Escalamiento multidimensional(1)
Orlando Moscote Flórez
2023-09-25
library(MASS)Más aplicaciones estadísticas en:
https://orlandomoscote.blogspot.com
Definición.
El escalamiento multidimensional trata de encontrar la estructura de un conjunto de medidas de distancia entre objetos. Esto se logra asignando las observaciones a posiciones específicas en un espacio conceptual (normalmente de dos o tres dimensiones) de modo que las distancias entre los objetos en el espacio concuerden al máximo con las similaridades o disimilaridades dadas.
El escalamiento multidimensional está relativamente libre de supuestos distribucionales.
Es una técnica de representación espacial que trata de visualizar sobre un mapa un conjunto de objetos cuya posición relativa se desea analizar, que, partiendo de una matriz de distancias (o bien de similitudes) entre individuos, produce una representación de los individuos en una escala euclidea ordinaria de modo que las distancias en dicha escala se aproximen lo mejor posible a las distancias de partida.
En el caso ideal en la que se dispone de una matriz que proporciona las distancias entre puntos en el plano (por ejemplo, las distancias entre las ciudades de una región), el MDS reconstruye el mapa de puntos, con poco más o menos una rotación simetràa. Para proporcionar una configuración óptima, el método MDS minimiza un criterio llamado “STRESS”. Mientras más se acerca a 0 mejor es la representación.
Hay dos tipos:
Escalamiento métrico. Todo modelo de escalamiento parte de la idea de que las distancias son una función de las proximidades. En el modelo de escalamiento métrico se parte del supuesto de que la relación entre las proximidades y las distancias es de tipo lineal.Los datos están medidos en escala de razón o en escala de intervalo.
Escalamiento no métrico.A diferencia del escalamiento métrico, el modelo de escalamiento no métrico no presupone una relación lineal entre las proximidades y las distancias, sino que establece una relación monótona creciente entre ambas.Los datos están medidos en escala ordinal.
En este caso se considera el escalamiento métrico cuando los datos son proximidades.
Datos.
Los datos corresponden a la distancia (Km) entre 27 ciudades colombianas.
distancias<-matrix(c(0,1098,286,725,235,194,974,935,533,81,95,348,739,288,594,44,343,596,1289,789,1191,433,1154,599,907,636,422,1098, 0 ,1302, 739, 1116, 1212, 124, 926,1849, 1179, 1003, 750, 424, 1386, 1612, 1054, 1361, 998, 284, 309, 93, 777, 364, 1418, 1003, 1524, 1053,286, 1302, 0 ,439, 519, 484, 1178, 649, 547, 205, 299, 552, 943, 302, 884, 330, 633, 800, 1147, 993, 1139, 147, 868, 116, 632, 618, 342,725, 739, 439, 0 ,937, 923, 917, 210, 986, 644, 738, 1543, 1217, 742, 1323, 769, 1072, 1791, 708, 1102, 700, 292, 429, 555, 417, 1043, 479,235, 1116, 519, 937, 0 ,129, 1154, 1138, 564, 319, 380, 499, 899, 531, 521, 268, 265, 606, 1459, 966, 1266, 660, 1048, 632, 1135, 632, 846,194, 1212, 484, 923, 129, 0, 1088, 1133, 521, 279, 275, 462, 933, 486, 400, 224, 149, 710, 1403, 893, 1305, 631, 1352, 600, 1092, 487, 802,974, 124, 1178, 917, 1154, 1088, 0 ,1050, 1507, 1055, 879, 626, 300, 1262, 1488, 930, 1237, 874, 408, 185, 217, 1554, 488, 1294, 1082, 1595, 1128, 935, 926, 649, 210, 1138, 1133, 1050, 0 ,1179, 854, 984, 1201, 1350, 951, 1533, 979, 1282, 1449, 1024, 1235, 833, 502, 562, 765, 346, 1170, 483, 533, 1849, 547, 986, 564, 521, 1507, 1179, 0, 452, 628, 881, 1272, 245, 623, 577, 372, 1129, 1694, 1322, 1724, 694, 1415, 663, 800, 136, 534,81, 1179, 205, 644, 319, 279, 1055, 854, 452, 0, 176, 429, 820, 207, 679, 125, 428, 677, 1370, 870, 1272, 352, 1073, 321, 824, 552, 534, 95, 1003, 299, 738, 380, 275, 879, 984, 628, 176, 0, 253, 644, 383, 675, 51, 424, 501, 1192, 694, 1096, 446, 1167, 415, 899, 722, 609,348, 750, 552, 1543, 499, 462, 626, 1201, 881, 429, 253, 0, 391, 636, 942, 304, 611, 248, 941, 441, 843, 699, 1114, 668, 818, 884, 629,739, 424, 943, 1217, 899, 933, 300, 1350, 1272, 820, 644, 391, 0, 1027, 1253, 695, 1002, 639, 708, 115, 517, 1090, 788, 1059, 1141, 1319, 940, 288, 1386, 302, 742, 531, 486, 1262, 951, 245, 207, 383, 636, 1027, 0 ,466, 332, 215, 884, 1577, 1077, 1479, 449, 1170, 418, 916, 327, 627,594, 1612, 884, 1323, 521, 400, 1488, 1533, 623, 679, 675, 942, 1253, 466, 0, 624, 251, 1110, 1803, 1303, 1705, 1031, 1752, 1000, 1347, 103, 1057,44, 1054, 330, 769, 268, 224, 930, 979, 577, 125, 51, 304, 695, 332, 624, 0, 373, 552, 1245, 745, 1147, 447, 1198, 446, 943, 671, 653, 343, 1361, 633, 1072, 265, 149, 1237, 1282, 372, 428, 424, 611, 1002, 215, 251, 373, 0, 859, 1552, 1052, 1454, 780, 1501, 749, 1219, 349, 929, 596, 998, 800, 1791, 606, 710, 874, 1449, 1129, 677, 501, 248, 639, 884, 1110, 552, 859, 0 ,1189, 689, 1091, 800, 1362, 916, 1005, 1026, 816,1289, 284, 1147, 708, 1459, 1403, 408, 1024, 1694, 1370, 1192, 941, 708, 1577, 1803, 1245, 1552, 1189, 0, 557, 191, 1000, 279, 1263, 1125, 1647, 1175,789, 309, 993, 1102, 966, 893, 185, 1235, 1322, 870, 694, 441, 115, 1077, 1303, 745, 1052, 689, 557, 0, 402, 1140, 673, 1109, 1025, 1383, 1075,1191, 93, 1139, 700, 1266, 1305, 217, 833, 1724, 1272, 1096, 843, 517, 1479, 1705, 1147, 1454, 1091, 191, 402, 0, 992, 271, 1255, 965, 1487, 1015,433, 777, 147, 292, 660, 631, 1554, 502, 694, 352, 446, 699, 1090, 449, 1031, 447, 780, 800, 1000, 1140, 992, 0, 721, 263, 479, 766, 219,1154, 364, 868, 429, 1048, 1352, 488, 562, 1415, 1073, 1167, 1114, 788, 1170, 1752, 1198, 1501, 1362, 279, 673, 271, 721, 0, 984, 871, 1392, 921,599, 1418, 116, 555, 632, 600, 1294, 765, 663, 321, 415, 668, 1059, 418, 1000, 446, 749, 916, 1263, 1109, 1255, 263, 984, 0, 683, 715, 262,907, 1003, 632, 417, 1135, 1092, 1082, 346, 800, 824, 899, 818, 1141, 916, 1347, 943, 1219, 1005, 1125, 1025, 965, 479, 871, 683, 0, 1243, 422,636, 1524, 618, 1043, 632, 487, 1595, 1170, 136, 552, 722, 884, 1319, 327, 103, 671, 349, 1026, 1647, 1383, 1487, 766, 1392, 715, 1243, 0 ,954,422, 1053, 342, 479, 846, 802, 1128, 483, 534, 534, 609, 629, 940, 627, 1057, 653, 929, 816, 1175, 1075, 1015, 219, 921, 262, 422, 954, 0),
nrow=27)
dimnames(distancias)<-list(ciudad=c("Arm", "Bquilla", "Bogo"," B/anga"," B/tura",
"Cali"," C/gena"," Cucuta", "Florenc"," Ibague"," Maniz."," Med."," Mont","Neiva"," Pasto"," Pei", "Popay"," Quib", "Rioha"," Sinc.","S.Marta"," Tunja"," V/dupar", "Villavo"," Arauca"," Mocoa"," Yopal"),Ciudad=c( "Arm", "Bquilla", "Bogo"," B/anga"," B/tura","Cali"," C/gena"," Cucuta", "Florenc"," Ibague"," Maniz."," Med."," Mont",
"Neiva"," Pasto"," Pei", "Popay"," Quib", "Rioha"," Sinc.","S.Marta"," Tunja",
" V/dupar", "Villavo"," Arauca"," Mocoa"," Yopal" ))
tabla1<-as.table(distancias);tabla1## Ciudad
## ciudad Arm Bquilla Bogo B/anga B/tura Cali C/gena Cucuta Florenc
## Arm 0 1098 286 725 235 194 974 935 533
## Bquilla 1098 0 1302 739 1116 1212 124 926 1849
## Bogo 286 1302 0 439 519 484 1178 649 547
## B/anga 725 739 439 0 937 923 917 210 986
## B/tura 235 1116 519 937 0 129 1154 1138 564
## Cali 194 1212 484 923 129 0 1088 1133 521
## C/gena 974 124 1178 917 1154 1088 0 1050 1507
## Cucuta 935 926 649 210 1138 1133 1050 0 1179
## Florenc 533 1849 547 986 564 521 1507 1179 0
## Ibague 81 1179 205 644 319 279 1055 854 452
## Maniz. 95 1003 299 738 380 275 879 984 628
## Med. 348 750 552 1543 499 462 626 1201 881
## Mont 739 424 943 1217 899 933 300 1350 1272
## Neiva 288 1386 302 742 531 486 1262 951 245
## Pasto 594 1612 884 1323 521 400 1488 1533 623
## Pei 44 1054 330 769 268 224 930 979 577
## Popay 343 1361 633 1072 265 149 1237 1282 372
## Quib 596 998 800 1791 606 710 874 1449 1129
## Rioha 1289 284 1147 708 1459 1403 408 1024 1694
## Sinc. 789 309 993 1102 966 893 185 1235 1322
## S.Marta 1191 93 1139 700 1266 1305 217 833 1724
## Tunja 433 777 147 292 660 631 1554 502 694
## V/dupar 1154 364 868 429 1048 1352 488 562 1415
## Villavo 599 1418 116 555 632 600 1294 765 663
## Arauca 907 1003 632 417 1135 1092 1082 346 800
## Mocoa 636 1524 618 1043 632 487 1595 1170 136
## Yopal 422 1053 342 479 846 802 1128 483 534
## Ciudad
## ciudad Ibague Maniz. Med. Mont Neiva Pasto Pei Popay Quib Rioha
## Arm 81 95 348 739 288 594 44 343 596 1289
## Bquilla 1179 1003 750 424 1386 1612 1054 1361 998 284
## Bogo 205 299 552 943 302 884 330 633 800 1147
## B/anga 644 738 1543 1217 742 1323 769 1072 1791 708
## B/tura 319 380 499 899 531 521 268 265 606 1459
## Cali 279 275 462 933 486 400 224 149 710 1403
## C/gena 1055 879 626 300 1262 1488 930 1237 874 408
## Cucuta 854 984 1201 1350 951 1533 979 1282 1449 1024
## Florenc 452 628 881 1272 245 623 577 372 1129 1694
## Ibague 0 176 429 820 207 679 125 428 677 1370
## Maniz. 176 0 253 644 383 675 51 424 501 1192
## Med. 429 253 0 391 636 942 304 611 248 941
## Mont 820 644 391 0 1027 1253 695 1002 639 708
## Neiva 207 383 636 1027 0 466 332 215 884 1577
## Pasto 679 675 942 1253 466 0 624 251 1110 1803
## Pei 125 51 304 695 332 624 0 373 552 1245
## Popay 428 424 611 1002 215 251 373 0 859 1552
## Quib 677 501 248 639 884 1110 552 859 0 1189
## Rioha 1370 1192 941 708 1577 1803 1245 1552 1189 0
## Sinc. 870 694 441 115 1077 1303 745 1052 689 557
## S.Marta 1272 1096 843 517 1479 1705 1147 1454 1091 191
## Tunja 352 446 699 1090 449 1031 447 780 800 1000
## V/dupar 1073 1167 1114 788 1170 1752 1198 1501 1362 279
## Villavo 321 415 668 1059 418 1000 446 749 916 1263
## Arauca 824 899 818 1141 916 1347 943 1219 1005 1125
## Mocoa 552 722 884 1319 327 103 671 349 1026 1647
## Yopal 534 609 629 940 627 1057 653 929 816 1175
## Ciudad
## ciudad Sinc. S.Marta Tunja V/dupar Villavo Arauca Mocoa Yopal
## Arm 789 1191 433 1154 599 907 636 422
## Bquilla 309 93 777 364 1418 1003 1524 1053
## Bogo 993 1139 147 868 116 632 618 342
## B/anga 1102 700 292 429 555 417 1043 479
## B/tura 966 1266 660 1048 632 1135 632 846
## Cali 893 1305 631 1352 600 1092 487 802
## C/gena 185 217 1554 488 1294 1082 1595 1128
## Cucuta 1235 833 502 562 765 346 1170 483
## Florenc 1322 1724 694 1415 663 800 136 534
## Ibague 870 1272 352 1073 321 824 552 534
## Maniz. 694 1096 446 1167 415 899 722 609
## Med. 441 843 699 1114 668 818 884 629
## Mont 115 517 1090 788 1059 1141 1319 940
## Neiva 1077 1479 449 1170 418 916 327 627
## Pasto 1303 1705 1031 1752 1000 1347 103 1057
## Pei 745 1147 447 1198 446 943 671 653
## Popay 1052 1454 780 1501 749 1219 349 929
## Quib 689 1091 800 1362 916 1005 1026 816
## Rioha 557 191 1000 279 1263 1125 1647 1175
## Sinc. 0 402 1140 673 1109 1025 1383 1075
## S.Marta 402 0 992 271 1255 965 1487 1015
## Tunja 1140 992 0 721 263 479 766 219
## V/dupar 673 271 721 0 984 871 1392 921
## Villavo 1109 1255 263 984 0 683 715 262
## Arauca 1025 965 479 871 683 0 1243 422
## Mocoa 1383 1487 766 1392 715 1243 0 954
## Yopal 1075 1015 219 921 262 422 954 0Numero de dimensiones.
dime1<-isoMDS(distancias,k=1)## initial value 30.014454
## final value 30.014354
## convergeddime2<-isoMDS(distancias,k=2) ## initial value 12.850268
## final value 12.850049
## convergeddime3<-isoMDS(distancias, k=3)## initial value 12.758115
## final value 12.757828
## convergeddime4<-isoMDS(distancias, k=4)## initial value 13.231726
## final value 13.231465
## convergeddime5<-isoMDS(distancias, k=5)## initial value 12.538085
## final value 12.537840
## convergeddime6<- isoMDS(distancias, k=6)## initial value 12.043380
## final value 12.043142
## convergedstres=c(dime1$stress,dime2$stress,dime3$stress,dime4$stress,dime5$stress,dime6$stress)
dimensions = 1:6
plot(dimensions,stres,type="b",xlab = "Dimensiones", ylab = "Stress")
Stress.
print(stres)## [1] 30.01435 12.85005 12.75783 13.23147 12.53784 12.04314Distancias..
d <- dist(distancias,method="euclidean") # distancias euclidianas
multi<- cmdscale(d,eig=TRUE, k=2) # k numero de dimensones
multi## $points
## [,1] [,2]
## Arm 1404.79639 330.88737
## Bquilla -2918.13956 408.09909
## Bogo 1113.10336 -729.68356
## B/anga -784.96659 -1797.78703
## B/tura 1303.81644 554.96869
## Cali 1547.21732 597.08989
## C/gena -2586.67523 926.08329
## Cucuta -1057.60629 -1755.11865
## Florenc 1830.04849 -367.39400
## Ibague 1489.61020 -15.62740
## Maniz. 1124.06002 461.30290
## Med. 201.80356 1185.99450
## Mont -1485.50798 1266.51096
## Neiva 1758.32976 -186.68402
## Pasto 1647.28918 602.13636
## Pei 1299.89074 470.08387
## Popay 1743.75826 638.70452
## Quib -31.40529 1262.50423
## Rioha -3164.98320 -26.88474
## Sinc. -1804.05033 1171.24798
## S.Marta -3048.76508 110.60874
## Tunja 587.77085 -1159.24958
## V/dupar -2519.96064 -760.55164
## Villavo 964.19624 -857.39562
## Arauca -653.66620 -1285.36450
## Mocoa 1695.01030 -25.11359
## Yopal 345.02527 -1019.36808
##
## $eig
## [1] 7.747448e+07 2.135611e+07 1.184741e+07 3.213633e+06 1.067384e+06
## [6] 9.493540e+05 5.019946e+05 3.887341e+05 3.152239e+05 2.382911e+05
## [11] 2.041680e+05 1.946216e+05 1.611404e+05 1.540985e+05 9.372661e+04
## [16] 8.184382e+04 4.061120e+04 3.493954e+04 2.342727e+04 1.984610e+04
## [21] 1.775408e+04 1.209875e+04 5.364977e+03 3.108033e+03 2.850483e+03
## [26] 2.404140e+02 -1.962239e-09
##
## $x
## NULL
##
## $ac
## [1] 0
##
## $GOF
## [1] 0.8347005 0.8347005#distancias entre ciudades
dist <- dist(distancias, method = "euclidean")
dist## Arm Bquilla Bogo B/anga B/tura Cali C/gena
## Bquilla 4417.7576
## Bogo 1245.4373 4310.1176
## B/anga 3194.4474 3154.2831 2441.7191
## B/tura 978.4140 4274.5468 1660.9028 3245.9190
## Cali 910.1687 4499.4176 1701.9521 3394.7487 488.8057
## C/gena 4153.1477 1038.3872 4188.7327 3355.0371 3988.8151 4201.1571
## Cucuta 3460.1386 2951.9903 2734.1256 1070.2014 3410.0705 3593.8175 3170.0800
## Florenc 2129.6401 5004.8012 2071.1270 3345.4690 1834.7875 1754.3147 4768.0072
## Ibague 507.1124 4518.1858 902.0837 3032.5133 1088.9247 1047.4674 4280.4052
## Maniz. 487.6761 4173.0742 1273.1669 3145.1308 1100.0509 1070.9785 3891.2011
## Med. 1697.1408 3419.8691 2220.0903 3420.0104 1781.0253 1887.7600 3053.6835
## Mont 3143.6382 1850.1646 3349.2571 3272.6132 3022.4260 3217.4589 1344.2273
## Neiva 1213.0363 4760.7070 1294.7197 3114.3881 1225.1371 1125.2386 4520.4760
## Pasto 2634.4827 4926.1775 2978.9540 3944.8575 2007.6053 1916.5798 4641.3540
## Pei 343.6917 4319.8134 1308.5916 3220.2717 953.8207 895.7092 4037.3573
## Popay 1529.2717 4731.6807 2129.9141 3618.8620 985.7637 785.6851 4413.3427
## Quib 2337.8449 3285.0645 2702.2182 3583.4898 2061.4245 2233.3016 2954.9648
## Rioha 4814.3810 1029.5251 4545.5955 3160.3876 4607.3448 4835.1750 1478.7420
## Sinc. 3394.5282 1545.2521 3543.8239 3236.2435 3279.3060 3473.0371 1001.2332
## S.Marta 4571.1134 546.7614 4358.1661 3049.4013 4419.2619 4646.1295 1124.8129
## Tunja 1857.1920 3963.1278 959.9917 1952.5875 2120.6909 2253.6923 3987.8215
## V/dupar 4221.0659 1407.2445 3777.6205 2159.6609 4086.1798 4336.5920 1849.7894
## Villavo 1603.3752 4201.8232 652.0583 2298.3390 1775.9032 1842.5067 4091.7050
## Arauca 2965.0934 3048.4657 2292.3209 1570.4117 2967.3330 3130.3025 3113.6572
## Mocoa 2290.9838 4875.5247 2371.6283 3480.8009 1769.1662 1710.3631 4635.3081
## Yopal 1936.3254 3715.6733 1140.8444 1916.6586 2181.0718 2298.9134 3669.3918
## Cucuta Florenc Ibague Maniz. Med. Mont Neiva
## Bquilla
## Bogo
## B/anga
## B/tura
## Cali
## C/gena
## Cucuta
## Florenc 3381.9562
## Ibague 3312.5102 1947.2036
## Maniz. 3392.4450 2343.2198 695.0475
## Med. 3452.7482 2957.6301 1926.9302 1404.8705
## Mont 3190.1107 3949.1333 3309.6683 2857.0497 1889.5597
## Neiva 3325.9937 1187.5083 950.1600 1429.9472 2390.6305 3604.1998
## Pasto 3915.9566 1502.1525 2637.5834 2772.0680 3094.8754 3847.4550 1994.0216
## Pei 3479.7125 2229.2674 588.0502 259.4456 1545.6529 3007.6468 1303.9551
## Popay 3760.8160 1372.5877 1576.3372 1705.3275 2322.7839 3471.4503 1113.3548
## Quib 3357.0133 2880.9863 2500.8686 2124.3340 1196.4782 1897.1025 2682.9570
## Rioha 2865.3909 5096.9137 4857.0031 4577.4038 3895.8482 2376.3743 4997.2559
## Sinc. 3156.2559 4199.1696 3547.7214 3104.6088 2179.5373 450.5186 3852.1512
## S.Marta 2808.4300 5037.3633 4636.9843 4328.1567 3610.0342 2066.3802 4844.6355
## Tunja 2211.4988 2479.1912 1629.6125 1847.8414 2492.2887 3315.7800 1894.5382
## V/dupar 1980.5757 4531.3097 4193.8298 4031.5234 3588.1132 2418.5810 4352.8917
## Villavo 2459.1110 1855.7799 1282.6554 1603.4488 2327.4589 3296.8477 1381.2114
## Arauca 1027.5524 2938.6888 2827.8030 2864.7326 2852.0926 2852.4908 2870.3665
## Mocoa 3521.7939 967.6973 2166.0392 2450.5887 2981.2095 3852.9913 1393.3270
## Yopal 1956.2185 2346.5875 1753.0759 1893.3917 2295.0431 2999.4971 1947.0811
## Pasto Pei Popay Quib Rioha Sinc. S.Marta
## Bquilla
## Bogo
## B/anga
## B/tura
## Cali
## C/gena
## Cucuta
## Florenc
## Ibague
## Maniz.
## Med.
## Mont
## Neiva
## Pasto
## Pei 2649.2959
## Popay 1286.2360 1542.4124
## Quib 2760.3724 2211.4780 2426.6976
## Rioha 5054.7315 4718.4688 4997.4365 3617.8763
## Sinc. 4108.3925 3258.2191 3738.5109 2219.5047 2113.8306
## S.Marta 5018.3381 4477.6472 4861.1892 3461.3276 673.6705 1763.4047
## Tunja 3306.6447 1917.9307 2627.0539 2846.3122 4159.6993 3456.7751 3984.7281
## V/dupar 4736.7423 4161.1343 4544.3234 3504.0965 1225.9458 2203.4934 1132.6513
## Villavo 2772.2992 1641.5255 2138.8268 2571.2120 4347.9627 3503.3321 4216.4744
## Arauca 3572.5593 2974.1770 3321.2087 2767.1231 3071.3113 2882.5140 2968.3246
## Mocoa 1012.4930 2331.6065 1169.1326 2847.2222 4970.1872 4092.3735 4917.6829
## Yopal 3206.3931 1994.5295 2622.6273 2554.5088 3894.9958 3159.2892 3716.0764
## Tunja V/dupar Villavo Arauca Mocoa
## Bquilla
## Bogo
## B/anga
## B/tura
## Cali
## C/gena
## Cucuta
## Florenc
## Ibague
## Maniz.
## Med.
## Mont
## Neiva
## Pasto
## Pei
## Popay
## Quib
## Rioha
## Sinc.
## S.Marta
## Tunja
## V/dupar 3340.2573
## Villavo 1030.0961 3613.9127
## Arauca 1850.0446 2341.6981 2013.5677
## Mocoa 2684.4800 4483.4058 2203.6563 3163.4241
## Yopal 902.6661 3125.1578 998.7632 1376.7080 2649.3499escala <- cmdscale(dist,eig = T)
escala## $points
## [,1] [,2]
## Arm 1404.79639 330.88737
## Bquilla -2918.13956 408.09909
## Bogo 1113.10336 -729.68356
## B/anga -784.96659 -1797.78703
## B/tura 1303.81644 554.96869
## Cali 1547.21732 597.08989
## C/gena -2586.67523 926.08329
## Cucuta -1057.60629 -1755.11865
## Florenc 1830.04849 -367.39400
## Ibague 1489.61020 -15.62740
## Maniz. 1124.06002 461.30290
## Med. 201.80356 1185.99450
## Mont -1485.50798 1266.51096
## Neiva 1758.32976 -186.68402
## Pasto 1647.28918 602.13636
## Pei 1299.89074 470.08387
## Popay 1743.75826 638.70452
## Quib -31.40529 1262.50423
## Rioha -3164.98320 -26.88474
## Sinc. -1804.05033 1171.24798
## S.Marta -3048.76508 110.60874
## Tunja 587.77085 -1159.24958
## V/dupar -2519.96064 -760.55164
## Villavo 964.19624 -857.39562
## Arauca -653.66620 -1285.36450
## Mocoa 1695.01030 -25.11359
## Yopal 345.02527 -1019.36808
##
## $eig
## [1] 7.747448e+07 2.135611e+07 1.184741e+07 3.213633e+06 1.067384e+06
## [6] 9.493540e+05 5.019946e+05 3.887341e+05 3.152239e+05 2.382911e+05
## [11] 2.041680e+05 1.946216e+05 1.611404e+05 1.540985e+05 9.372661e+04
## [16] 8.184382e+04 4.061120e+04 3.493954e+04 2.342727e+04 1.984610e+04
## [21] 1.775408e+04 1.209875e+04 5.364977e+03 3.108033e+03 2.850483e+03
## [26] 2.404140e+02 -1.962239e-09
##
## $x
## NULL
##
## $ac
## [1] 0
##
## $GOF
## [1] 0.8347005 0.8347005Mapa perceptual..
x <- multi$points[,1]
y <- multi$points[,2]
plot(x, y, xlab="Coordenada 1", ylab="Coordenada 2", type="n")
text(x, y, labels =row.names(tabla1), cex=.7)
escala$eig## [1] 7.747448e+07 2.135611e+07 1.184741e+07 3.213633e+06 1.067384e+06
## [6] 9.493540e+05 5.019946e+05 3.887341e+05 3.152239e+05 2.382911e+05
## [11] 2.041680e+05 1.946216e+05 1.611404e+05 1.540985e+05 9.372661e+04
## [16] 8.184382e+04 4.061120e+04 3.493954e+04 2.342727e+04 1.984610e+04
## [21] 1.775408e+04 1.209875e+04 5.364977e+03 3.108033e+03 2.850483e+03
## [26] 2.404140e+02 -1.962239e-09escala$GOF## [1] 0.8347005 0.8347005mds <- isoMDS(distancias, k = 2, trace = FALSE)
stress_mds <- round(mds$stress, 2)
mds## $points
## [,1] [,2]
## Arm 275.318329 92.374106
## Bquilla -868.920878 174.638349
## Bogo 224.041460 -241.026347
## B/anga -253.190779 -788.129462
## B/tura 352.143122 171.793289
## Cali 410.807428 188.716504
## C/gena -727.973540 383.256294
## Cucuta -298.980547 -707.348003
## Florenc 761.344760 -218.052645
## Ibague 317.713846 -23.951763
## Maniz. 196.980514 150.998315
## Med. 3.067133 506.107108
## Mont -402.448803 520.147987
## Neiva 513.352157 -106.490082
## Pasto 800.331832 262.626210
## Pei 248.707262 146.297943
## Popay 567.026594 229.501308
## Quib 66.662179 676.170548
## Rioha -968.906851 -8.611261
## Sinc. -495.105947 453.377641
## S.Marta -901.799299 31.262240
## Tunja 104.651841 -397.989620
## V/dupar -759.985034 -348.981458
## Villavo 274.319774 -302.568005
## Arauca -174.777342 -443.765171
## Mocoa 674.302047 -88.830562
## Yopal 61.318742 -311.523464
##
## $stress
## [1] 12.85005—|—|—|
O.M.F.
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