177148910 0.1905486405 0.1701782202 -0.231908888
[26,] -0.046455878 -0.084618930 -0.0009438096 0.0840122584 -0.021165312
[27,] 0.048213450 0.085779544 -0.0247081777 -0.0050374311 -0.034485492
[28,] 0.004765668 0.035545166 -0.0166058865 -0.0196681955 -0.158155912
[29,] 0.063991897 -0.011753803 -0.0859312177 -0.2633205670 0.422420054
[30,] -0.103072799 0.345198035 0.2410312607 0.1146979217 -0.166613076
[31,] -0.089116637 0.080631714 0.1440449773 0.3597896587 0.035758516
[32,] -0.011610488 -0.033807670 -0.0769054300 0.1058109256 0.313507049
[33,] 0.034712356 -0.035066052 0.1332078484 0.0346181744 0.263248210
[34,] -0.058737570 -0.077197702 -0.1409858197 0.2007192348 0.061457326
[35,] -0.050105110 0.017562748 -0.0009070246 0.2090534094 0.200691458
[36,] 0.085098595 -0.008524769 0.2623287104 0.2199799735 0.085941052
[37,] 0.007047829 -0.045200888 0.1832346935 -0.1729788572 -0.099939212
[38,] -0.002861608 -0.022253925 -0.1601003288 0.1031788559 -0.091291934
[,11] [,12] [,13] [,14] [,15]
[1,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000
[2,] -0.039291098 0.065884177 -0.03181125 0.11191840 0.03915760
[3,] 0.179118188 -0.253018430 -0.35222596 0.11019499 -0.03655764
[4,] -0.097214341 0.103316180 -0.09695456 0.06996785 0.26477624
[5,] 0.253904322 -0.208683741 -0.12786287 -0.28428066 -0.14903420
[6,] -0.300109340 0.003573990 -0.10697298 0.17520491 0.01009274
[7,] -0.039297603 0.068142225 -0.09457614 0.10624526 0.09526655
[8,] -0.123224725 0.153429796 -0.04649496 0.36680400 -0.04068201
[9,] -0.081374277 0.081095355 -0.07183665 -0.05762245 0.01091211
[10,] -0.274241979 0.046022855 -0.05532404 -0.04323062 -0.03888236
[11,] -0.022833166 -0.014315837 -0.05487867 0.05808457 0.02125364
[12,] 0.360491325 0.274051846 -0.20945891 -0.03523719 0.07217933
[13,] -0.050706989 0.112858374 -0.33515603 -0.12724739 -0.18780129
[14,] 0.169805107 -0.269964594 -0.03444780 0.14116037 -0.07846101
[15,] -0.150508932 -0.036645343 0.11985490 0.28431967 -0.07549624
[16,] 0.197295738 -0.076138773 0.08161626 0.38319431 0.12668674
[17,] -0.035370079 -0.065023277 0.09516227 -0.10862033 -0.04121288
[18,] -0.184783865 -0.036541350 0.22601803 -0.11333416 0.09915432
[19,] 0.178484915 -0.085124597 -0.05581984 0.34195227 -0.04533874
[20,] 0.170687707 0.264942650 0.18418404 -0.15956734 0.27559531
[21,] -0.137236138 -0.198268488 0.06649345 -0.03580605 0.47813322
[22,] -0.081469447 -0.377682999 0.10262845 0.13351470 0.08858880
[23,] 0.119103455 0.007637752 0.04595174 0.09601214 0.06242034
[24,] 0.090647446 -0.136672691 -0.29782822 0.02673632 -0.10546831
[25,] 0.105622203 0.216180456 -0.38889004 -0.06632933 0.30699617
[26,] -0.172408397 -0.045355811 -0.23607767 -0.21267074 0.01366184
[27,] -0.099000541 -0.239891364 -0.07170806 -0.04926478 -0.17074997
[28,] -0.223145097 -0.165475771 0.08211517 -0.21832062 0.02485006
[29,] 0.100322713 -0.066803965 0.09015105 -0.20242680 0.08251576
[30,] 0.362782681 -0.123134664 0.22258049 -0.04997870 -0.03801879
[31,] 0.065698101 -0.003732014 -0.12470831 0.16435525 0.25713165
[32,] 0.049064622 0.159409740 0.07852091 0.08233453 -0.34684875
[33,] 0.150045632 -0.340002144 -0.05084300 -0.17783557 0.15368503
[34,] -0.004872241 0.238777284 0.01788850 -0.14544593 -0.22342965
[35,] 0.143523017 0.128101855 0.28936786 0.04104405 -0.15941366
[36,] -0.133971306 -0.105375572 -0.08520906 -0.04974097 -0.13656849
[37,] 0.159753008 0.023484387 0.20029301 -0.08729597 0.05197418
[38,] 0.025094469 -0.096484502 -0.04211966 0.04323913 -0.20810783
[,16] [,17] [,18] [,19] [,20]
[1,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
[2,] -0.010100744 -0.071528087 0.049164859 -0.131893810 -0.095903026
[3,] -0.380586609 -0.007439030 0.068185951 -0.038588563 0.135455116
[4,] -0.260804148 -0.102584581 -0.014902063 -0.072065804 0.135738038
[5,] 0.124029112 -0.097068575 0.155729694 0.312520398 0.182369129
[6,] 0.074260870 -0.022850821 -0.049784191 -0.447454207 -0.069167230
[7,] -0.032130653 -0.054589806 0.030931720 0.118019065 0.336319189
[8,] 0.050145741 -0.021435886 -0.049588756 0.248930178 -0.071052179
[9,] 0.006693646 0.026863662 -0.082891306 0.574979992 -0.066135564
[10,] -0.004217622 -0.041556695 -0.001254957 -0.002230126 -0.029312156
[11,] -0.019758571 -0.038759929 -0.003970722 0.040267889 0.032160785
[12,] -0.034545191 -0.123687956 -0.155124573 -0.044777013 -0.179046658
[13,] 0.069905104 0.131944115 -0.198236105 -0.003542486 0.364915972
[14,] -0.165139245 0.004599706 0.105640439 0.023644737 0.063774576
[15,] -0.027285287 0.112303429 0.223257864 0.155934059 0.016418156
[16,] 0.156599437 0.017710468 -0.010138465 0.135493474 0.229326287
[17,] 0.030366023 0.081787333 -0.079633313 -0.139136638 0.149124694
[18,] -0.319805982 -0.206408105 0.078505689 0.071848259 0.038695228
[19,] 0.202489494 0.026879131 0.067557781 0.132603008 -0.023440798
[20,] 0.196649504 0.012619742 -0.044759629 0.036286272 0.216283790
[21,] 0.208204990 -0.027240490 0.269045502 0.017892355 0.027712099
[22,] 0.018250423 0.114925750 -0.584713307 0.116732832 -0.265150067
[23,] -0.122866822 -0.060400432 0.043275621 -0.124344518 -0.038822015
[24,] 0.002494039 0.093419551 -0.086169673 -0.053723590 -0.243240790
[25,] 0.164446157 -0.200570140 0.078976550 -0.029494221 -0.231672370
[26,] -0.346472252 0.043401408 0.050786033 0.136157721 -0.022209541
[27,] 0.127423812 -0.169747451 0.405098561 0.019732995 -0.196211010
[28,] 0.103898227 -0.179173572 -0.238435076 0.143068512 0.065610542
[29,] -0.197678226 0.208161860 0.065695986 0.018703646 -0.297106428
[30,] 0.008437584 0.087182270 -0.134383825 -0.197347538 0.054988980
[31,] -0.209556410 0.183202939 -0.035640675 0.018104604 0.091295242
[32,] -0.031725829 -0.600445389 -0.199253182 0.036989804 -0.053760297
[33,] 0.230508780 -0.205726501 -0.019444174 -0.103948615 -0.021404829
[34,] 0.140337054 0.491742123 0.104880260 0.021648687 -0.120659543
[35,] -0.157959342 -0.100683008 0.245867679 -0.056685096 -0.011842020
[36,] 0.078191232 0.013616000 -0.067865283 -0.208663681 0.387717381
[37,] -0.306791395 0.017026345 -0.106920526 0.047252472 0.039264993
[38,] 0.075233356 0.044819582 0.087049784 -0.086187871 0.009439358
[,21] [,22] [,23] [,24] [,25]
[1,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.0000000000
[2,] -0.0095135405 0.100746466 -0.031911108 -0.101038047 0.0397948652
[3,] -0.2982831608 0.065557165 0.062884431 0.231912419 0.0389778344
[4,] -0.0792214329 -0.009541716 -0.033146295 -0.053379715 -0.0449823103
[5,] 0.0158168222 0.036531011 0.152555613 -0.023418533 0.1271868252
[6,] 0.1378126978 -0.310658629 0.231341118 -0.085513857 0.0293247165
[7,] -0.0494003059 -0.156431488 -0.054138584 -0.368085821 0.1440946581
[8,] 0.0508128373 0.511913838 0.076592672 -0.025000886 -0.0131192952
[9,] -0.0277136727 -0.242407583 -0.058941271 -0.006593932 0.0689080461
[10,] 0.0970431738 0.174484191 -0.096596927 0.065930521 0.0134391520
[11,] -0.0296407177 -0.004551531 0.067250345 0.016703386 0.0391824269
[12,] -0.1049350185 0.077601611 -0.026146817 -0.065200216 0.0095894830
[13,] 0.1371969438 -0.138114883 -0.131325921 0.288525469 0.1745884012
[14,] 0.1993881562 -0.183404422 0.078923117 0.048387586 0.0076860953
[15,] -0.3566496785 0.118263546 0.217855283 0.098969846 -0.0696527352
[16,] 0.2531119471 -0.133112726 -0.101437408 -0.044516059 -0.1865946320
[17,] 0.0849049855 0.106079699 -0.068778628 0.005990586 -0.0390383764
[18,] -0.3037159396 -0.361468363 -0.069901060 0.052432893 -0.0379556032
[19,] -0.0049496596 -0.083754338 0.114754224 -0.018761839 0.0225650691
[20,] -0.2317551214 0.014556288 0.023956944 -0.054422438 -0.0693055511
[21,] 0.2365319497 0.079011761 0.116905141 0.362840651 0.1032570426
[22,] -0.1477645392 -0.088141270 0.040786615 0.073052482 0.3813618107
[23,] -0.2893125288 0.119892254 -0.020807204 0.010190568 0.0008701292
[24,] 0.0028275920 -0.010112678 -0.017324818 -0.387789837 -0.0821035205
[25,] -0.0183077934 -0.047992296 0.056179915 0.119478018 0.3067608249
[26,] 0.2333986280 0.085141863 0.449967393 -0.059079004 -0.2153112756
[27,] -0.0493430639 -0.058147633 -0.487429738 -0.192173283 0.0384684590
[28,] -0.0726955441 0.221983857 -0.028729373 -0.117285294 -0.0167076592
[29,] 0.1268471623 0.150058901 -0.254602753 0.192077748 0.0384690602
[30,] -0.0009553878 -0.053094342 0.059809015 0.110548530 -0.0685091741
[31,] 0.0078411820 0.121049305 -0.364622368 0.119707941 -0.0801036669
[32,] 0.0847228816 -0.018357739 -0.009748938 0.350024598 -0.1953883669
[33,] -0.1585475573 0.120793633 0.209158449 -0.098828253 -0.2351695338
[34,] -0.2083178306 -0.092923274 0.149551657 0.087717628 -0.0989849839
[35,] 0.0852976382 0.071760102 0.200216215 -0.071607494 0.6218939170
[36,] -0.1668534054 0.290355059 -0.061453546 -0.071902889 0.2467594412
[37,] 0.3212374643 0.137143722 -0.007554768 -0.281267672 0.0549441281
[38,] 0.0330992360 0.098845784 -0.119005197 0.167456921 -0.0163785670
[,26] [,27] [,28] [,29] [,30]
[1,] 0.0000000000 0.00000000 0.000000000 0.000000000 0.000000000
[2,] 0.0456177954 0.09418243 -0.075241525 -0.030329671 0.038453415
[3,] -0.1623740648 0.20768563 0.138217020 0.259902506 -0.228290771
[4,] -0.0761943082 0.17394546 -0.214303609 0.012612614 -0.112273380
[5,] -0.0005563272 0.06194794 -0.124955466 -0.302398122 0.114300154
[6,] 0.0087867332 0.04285754 -0.032342552 -0.066439381 -0.011704436
[7,] 0.0514113249 -0.18783827 -0.270294084 0.085165914 0.182456987
[8,] 0.0006640760 -0.02892826 0.080638670 -0.024095379 0.073518032
[9,] -0.0434575763 -0.03590298 0.082222823 0.057321200 -0.037854159
[10,] 0.0545973454 -0.03594763 -0.092180786 -0.044870400 -0.081680764
[11,] -0.0055889279 0.02644745 -0.001923448 0.011304703 0.049353058
[12,] 0.0397719527 -0.01237784 0.199889072 0.005391871 0.417164732
[13,] 0.1491062993 -0.11381716 0.044131466 0.242308095 0.060032070
[14,] 0.0458220569 -0.16973563 -0.237717924 -0.152706352 -0.002756676
[15,] 0.0299407750 -0.22867051 -0.291438573 0.023665931 0.090067203
[16,] -0.2410420685 0.21700028 0.059954000 -0.098326136 -0.186091698
[17,] 0.0375399530 0.04965789 -0.060819133 0.109649928 -0.132169811
[18,] -0.1204877135 -0.10475033 0.065475004 -0.082152399 0.188588148
[19,] 0.0041018188 0.12867742 -0.007347233 0.046775189 -0.062826358
[20,] 0.0354549037 0.02094105 0.217535758 -0.125364062 -0.308692461
[21,] -0.2573128754 -0.01277457 0.149912030 0.272540209 0.375935479
[22,] 0.1434782660 0.20567834 0.010542552 -0.097364434 0.039765208
[23,] -0.0613195404 0.04641324 0.022671997 0.009472727 -0.041450943
[24,] -0.4179380595 -0.37635539 0.124175679 0.160739541 0.054368614
[25,] -0.1114300158 0.01724404 -0.387612877 -0.066605797 -0.256367263
[26,] 0.1061069398 0.13962010 0.233886719 -0.129021309 -0.095070886
[27,] 0.1077223235 0.34185531 0.122831092 0.127134587 0.001007423
[28,] -0.2274178901 -0.12386784 -0.139549235 0.352761576 -0.286890699
[29,] -0.1803676733 -0.13375088 -0.190358163 -0.302884758 -0.072166001
[30,] -0.1640161874 -0.13219393 -0.025464504 0.118862727 0.016959126
[31,] 0.3505992163 -0.08270111 -0.031341688 0.064281616 0.110710588
[32,] -0.1039373405 0.09476273 -0.141820881 0.044834782 0.114329345
[33,] 0.4216115774 -0.02649442 -0.147995004 0.122194193 0.082383458
[34,] -0.1119992189 0.35723366 -0.266075487 0.227246797 0.140034974
[35,] 0.1305670936 -0.10429224 0.190217671 0.206473718 -0.152160886
[36,] -0.2994481834 0.16698344 0.018489511 -0.374389248 0.239353997
[37,] -0.0302883160 0.29345766 -0.325835074 0.243415732 0.155534474
[38,] 0.1126782967 -0.24143091 -0.064199104 -0.035811343 -0.179448822
[,31] [,32] [,33] [,34] [,35]
[1,] 0.0000000000 0.000000000 0.000000e+00 0.000000000 0.000000000
[2,] -0.0050008723 0.006087313 7.172497e-02 0.026900651 -0.060390057
[3,] -0.2015192274 -0.015111587 -1.609932e-02 0.172404105 -0.097637825
[4,] 0.0485491456 -0.211619408 -3.455857e-02 -0.261760496 -0.067353767
[5,] 0.0688930272 -0.038598470 -1.471516e-01 0.282938749 -0.110717146
[6,] -0.1209256019 -0.032482350 -1.280631e-01 0.309574356 0.248474521
[7,] -0.0479360126 0.002563104 3.920942e-01 -0.150819594 -0.048795263
[8,] -0.0097145815 -0.066791786 1.770061e-01 0.137407327 0.325228213
[9,] 0.0519910819 0.025653003 1.025203e-01 0.019833873 0.064636762
[10,] -0.1920383775 0.017663100 -2.326354e-02 -0.069772035 0.083328183
[11,] 0.0347386208 0.015815382 2.063037e-02 0.013838238 0.185376245
[12,] -0.3371405757 -0.307608678 -2.530391e-01 -0.147622671 0.057414635
[13,] 0.1642184168 -0.040017849 -1.842929e-01 -0.147962049 0.294045574
[14,] -0.4783008768 0.183797934 7.721023e-02 0.026705645 0.191246007
[15,] -0.0003330675 0.081004638 -4.972955e-01 -0.315849253 -0.009553851
[16,] 0.0785828428 -0.365713230 -1.382534e-01 -0.096903036 0.212521194
[17,] 0.2957760242 0.043438133 -2.538204e-01 0.009031273 -0.070978225
[18,] 0.1546922825 -0.137628644 -6.850577e-02 0.167028546 0.352298081
[19,] 0.1837411308 0.058277582 -1.902325e-02 0.101315268 0.020359683
[20,] -0.2556634237 0.448778300 -1.329819e-01 -0.003169558 0.297311014
[21,] -0.0496409366 0.133744170 3.848833e-02 -0.033261958 -0.018663014
[22,] -0.0242815772 0.091451859 -1.186481e-02 -0.170177983 0.022870882
[23,] 0.3064626288 0.148060562 2.320478e-01 0.039103760 0.144861077
[24,] 0.1981054270 0.247102065 -1.404212e-01 0.029808317 0.115077479
[25,] 0.1361845083 0.088593129 -3.235489e-03 -0.083562133 0.079908012
[26,] 0.1038516657 0.070780425 1.185872e-01 -0.314284029 0.163033019
[27,] -0.0940273618 0.108966347 -3.488633e-02 -0.269878712 0.197008569
[28,] -0.2692773953 -0.235107795 2.687548e-05 0.152934499 0.055124701
[29,] 0.0661561209 -0.204052389 -1.286727e-02 0.028232105 0.220683105
[30,] 0.0170619469 0.002206848 3.012752e-01 -0.340949969 0.093953633
[31,] 0.0815992270 0.145934477 3.466784e-02 0.313941696 0.044790756
[32,] 0.0700943193 0.231236911 5.761923e-02 0.006459068 0.029871616
[33,] 0.1598345539 -0.202246720 5.036414e-02 0.038269622 0.271227880
[34,] -0.0917812773 -0.081396125 1.977279e-01 0.112887150 0.195235129
[35,] 0.0765809283 -0.166736205 -1.063696e-02 0.032785546 0.137213215
[36,] 0.0258699500 0.060439728 5.782380e-02 -0.050691097 0.124835107
[37,] 0.0033886519 0.256154892 -2.472832e-01 0.053832699 0.150380372
[38,] -0.0684410329 -0.023019181 9.538158e-02 -0.124091566 0.161386081
[,36] [,37] [,38]
[1,] 0.000000000 0.704310652 0.000000000
[2,] -0.143391457 0.120842334 -0.068983640
[3,] 0.024357085 -0.020673183 0.002433953
[4,] -0.218809741 0.007718204 0.002524767
[5,] 0.044252494 0.174542542 -0.199298060
[6,] 0.268484939 -0.033365612 -0.068248427
[7,] 0.305325606 0.025887935 -0.030011495
[8,] -0.137801736 -0.128221196 0.013658459
[9,] 0.117617688 -0.102486630 0.250780420
[10,] 0.032455359 0.548150967 0.090147909
[11,] 0.017984081 -0.093115541 -0.613001668
[12,] 0.327349372 0.018675137 0.087850083
[13,] -0.200967764 0.015330822 0.049403019
[14,] -0.134444049 -0.067498135 0.342257738
[15,] 0.060980696 -0.013145210 -0.047535053
[16,] -0.037025903 0.111212469 0.044225292
[17,] 0.424205891 -0.086751635 0.253983175
[18,] -0.029939289 0.062035469 -0.044315703
[19,] 0.284925596 0.095823255 -0.045402872
[20,] -0.003439573 0.020282255 -0.046820301
[21,] 0.066814492 0.021189883 0.058555059
[22,] 0.001733657 0.063156968 -0.031268171
[23,] 0.208317269 0.125321209 0.331040694
[24,] -0.179657249 0.108897635 -0.002814995
[25,] -0.009754035 -0.058889621 -0.021065982
[26,] 0.212676072 0.028824199 -0.064550335
[27,] 0.043846538 -0.052646176 -0.075778200
[28,] 0.170421264 -0.010983439 -0.093942620
[29,] 0.138812093 -0.067549993 -0.007234677
[30,] 0.038089916 0.080335844 -0.260951822
[31,] 0.085364635 0.080342254 -0.192000264
[32,] 0.052544095 0.011183386 -0.011856862
[33,] -0.195635552 -0.029300869 0.181414041
[34,] -0.025441408 0.069852598 0.036028089
[35,] -0.057718194 0.062413978 0.036589730
[36,] -0.001744445 -0.094248858 0.106012125
[37,] -0.012583773 -0.045102761 -0.030879484
[38,] 0.259107614 -0.067343341 -0.1210926183.7 Menghitung Tingkat Kumulatif Keragaman
> cumulative_variance <- cumsum(eigenvalues) / sum(eigenvalues)
> cumulative_variance
[1] 0.8735839 1.0000000 1.0000000 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
[36] 1.0000000 1.0000000 1.00000003.8 MDS Klasik (2 dimensi)
> fit <- cmdscale(D, k=2)
> fit
[,1] [,2]
1 -205126.333 -37281.477
2 -141370.543 -22411.889
3 -45947.105 -50053.399
4 15803.748 -52054.122
5 -41158.112 -21720.758
6 -177228.594 -13209.576
7 -67498.806 20526.246
8 -229237.903 23656.999
9 172302.324 -98302.725
10 457082.973 15431.152
11 997707.444 66003.660
12 90400.524 2688.323
13 -159897.870 64370.734
14 234550.754 126213.445
15 -103373.075 43364.226
16 182034.517 -33114.308
17 309581.876 96948.964
18 -197703.688 -42377.698
19 -376238.960 85779.969
20 -98956.901 -5583.514
21 35340.776 -55555.385
22 1663.777 -31729.444
23 402880.876 5645.048
24 98137.101 -25974.362
25 -94892.733 15675.744
26 -195278.593 52109.955
27 -143932.777 82950.872
28 -178327.767 103532.962
29 -154822.410 95475.588
30 -273536.961 88568.153
31 -151180.276 75165.704
32 -39876.178 30236.685
33 83018.825 -36306.610
34 95659.259 -2678.844
35 60658.869 31669.425
36 -70272.907 -8017.070
37 -85881.186 -164875.063
38 -5083.963 -424767.6113.9 Visualisasi
> plot(fit, type="n",
+ xlab="Dimensi 1",
+ ylab="Dimensi 2",
+ main="MDS Pengeluaran Per Kapita Provinsi")
> text(fit, labels = data$Provinsi, cex=0.6)
3.10 Hitung Disparities
> disparities <- matrix(0, n, n)
> disparities
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
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[14,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
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[33,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[34,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[35,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[36,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[37,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[38,] 0 0 0 0 0 0 0 0 0 0 0 0 0
[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
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[5,] 0 0 0 0 0 0 0 0 0 0 0 0
[6,] 0 0 0 0 0 0 0 0 0 0 0 0
[7,] 0 0 0 0 0 0 0 0 0 0 0 0
[8,] 0 0 0 0 0 0 0 0 0 0 0 0
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[11,] 0 0 0 0 0 0 0 0 0 0 0 0
[12,] 0 0 0 0 0 0 0 0 0 0 0 0
[13,] 0 0 0 0 0 0 0 0 0 0 0 0
[14,] 0 0 0 0 0 0 0 0 0 0 0 0
[15,] 0 0 0 0 0 0 0 0 0 0 0 0
[16,] 0 0 0 0 0 0 0 0 0 0 0 0
[17,] 0 0 0 0 0 0 0 0 0 0 0 0
[18,] 0 0 0 0 0 0 0 0 0 0 0 0
[19,] 0 0 0 0 0 0 0 0 0 0 0 0
[20,] 0 0 0 0 0 0 0 0 0 0 0 0
[21,] 0 0 0 0 0 0 0 0 0 0 0 0
[22,] 0 0 0 0 0 0 0 0 0 0 0 0
[23,] 0 0 0 0 0 0 0 0 0 0 0 0
[24,] 0 0 0 0 0 0 0 0 0 0 0 0
[25,] 0 0 0 0 0 0 0 0 0 0 0 0
[26,] 0 0 0 0 0 0 0 0 0 0 0 0
[27,] 0 0 0 0 0 0 0 0 0 0 0 0
[28,] 0 0 0 0 0 0 0 0 0 0 0 0
[29,] 0 0 0 0 0 0 0 0 0 0 0 0
[30,] 0 0 0 0 0 0 0 0 0 0 0 0
[31,] 0 0 0 0 0 0 0 0 0 0 0 0
[32,] 0 0 0 0 0 0 0 0 0 0 0 0
[33,] 0 0 0 0 0 0 0 0 0 0 0 0
[34,] 0 0 0 0 0 0 0 0 0 0 0 0
[35,] 0 0 0 0 0 0 0 0 0 0 0 0
[36,] 0 0 0 0 0 0 0 0 0 0 0 0
[37,] 0 0 0 0 0 0 0 0 0 0 0 0
[38,] 0 0 0 0 0 0 0 0 0 0 0 0
[,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
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[8,] 0 0 0 0 0 0 0 0 0 0 0 0
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[10,] 0 0 0 0 0 0 0 0 0 0 0 0
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[20,] 0 0 0 0 0 0 0 0 0 0 0 0
[21,] 0 0 0 0 0 0 0 0 0 0 0 0
[22,] 0 0 0 0 0 0 0 0 0 0 0 0
[23,] 0 0 0 0 0 0 0 0 0 0 0 0
[24,] 0 0 0 0 0 0 0 0 0 0 0 0
[25,] 0 0 0 0 0 0 0 0 0 0 0 0
[26,] 0 0 0 0 0 0 0 0 0 0 0 0
[27,] 0 0 0 0 0 0 0 0 0 0 0 0
[28,] 0 0 0 0 0 0 0 0 0 0 0 0
[29,] 0 0 0 0 0 0 0 0 0 0 0 0
[30,] 0 0 0 0 0 0 0 0 0 0 0 0
[31,] 0 0 0 0 0 0 0 0 0 0 0 0
[32,] 0 0 0 0 0 0 0 0 0 0 0 0
[33,] 0 0 0 0 0 0 0 0 0 0 0 0
[34,] 0 0 0 0 0 0 0 0 0 0 0 0
[35,] 0 0 0 0 0 0 0 0 0 0 0 0
[36,] 0 0 0 0 0 0 0 0 0 0 0 0
[37,] 0 0 0 0 0 0 0 0 0 0 0 0
[38,] 0 0 0 0 0 0 0 0 0 0 0 0
[,38]
[1,] 0
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 0
[8,] 0
[9,] 0
[10,] 0
[11,] 0
[12,] 0
[13,] 0
[14,] 0
[15,] 0
[16,] 0
[17,] 0
[18,] 0
[19,] 0
[20,] 0
[21,] 0
[22,] 0
[23,] 0
[24,] 0
[25,] 0
[26,] 0
[27,] 0
[28,] 0
[29,] 0
[30,] 0
[31,] 0
[32,] 0
[33,] 0
[34,] 0
[35,] 0
[36,] 0
[37,] 0
[38,] 0> for (i in 1:n) {
+ for (j in 1:n) {
+ disparities[i, j] <- sqrt(sum((fit[i,] - fit[j,])^2))
+ }
+ }3.11 Hitung Stress
> stress <- sqrt(sum((D - disparities)^2) / sum(D^2))
> cat("Nilai Stress:", stress, "\n")
Nilai Stress: 5.768386e-16 4 HASIL DAN PEMBAHASAN
Data yang digunakan dalam penelitian ini adalah Rata-rata Pengeluaran per Kapita Sebulan untuk Komoditas Makanan dan Bukan Makanan di Indonesia Menurut Provinsi Tahun 2024. Data terdiri dari beberapa provinsi sebagai objek (observasi) dan dua variabel numerik, yaitu: - Rata-rata Pengeluaran per Kapita Sebulan di Perkotaan dan Perdesaan - Makanan (X1) - Rata-rata Pengeluaran per Kapita Sebulan di Perkotaan dan Perdesaan - Bukan Makanan (X2)
Matriks jarak D berukuran n x n yakni 38x38 dengan elemen matriks dij, yaitu jarak Euclidean antar objek.
> D <- as.matrix(dist(Data))> head(D)
1 2 3 4 5 6 7
1 0.00 65466.83 159690.79 221423.42 164704.93 36847.53 149275.15
2 65466.83 0.00 99346.29 159945.05 100214.81 37020.03 85444.23
3 159690.79 99346.29 0.00 61783.26 28734.53 136353.57 73796.76
4 221423.42 159945.05 61783.26 0.00 64535.00 196901.97 110486.31
5 164704.93 100214.81 28734.53 64535.00 0.00 136336.41 49785.96
6 36847.53 37020.03 136353.57 196901.97 136336.41 0.00 114798.66
8 9 10 11 12 13 14 15
1 65535.22 382329.7 664304.0 1207260.1 298217.55 111259.99 469091.2 129836.26
2 99211.97 322722.9 599648.8 1142504.3 233126.25 88738.30 404235.5 75962.52
3 197556.93 223519.2 507274.6 1050087.6 146192.90 161485.79 331283.9 109656.71
4 256471.41 163189.3 446409.7 988975.5 92527.91 210774.30 282187.1 152668.84
5 193476.48 226782.2 499624.3 1042562.8 133803.88 146665.86 312889.6 90037.53
6 63750.39 359739.8 634957.8 1177603.3 268100.89 79492.51 434742.5 93033.50
16 17 18 19 20 21 22 23
1 387183.3 531923.3 9003.729 210769.2 110800.31 241160.46 206864.63 609520.7
2 323582.1 466481.6 59766.686 258589.7 45630.16 179792.61 143337.48 544974.1
3 228610.0 384721.4 151950.574 357132.2 69192.55 81473.87 51015.33 452270.8
4 167306.3 329404.8 213726.597 415566.7 123812.45 19848.28 24759.47 391353.9
5 223483.2 370271.6 157902.585 351902.8 60009.25 83647.25 43975.99 444881.5
6 359814.1 499118.6 35637.183 222270.2 78642.32 216746.18 179848.45 580415.8
24 25 26 27 28 29 30 31
1 303474.15 122294.37 89932.23 134909.1 143341.8 141968.0 143241.6 124717.86
2 239534.14 60090.39 91975.99 105393.9 131255.3 118652.5 172582.0 98069.45
3 146082.37 81951.17 180934.36 165200.9 202764.4 181748.5 266482.8 163566.02
4 86365.13 129773.05 235384.60 209146.1 248785.8 225562.2 321702.8 209925.10
5 139360.14 65466.85 170892.06 146692.8 185752.5 163262.2 257222.8 146601.03
6 275661.40 87255.69 67767.57 101761.7 116747.7 110970.7 140121.4 92134.17
32 33 34 35 36 37 38
1 178511.39 288146.81 302769.41 274583.32 137992.22 174641.1 436076.2
2 114337.13 224819.15 237849.78 209142.71 72540.23 152888.3 424810.7
3 80519.28 129696.51 149320.83 134325.92 48567.45 121567.9 376935.7
4 99358.10 69035.14 93887.28 94982.18 96687.40 151882.8 373298.3
5 51973.26 125030.63 138136.12 114966.12 32178.60 149977.7 404658.0
6 144059.93 261270.34 273090.97 242083.81 107081.66 177050.2 446109.6Nilai eigen dan vektor eigen melalui perhitungan matriks pusat B.
> n <- nrow(Data)
> A <- D^2
> I <- diag(n)
> J <- matrix(1, n, n)
>
> V <- I - (1/n)*J
>
> aa <- V %*% A
> BB <- aa %*% V
> B <- (-1/2) * BB
>
> eigen_result <- eigen(B)Nilai eigen dan vektor eigen melalui perhitungan matriks pusat B.
> eigenvalues <- eigen_result$values
> head(eigenvalues)
[1] 2.235670e+12 3.235232e+11 3.328804e-04 3.199061e-04 1.821462e-04
[6] 1.724790e-04> eigenvectors <- eigen_result$vectors
> head(eigenvectors)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.13718845 -0.06554512 0.0000000 0.00000000 0.00000000 0.693418827
[2,] -0.09454859 -0.03940268 0.6146316 -0.56140431 0.11159433 -0.145170809
[3,] -0.03072942 -0.08799963 -0.1466593 -0.25494839 -0.01655698 0.006600160
[4,] 0.01056954 -0.09151713 -0.1844385 0.29314516 0.14656380 -0.014398939
[5,] -0.02752654 -0.03818759 -0.1095587 0.01304440 -0.25192724 -0.186339771
[6,] -0.11853045 -0.02322395 -0.1485417 0.03859326 -0.15692389 0.008243978
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000
[2,] 0.30960915 -0.1257578 -0.06210406 0.02751842 -0.03929110 0.06588418
[3,] -0.08746667 0.1000892 -0.07942912 0.18788374 0.17911819 -0.25301843
[4,] 0.39018247 -0.4174659 0.17312010 0.10024021 -0.09721434 0.10331618
[5,] 0.26478576 -0.2039680 -0.04317330 -0.09261072 0.25390432 -0.20868374
[6,] 0.31516832 0.1044321 -0.11573358 0.12443757 -0.30010934 0.00357399
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
[2,] -0.03181125 0.11191840 0.03915760 -0.01010074 -0.07152809 0.04916486
[3,] -0.35222596 0.11019499 -0.03655764 -0.38058661 -0.00743903 0.06818595
[4,] -0.09695456 0.06996785 0.26477624 -0.26080415 -0.10258458 -0.01490206
[5,] -0.12786287 -0.28428066 -0.14903420 0.12402911 -0.09706857 0.15572969
[6,] -0.10697298 0.17520491 0.01009274 0.07426087 -0.02285082 -0.04978419
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.00000000 0.00000000 0.00000000 0.000000000 0.00000000 0.00000000
[2,] -0.13189381 -0.09590303 -0.00951354 0.100746466 -0.03191111 -0.10103805
[3,] -0.03858856 0.13545512 -0.29828316 0.065557165 0.06288443 0.23191242
[4,] -0.07206580 0.13573804 -0.07922143 -0.009541716 -0.03314630 -0.05337972
[5,] 0.31252040 0.18236913 0.01581682 0.036531011 0.15255561 -0.02341853
[6,] -0.44745421 -0.06916723 0.13781270 -0.310658629 0.23134112 -0.08551386
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.00000000 0.0000000000 0.00000000 0.00000000 0.00000000 0.00000000
[2,] 0.03979487 0.0456177954 0.09418243 -0.07524153 -0.03032967 0.03845342
[3,] 0.03897783 -0.1623740648 0.20768563 0.13821702 0.25990251 -0.22829077
[4,] -0.04498231 -0.0761943082 0.17394546 -0.21430361 0.01261261 -0.11227338
[5,] 0.12718683 -0.0005563272 0.06194794 -0.12495547 -0.30239812 0.11430015
[6,] 0.02932472 0.0087867332 0.04285754 -0.03234255 -0.06643938 -0.01170444
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
[2,] -0.005000872 0.006087313 0.07172497 0.02690065 -0.06039006 -0.14339146
[3,] -0.201519227 -0.015111587 -0.01609932 0.17240411 -0.09763783 0.02435708
[4,] 0.048549146 -0.211619408 -0.03455857 -0.26176050 -0.06735377 -0.21880974
[5,] 0.068893027 -0.038598470 -0.14715157 0.28293875 -0.11071715 0.04425249
[6,] -0.120925602 -0.032482350 -0.12806314 0.30957436 0.24847452 0.26848494
[,37] [,38]
[1,] 0.704310652 0.000000000
[2,] 0.120842334 -0.068983640
[3,] -0.020673183 0.002433953
[4,] 0.007718204 0.002524767
[5,] 0.174542542 -0.199298060
[6,] -0.033365612 -0.068248427Tingkat kumulatif keragaman untuk menentukan banyak dimensi.
> head(cumulative_variance)
[1] 0.8735839 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000Berdasarkan nilai eigen dan tingkat kumulatif keragaman, komponen pertama menjelaskan sebesar 87.36%, sedangkan komponen kedua meningkatkan keragaman total menjadi 100%. Karena dua komponen pertama telah mampu menjelaskan seluruh variasi data dan memenuhi kriteria keragaman kumulatif ≥ 80%, maka penggunaan dua dimensi sudah sesuai dan layak digunakan dalam analisis MDS
Titik koordinat pada dimensi 2
> head(fit)
[,1] [,2]
1 -205126.33 -37281.48
2 -141370.54 -22411.89
3 -45947.11 -50053.40
4 15803.75 -52054.12
5 -41158.11 -21720.76
6 -177228.59 -13209.58Titik koordinat yang diperoleh digunakan untuk menggambarkan posisi 38 provinsi menggunakan peta persepsi, dengan dimensi 1 adalah koordinat X dan dimensi 2 adalah koordinat Y.
> plot(fit, type="n",
+ xlab="Dimensi 1",
+ ylab="Dimensi 2",
+ main="MDS Pengeluaran Per Kapita Provinsi")
> text(fit, labels = data$Provinsi, cex=0.6)
Hasil MDS menunjukkan bahwa provinsi-provinsi di Indonesia memiliki pola pengeluaran per kapita yang berbeda. DKI Jakarta berada paling jauh dari provinsi lain, menandakan pengeluaran per kapita yang jauh lebih tinggi. Beberapa provinsi seperti Riau, Kepulauan Riau, Bali, dan Kalimantan Timur juga berada di sisi kanan grafik, menunjukkan pengeluaran yang relatif tinggi. Sementara itu, sebagian besar provinsi lainnya berkelompok rapat di tengah, mencerminkan pola pengeluaran yang serupa. Secara keseluruhan, pemetaan dua dimensi sudah mampu menggambarkan variasi pengeluaran antarprovinsi secara jelas.
Disparities yang merupakan jarak Euclidean dari koordinat yang terbentuk.
> head(disparities)
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.00 65466.83 159690.79 221423.42 164704.93 36847.53 149275.15
[2,] 65466.83 0.00 99346.29 159945.05 100214.81 37020.03 85444.23
[3,] 159690.79 99346.29 0.00 61783.26 28734.53 136353.57 73796.76
[4,] 221423.42 159945.05 61783.26 0.00 64535.00 196901.97 110486.31
[5,] 164704.93 100214.81 28734.53 64535.00 0.00 136336.41 49785.96
[6,] 36847.53 37020.03 136353.57 196901.97 136336.41 0.00 114798.66
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 65535.22 382329.7 664304.0 1207260.1 298217.55 111259.99 469091.2
[2,] 99211.97 322722.9 599648.8 1142504.3 233126.25 88738.30 404235.5
[3,] 197556.93 223519.2 507274.6 1050087.6 146192.90 161485.79 331283.9
[4,] 256471.41 163189.3 446409.7 988975.5 92527.91 210774.30 282187.1
[5,] 193476.48 226782.2 499624.3 1042562.8 133803.88 146665.86 312889.6
[6,] 63750.39 359739.8 634957.8 1177603.3 268100.89 79492.51 434742.5
[,15] [,16] [,17] [,18] [,19] [,20] [,21]
[1,] 129836.26 387183.3 531923.3 9003.729 210769.2 110800.31 241160.46
[2,] 75962.52 323582.1 466481.6 59766.686 258589.7 45630.16 179792.61
[3,] 109656.71 228610.0 384721.4 151950.574 357132.2 69192.55 81473.87
[4,] 152668.84 167306.3 329404.8 213726.597 415566.7 123812.45 19848.28
[5,] 90037.53 223483.2 370271.6 157902.585 351902.8 60009.25 83647.25
[6,] 93033.50 359814.1 499118.6 35637.183 222270.2 78642.32 216746.18
[,22] [,23] [,24] [,25] [,26] [,27] [,28]
[1,] 206864.63 609520.7 303474.15 122294.37 89932.23 134909.1 143341.8
[2,] 143337.48 544974.1 239534.14 60090.39 91975.99 105393.9 131255.3
[3,] 51015.33 452270.8 146082.37 81951.17 180934.36 165200.9 202764.4
[4,] 24759.47 391353.9 86365.13 129773.05 235384.60 209146.1 248785.8
[5,] 43975.99 444881.5 139360.14 65466.85 170892.06 146692.8 185752.5
[6,] 179848.45 580415.8 275661.40 87255.69 67767.57 101761.7 116747.7
[,29] [,30] [,31] [,32] [,33] [,34] [,35]
[1,] 141968.0 143241.6 124717.86 178511.39 288146.81 302769.41 274583.32
[2,] 118652.5 172582.0 98069.45 114337.13 224819.15 237849.78 209142.71
[3,] 181748.5 266482.8 163566.02 80519.28 129696.51 149320.83 134325.92
[4,] 225562.2 321702.8 209925.10 99358.10 69035.14 93887.28 94982.18
[5,] 163262.2 257222.8 146601.03 51973.26 125030.63 138136.12 114966.12
[6,] 110970.7 140121.4 92134.17 144059.93 261270.34 273090.97 242083.81
[,36] [,37] [,38]
[1,] 137992.22 174641.1 436076.2
[2,] 72540.23 152888.3 424810.7
[3,] 48567.45 121567.9 376935.7
[4,] 96687.40 151882.8 373298.3
[5,] 32178.60 149977.7 404658.0
[6,] 107081.66 177050.2 446109.6Nilai STRESS:
> cat("Nilai Stress:", stress, "\n")
Nilai Stress: 5.768386e-16 Berdasarkan output, diperoleh nilai STRESS sebesar 5.768386×10⁻¹⁶ atau sekitar 0.0000000000005768% yang menunjukkan kriteria yang tergolong sangat baik (mendekati 0). Dengan kata lain, hubungan antara jarak dalam data asli dan peta dimensi dapat direpresentasikan dengan sangat akurat melalui MDS.
5 KESIMPULAN
5.1 Kesesuaian model MDS:
Hasil analisis menunjukkan bahwa nilai STRESS sebesar 5.768386 × 10⁻¹⁶, yang tergolong sangat baik karena mendekati nol. Hal ini menandakan bahwa konfigurasi dua dimensi yang digunakan mampu merepresentasikan jarak antarprovinsi pada data asli hampir tanpa distorsi. Dengan demikian, MDS dua dimensi merupakan pilihan yang tepat untuk menggambarkan pola kemiripan pengeluaran per kapita antar provinsi di Indonesia.
5.2 Tingkat keragaman yang dijelaskan:
Berdasarkan nilai eigen dan tingkat kumulatif keragaman, dua dimensi pertama mampu menjelaskan 87,35% dari total variasi data. Persentase ini menunjukkan bahwa sebagian besar informasi dalam data telah berhasil divisualisasikan dalam peta MDS dua dimensi sehingga interpretasi menjadi valid dan representatif.
5.3 Pola pengelompokan provinsi:
Hasil pemetaan MDS menunjukkan pola pengelompokan yang jelas antara provinsi dengan tingkat pengeluaran yang relatif sama. Provinsi dengan pengeluaran per kapita tinggi seperti DKI Jakarta, Kepulauan Riau, Bali, dan Kalimantan Timur muncul pada posisi terpisah dari provinsi lain, menandakan karakteristik ekonomi rumah tangga yang lebih kuat. Sebaliknya, provinsi seperti Nusa Tenggara Timur, Sulawesi Barat, dan Lampung berada lebih berdekatan, mencerminkan tingkat pengeluaran yang lebih rendah dan lebih homogen.
5.4 Interpretasi makna praktis:
Secara praktis, hasil MDS memberikan gambaran yang informatif mengenai ketimpangan pengeluaran antarprovinsi di Indonesia. Perbedaan posisi pada peta MDS mencerminkan kondisi sosial ekonomi yang beragam, yang dapat menjadi dasar untuk identifikasi provinsi yang membutuhkan perhatian lebih dalam perencanaan ekonomi, pemberdayaan masyarakat, maupun kebijakan pemerataan kesejahteraan.
5.5 Kesimpulan umum:
Secara keseluruhan, analisis MDS berhasil memvisualisasikan kemiripan dan perbedaan pola pengeluaran antarprovinsi dengan sangat baik. MDS dua dimensi memberikan peta persepsi yang akurat dan mudah dipahami, serta mampu mengungkap struktur pengelompokan provinsi berdasarkan tingkat pengeluaran makanan, non-makanan, dan total per kapita.
6 DAFTAR PUSTAKA
- Hout, M. C. (2012). Multidimensional scaling. PLoS ONE, 7(7), e40253. https://doi.org/10.1371/journal.pone.0040253 (diakses: https://pmc.ncbi.nlm.nih.gov/articles/PMC3555222/)
- SSR Network. (2024). Multidimensional scaling method and some practical applications. SSRN. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4934816