Escalamiento multidimensional.
Orlando Moscote Flórez
2023-09-26
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 no son proximidades.
Datos.
Los datos sobre las Necesidades Básicas Insatisfechas en los departamentos de Colombia. De acuerdo con el Departamento nacional de Estadística (DANE) de Colombia: “La metodología de NBI busca determinar, con ayuda de algunos indicadores simples, si las necesidades básicas de la población se encuentran cubiertas. Los grupos que no alcancen un umbral mínimo fijado, son clasificados como pobres. Los indicadores simples seleccionados, son: Viviendas inadecuadas, Viviendas con hacinamiento crítico, Viviendas con servicios inadecuados, Viviendas con alta dependencia económica, Viviendas con niños en edad escolar que no asisten a la escuela”
Dpto<-c("ANTI","ATLA","BOGO","BOLI","BOYA","CALD","CAQU","CAUC","CESA","CORDO","CUND","CHOC","HUIL","GUAJ","MAGD","META","NARI","NDES","QUIN","RISA","SANT","SUCR","TOLI","VALL","ARAU","CASA","PUTU","SANA","AMAZ","GUAI","GUAV","VAUP","VICH")
nbi<-c(10.73,11.37,3.47,26.73,10.15,8.95,23.62,18.81,23.04,35.08,6.36,65.51,12.86,53.33,26.71,13.45,21.98,18.43,6.76,8.19,9.58,29.13,12.22,6.25,32.45,16.08,18.96,14.89,35.24,59.46,27.91,68.94,67.76)
vivienda<-c(3.53,2.16,0.36,13.16,2.33,1.74,10.12,5.99,9.31,25.99,1.41,8.52,4.02,29.24,11.54,6.99,3.30,5.65,1.14,0.82,2.92,16.60,3.26,0.70,24.20,7.00,3.54,0.80,5.72,32.84,14.76,37.33,56.59)
servicios<-c(1.89,1.49,0.10,9.55,1.80,1.55,5.91,5.88,5.04,6.17,0.63,57.47,1.70,15.23,8.04,2.67,10.11,3.29,0.34,1.25,0.86,4.47,1.61,0.68,2.96,1.33,7.55,9.40,19.13,39.72,11.79,56.68,45.70)
hacinamiento<-c(2.77,4.07,1.43,4.82,3.21,2.07,4.71,4.09,8.06,7.20,1.93,12.80,2.80,32.69,7.76,3.46,6.52,6.54,1.35,2.42,2.58,6.28,3.53,1.39,8.46,6.10,5.60,3.61,16.18,22.69,4.94,28.44,34.02)
inasistencia<-c(1.73,2.95,1.04,3.20,1.32,1.22,2.93,1.58,3.12,1.86,1.35,4.57,1.41,6.80,3.30,1.76,1.91,2.57,1.42,1.79,1.45,1.58,1.87,1.61,2.63,1.62,1.61,1.85,3.71,5.98,2.25,8.84,10.08)
dependencia<-c(4.15,3.39,0.81,6.22,4.53,4.37,7.68,5.18,7.73,8.67,1.87,10.98,5.24,18.19,8.07,3.87,5.72,6.52,3.32,4.21,3.50,10.10,4.63,2.69,6.87,4.59,4.81,0.38,6.15,14.14,6.90,11.84,16.75)datos<-data.frame(vivienda,servicios,hacinamiento,inasistencia, dependencia,nbi)
rownames(datos)<-Dpto
datos## vivienda servicios hacinamiento inasistencia dependencia nbi
## ANTI 3.53 1.89 2.77 1.73 4.15 10.73
## ATLA 2.16 1.49 4.07 2.95 3.39 11.37
## BOGO 0.36 0.10 1.43 1.04 0.81 3.47
## BOLI 13.16 9.55 4.82 3.20 6.22 26.73
## BOYA 2.33 1.80 3.21 1.32 4.53 10.15
## CALD 1.74 1.55 2.07 1.22 4.37 8.95
## CAQU 10.12 5.91 4.71 2.93 7.68 23.62
## CAUC 5.99 5.88 4.09 1.58 5.18 18.81
## CESA 9.31 5.04 8.06 3.12 7.73 23.04
## CORDO 25.99 6.17 7.20 1.86 8.67 35.08
## CUND 1.41 0.63 1.93 1.35 1.87 6.36
## CHOC 8.52 57.47 12.80 4.57 10.98 65.51
## HUIL 4.02 1.70 2.80 1.41 5.24 12.86
## GUAJ 29.24 15.23 32.69 6.80 18.19 53.33
## MAGD 11.54 8.04 7.76 3.30 8.07 26.71
## META 6.99 2.67 3.46 1.76 3.87 13.45
## NARI 3.30 10.11 6.52 1.91 5.72 21.98
## NDES 5.65 3.29 6.54 2.57 6.52 18.43
## QUIN 1.14 0.34 1.35 1.42 3.32 6.76
## RISA 0.82 1.25 2.42 1.79 4.21 8.19
## SANT 2.92 0.86 2.58 1.45 3.50 9.58
## SUCR 16.60 4.47 6.28 1.58 10.10 29.13
## TOLI 3.26 1.61 3.53 1.87 4.63 12.22
## VALL 0.70 0.68 1.39 1.61 2.69 6.25
## ARAU 24.20 2.96 8.46 2.63 6.87 32.45
## CASA 7.00 1.33 6.10 1.62 4.59 16.08
## PUTU 3.54 7.55 5.60 1.61 4.81 18.96
## SANA 0.80 9.40 3.61 1.85 0.38 14.89
## AMAZ 5.72 19.13 16.18 3.71 6.15 35.24
## GUAI 32.84 39.72 22.69 5.98 14.14 59.46
## GUAV 14.76 11.79 4.94 2.25 6.90 27.91
## VAUP 37.33 56.68 28.44 8.84 11.84 68.94
## VICH 56.59 45.70 34.02 10.08 16.75 67.76Tipificar los datos.
dato<-scale(datos,center=T,scale=T)
dato## vivienda servicios hacinamiento inasistencia dependencia nbi
## ANTI -0.55556986 -0.53659165 -0.594731579 -0.50148604 -0.56533774 -0.72575454
## ATLA -0.66150986 -0.56192250 -0.447345612 0.06216075 -0.74918980 -0.69171591
## BOGO -0.80070109 -0.64994717 -0.746652499 -0.82026987 -1.37331915 -1.11188025
## BOLI 0.18910324 -0.05150604 -0.362315247 0.17766214 -0.06458280 0.12521123
## BOYA -0.64836402 -0.54229109 -0.544847098 -0.69090832 -0.47341171 -0.75660204
## CALD -0.69398781 -0.55812287 -0.674093254 -0.73710887 -0.51211741 -0.82042448
## CAQU -0.04597529 -0.28201670 -0.374786367 0.05292064 0.28860668 -0.04019524
## CAUC -0.36534184 -0.28391651 -0.445078136 -0.57078687 -0.31616982 -0.29601682
## CESA -0.10861134 -0.33711128 0.005015933 0.14070169 0.30070221 -0.07104275
## CORDO 1.18122743 -0.26555165 -0.092485553 -0.44142531 0.52809817 0.56930899
## CUND -0.71950621 -0.61638380 -0.689965588 -0.67704815 -1.11689391 -0.95817456
## CHOC -0.16970083 2.98312874 0.542407843 0.81060976 1.08691166 2.18773951
## HUIL -0.51767892 -0.54862380 -0.591330364 -0.64932782 -0.30165519 -0.61246972
## GUAJ 1.43254494 0.30819190 2.797413137 1.84088216 2.83108709 1.53994182
## MAGD 0.06383113 -0.14712997 -0.028996214 0.22386269 0.38295181 0.12414752
## META -0.28801338 -0.48719651 -0.516503643 -0.48762587 -0.63307271 -0.58109036
## NARI -0.57335541 -0.01604287 -0.169579751 -0.41832504 -0.18553810 -0.12741923
## NDES -0.39163352 -0.44793371 -0.167312275 -0.11340137 0.00799038 -0.31622726
## QUIN -0.74038489 -0.63474866 -0.755722404 -0.64470776 -0.76612354 -0.93690042
## RISA -0.76513000 -0.57712100 -0.634412416 -0.47376570 -0.55082311 -0.86084535
## SANT -0.60274023 -0.60181857 -0.616272605 -0.63084759 -0.72257963 -0.78691770
## SUCR 0.45511316 -0.37320773 -0.196789468 -0.57078687 0.87403033 0.25285610
## TOLI -0.57644855 -0.55432324 -0.508567475 -0.43680526 -0.44922065 -0.64650835
## VALL -0.77440941 -0.61321745 -0.751187452 -0.55692670 -0.91852722 -0.96402495
## ARAU 1.04280948 -0.46883165 0.050365461 -0.08568103 0.09265909 0.42943149
## CASA -0.28724009 -0.57205483 -0.217196756 -0.55230665 -0.45889708 -0.44121286
## PUTU -0.55479658 -0.17816025 -0.273883666 -0.55692670 -0.40567675 -0.28803902
## SANA -0.76667657 -0.06100511 -0.499497570 -0.44604537 -1.47734071 -0.50450344
## AMAZ -0.38622053 0.55516760 0.925611357 0.41328498 -0.08151654 0.57781865
## GUAI 1.71092741 1.85907266 1.663674930 1.46203760 1.85134916 1.86596808
## GUAV 0.31282879 0.09034667 -0.348710388 -0.26124314 0.09991641 0.18796996
## VAUP 2.05813221 2.93310033 2.315574399 2.78337351 1.29495478 2.37016530
## VICH 3.54747842 2.23776874 2.948200319 3.35626040 2.48273583 2.30740657
## attr(,"scaled:center")
## vivienda servicios hacinamiento inasistencia dependencia nbi
## 10.714545 10.363333 8.015758 2.815455 6.486970 24.375758
## attr(,"scaled:scale")
## vivienda servicios hacinamiento inasistencia dependencia nbi
## 12.931849 15.791027 8.820378 2.164476 4.133758 18.802166datos<-as.data.frame(dato)
datos## vivienda servicios hacinamiento inasistencia dependencia nbi
## ANTI -0.55556986 -0.53659165 -0.594731579 -0.50148604 -0.56533774 -0.72575454
## ATLA -0.66150986 -0.56192250 -0.447345612 0.06216075 -0.74918980 -0.69171591
## BOGO -0.80070109 -0.64994717 -0.746652499 -0.82026987 -1.37331915 -1.11188025
## BOLI 0.18910324 -0.05150604 -0.362315247 0.17766214 -0.06458280 0.12521123
## BOYA -0.64836402 -0.54229109 -0.544847098 -0.69090832 -0.47341171 -0.75660204
## CALD -0.69398781 -0.55812287 -0.674093254 -0.73710887 -0.51211741 -0.82042448
## CAQU -0.04597529 -0.28201670 -0.374786367 0.05292064 0.28860668 -0.04019524
## CAUC -0.36534184 -0.28391651 -0.445078136 -0.57078687 -0.31616982 -0.29601682
## CESA -0.10861134 -0.33711128 0.005015933 0.14070169 0.30070221 -0.07104275
## CORDO 1.18122743 -0.26555165 -0.092485553 -0.44142531 0.52809817 0.56930899
## CUND -0.71950621 -0.61638380 -0.689965588 -0.67704815 -1.11689391 -0.95817456
## CHOC -0.16970083 2.98312874 0.542407843 0.81060976 1.08691166 2.18773951
## HUIL -0.51767892 -0.54862380 -0.591330364 -0.64932782 -0.30165519 -0.61246972
## GUAJ 1.43254494 0.30819190 2.797413137 1.84088216 2.83108709 1.53994182
## MAGD 0.06383113 -0.14712997 -0.028996214 0.22386269 0.38295181 0.12414752
## META -0.28801338 -0.48719651 -0.516503643 -0.48762587 -0.63307271 -0.58109036
## NARI -0.57335541 -0.01604287 -0.169579751 -0.41832504 -0.18553810 -0.12741923
## NDES -0.39163352 -0.44793371 -0.167312275 -0.11340137 0.00799038 -0.31622726
## QUIN -0.74038489 -0.63474866 -0.755722404 -0.64470776 -0.76612354 -0.93690042
## RISA -0.76513000 -0.57712100 -0.634412416 -0.47376570 -0.55082311 -0.86084535
## SANT -0.60274023 -0.60181857 -0.616272605 -0.63084759 -0.72257963 -0.78691770
## SUCR 0.45511316 -0.37320773 -0.196789468 -0.57078687 0.87403033 0.25285610
## TOLI -0.57644855 -0.55432324 -0.508567475 -0.43680526 -0.44922065 -0.64650835
## VALL -0.77440941 -0.61321745 -0.751187452 -0.55692670 -0.91852722 -0.96402495
## ARAU 1.04280948 -0.46883165 0.050365461 -0.08568103 0.09265909 0.42943149
## CASA -0.28724009 -0.57205483 -0.217196756 -0.55230665 -0.45889708 -0.44121286
## PUTU -0.55479658 -0.17816025 -0.273883666 -0.55692670 -0.40567675 -0.28803902
## SANA -0.76667657 -0.06100511 -0.499497570 -0.44604537 -1.47734071 -0.50450344
## AMAZ -0.38622053 0.55516760 0.925611357 0.41328498 -0.08151654 0.57781865
## GUAI 1.71092741 1.85907266 1.663674930 1.46203760 1.85134916 1.86596808
## GUAV 0.31282879 0.09034667 -0.348710388 -0.26124314 0.09991641 0.18796996
## VAUP 2.05813221 2.93310033 2.315574399 2.78337351 1.29495478 2.37016530
## VICH 3.54747842 2.23776874 2.948200319 3.35626040 2.48273583 2.30740657Distancias.
diseuclidea<-dist(datos,method="euclidean",diag=T,upper=T)
diseuclidea## ANTI ATLA BOGO BOLI BOYA CALD CAQU
## ANTI 0.0000000 0.6214865 0.9997844 1.5099682 0.2375173 0.3053430 1.3709305
## ATLA 0.6214865 0.0000000 1.2089113 1.4631114 0.8108277 0.8741195 1.4014567
## BOGO 0.9997844 1.2089113 0.0000000 2.3926166 1.0140573 0.9266148 2.3486669
## BOLI 1.5099682 1.4631114 2.3926166 0.0000000 1.6354478 1.7507244 0.5255618
## BOYA 0.2375173 0.8108277 1.0140573 1.6354478 0.0000000 0.1635319 1.4514571
## CALD 0.3053430 0.8741195 0.9266148 1.7507244 0.1635319 0.0000000 1.5683759
## CAQU 1.3709305 1.4014567 2.3486669 0.5255618 1.4514571 1.5683759 0.0000000
## CAUC 0.6115467 0.9537897 1.5032973 1.0812857 0.6388315 0.7594123 0.9628862
## CESA 1.4799795 1.4333684 2.4394705 0.6917018 1.5480957 1.6868613 0.4000148
## CORDO 2.4937076 2.6617080 3.3300215 1.4264280 2.5400639 2.6535135 1.5030705
## CUND 0.6567852 0.9043398 0.3475979 2.0648549 0.6974978 0.6266055 2.0039350
## CHOC 5.1740104 5.1001553 5.9041573 4.0170708 5.2151836 5.3194541 4.2062816
## HUIL 0.3252863 0.8685499 1.2416073 1.4434001 0.2669883 0.3650614 1.2286314
## GUAJ 6.1910157 6.0525327 7.0891990 4.9811726 6.2312114 6.3810957 4.9754461
## MAGD 1.7329489 1.6872208 2.6865846 0.5816885 1.8097958 1.9432412 0.4636307
## META 0.3253518 0.6912691 1.1325457 1.3060978 0.4809481 0.5734397 1.2470028
## NARI 0.9804132 1.1179938 1.8243028 1.0263532 0.9881462 1.1186913 0.9194974
## NDES 0.9297581 0.9536147 1.8932838 0.9040404 0.9881997 1.1287713 0.6104554
## QUIN 0.4184727 0.8165087 0.6588458 1.9119158 0.4263881 0.3182943 1.7762202
## RISA 0.2576068 0.6333509 0.9374168 1.7011656 0.2947532 0.2819190 1.5255108
## SANT 0.2283505 0.7236117 0.7895867 1.7067458 0.2780964 0.2651173 1.5868860
## SUCR 2.0593189 2.2962842 2.9885331 1.2880667 2.0533948 2.1641269 1.0529479
## TOLI 0.1792242 0.5933242 1.1548557 1.4076050 0.2896671 0.4069567 1.2350248
## VALL 0.5126695 0.7705803 0.5478206 1.9622373 0.5679767 0.4834276 1.8613262
## ARAU 2.2171754 2.2690581 3.0217423 1.1224549 2.3050280 2.4293067 1.2958632
## CASA 0.5573754 0.8471959 1.3812312 1.2361666 0.5979486 0.7451026 1.1193938
## PUTU 0.6719950 0.9235669 1.4801885 1.1849008 0.6759125 0.8069343 1.0932687
## SANA 1.0786998 1.0431797 0.9637775 1.9271380 1.1743405 1.1828244 2.0413056
## AMAZ 2.5104287 2.3215252 3.2351285 1.6181668 2.5668826 2.7123971 1.7766467
## GUAI 5.6911725 5.5866170 6.5489030 4.2920328 5.7556873 5.8932619 4.4595435
## GUAV 1.5946368 1.7274080 2.4736382 0.5091677 1.6637684 1.7770648 0.6741195
## VAUP 7.1537257 6.9429106 7.9132145 5.7662926 7.2498212 7.3851260 6.0233076
## VICH 8.3938950 8.2082128 9.2142061 6.9880807 8.4877405 8.6276417 7.1792729
## CAUC CESA CORDO CUND CHOC HUIL GUAJ
## ANTI 0.6115467 1.4799795 2.4937076 0.6567852 5.1740104 0.3252863 6.1910157
## ATLA 0.9537897 1.4333684 2.6617080 0.9043398 5.1001553 0.8685499 6.0525327
## BOGO 1.5032973 2.4394705 3.3300215 0.3475979 5.9041573 1.2416073 7.0891990
## BOLI 1.0812857 0.6917018 1.4264280 2.0648549 4.0170708 1.4434001 4.9811726
## BOYA 0.6388315 1.5480957 2.5400639 0.6974978 5.2151836 0.2669883 6.2312114
## CALD 0.7594123 1.6868613 2.6535135 0.6266055 5.3194541 0.3650614 6.3810957
## CAQU 0.9628862 0.4000148 1.5030705 2.0039350 4.2062816 1.2286314 4.9754461
## CAUC 0.0000000 1.0994023 1.9987113 1.1776418 4.6618589 0.4703063 5.7609771
## CESA 1.0994023 0.0000000 1.5744658 2.0974941 4.1815685 1.3593480 4.7410752
## CORDO 1.9987113 1.5744658 0.0000000 3.0311016 4.1570666 2.3116171 4.4942931
## CUND 1.1776418 2.0974941 3.0311016 0.0000000 5.6341975 0.9164873 6.7686843
## CHOC 4.6618589 4.1815685 4.1570666 5.6341975 0.0000000 5.0774437 4.3966781
## HUIL 0.4703063 1.3593480 2.3116171 0.9164873 5.0774437 0.0000000 6.0555086
## GUAJ 5.7609771 4.7410752 4.4942931 6.7686843 4.3966781 6.0555086 0.0000000
## MAGD 1.2933682 0.3446246 1.3886949 2.3459104 3.9086830 1.6091378 4.5477332
## META 0.4909319 1.3614599 2.2497683 0.8031941 5.0486265 0.4461932 6.0412034
## NARI 0.5095682 0.9495654 2.0351903 1.5090018 4.2607819 0.8756343 5.4695474
## NDES 0.6476392 0.5765797 1.9170394 1.5505487 4.5401392 0.8226022 5.2842608
## QUIN 0.9893911 1.8897469 2.8729399 0.3600493 5.5149726 0.6364335 6.5945707
## RISA 0.8155694 1.6198592 2.7183682 0.6147700 5.2953267 0.4674370 6.3205752
## SANT 0.7723258 1.6897052 2.6475263 0.4541192 5.3462655 0.4675877 6.3856108
## SUCR 1.5686314 1.1400199 0.8867113 2.6690362 4.2307385 1.8083008 4.6570093
## TOLI 0.5293530 1.3254734 2.4040223 0.8110871 5.0726982 0.2800644 6.0364177
## VALL 1.0856978 1.9651942 2.9726173 0.2461407 5.5496241 0.7799342 6.6626686
## ARAU 1.7864188 1.3000701 0.6454577 2.7228298 4.3025388 2.1004771 4.5547554
## CASA 0.4276073 1.1535869 2.0672452 1.0621201 4.9384817 0.5070444 5.7703284
## PUTU 0.2909506 1.1553682 2.1620924 1.1668907 4.5864839 0.6033300 5.7607786
## SANA 1.2732107 2.1112592 3.0293081 0.8579337 5.1099356 1.3203871 6.6192784
## AMAZ 2.0905348 1.5369250 2.2954796 2.9519161 3.1943165 2.4761144 4.2801310
## GUAI 5.1821645 4.3344596 3.8644792 6.2399080 2.6776416 5.5753639 2.2310968
## GUAV 1.0547338 0.8685716 1.1435277 2.1561092 3.9391904 1.4523994 4.9905276
## VAUP 6.6931508 5.8872312 5.5704191 7.6299909 3.4753734 7.1018318 3.3839231
## VICH 7.9508983 7.0297542 6.5096494 8.9150731 5.3482523 8.3151075 3.3504730
## MAGD META NARI NDES QUIN RISA SANT
## ANTI 1.7329489 0.3253518 0.9804132 0.9297581 0.4184727 0.2576068 0.2283505
## ATLA 1.6872208 0.6912691 1.1179938 0.9536147 0.8165087 0.6333509 0.7236117
## BOGO 2.6865846 1.1325457 1.8243028 1.8932838 0.6588458 0.9374168 0.7895867
## BOLI 0.5816885 1.3060978 1.0263532 0.9040404 1.9119158 1.7011656 1.7067458
## BOYA 1.8097958 0.4809481 0.9881462 0.9881997 0.4263881 0.2947532 0.2780964
## CALD 1.9432412 0.5734397 1.1186913 1.1287713 0.3182943 0.2819190 0.2651173
## CAQU 0.4636307 1.2470028 0.9194974 0.6104554 1.7762202 1.5255108 1.5868860
## CAUC 1.2933682 0.4909319 0.5095682 0.6476392 0.9893911 0.8155694 0.7723258
## CESA 0.3446246 1.3614599 0.9495654 0.5765797 1.8897469 1.6198592 1.6897052
## CORDO 1.3886949 2.2497683 2.0351903 1.9170394 2.8729399 2.7183682 2.6475263
## CUND 2.3459104 0.8031941 1.5090018 1.5505487 0.3600493 0.6147700 0.4541192
## CHOC 3.9086830 5.0486265 4.2607819 4.5401392 5.5149726 5.2953267 5.3462655
## HUIL 1.6091378 0.4461932 0.8756343 0.8226022 0.6364335 0.4674370 0.4675877
## GUAJ 4.5477332 6.0412034 5.4695474 5.2842608 6.5945707 6.3205752 6.3856108
## MAGD 0.0000000 1.5852399 1.1143724 0.8748345 2.1478543 1.8887640 1.9438935
## META 1.5852399 0.0000000 0.9136024 0.8691212 0.6727669 0.5786615 0.4393562
## NARI 1.1143724 0.9136024 0.0000000 0.6209975 1.3408383 1.1144847 1.1454470
## NDES 0.8748345 0.8691212 0.6209975 0.0000000 1.3302360 1.0550428 1.1370332
## QUIN 2.1478543 0.6727669 1.3408383 1.3302360 0.0000000 0.3162423 0.2531001
## RISA 1.8887640 0.5786615 1.1144847 1.0550428 0.3162423 0.0000000 0.2948725
## SANT 1.9438935 0.4393562 1.1454470 1.1370332 0.2531001 0.2948725 0.0000000
## SUCR 1.0590370 1.9081902 1.5737198 1.4165152 2.4333341 2.2365239 2.2318564
## TOLI 1.5901750 0.3583680 0.8625494 0.7646228 0.5678093 0.3310391 0.3829358
## VALL 2.2201450 0.7351630 1.4112761 1.4105098 0.1825102 0.4096261 0.3507549
## ARAU 1.1582203 1.9499149 1.8339877 1.6338272 2.6026851 2.4451556 2.3688081
## CASA 1.4035713 0.3884232 0.7644745 0.6745633 0.9208218 0.7701843 0.6744603
## PUTU 1.3583438 0.6065738 0.3619060 0.6923779 1.0167267 0.8303500 0.8085709
## SANA 2.2854319 1.0636868 1.3999840 1.6592247 1.0619736 1.1272812 1.0082483
## AMAZ 1.4368275 2.3737708 1.6614754 1.8125815 2.8723902 2.6336639 2.6695662
## GUAI 4.0405591 5.4968679 4.8737147 4.8721157 6.1014073 5.8566529 5.8864493
## GUAV 0.7349300 1.3793832 1.0170341 1.0504478 1.9907498 1.8049308 1.7755174
## VAUP 5.6026340 6.9534260 6.3622972 6.3923201 7.5452354 7.3109621 7.3393559
## VICH 6.7583184 8.1833823 7.6861595 7.5817143 8.8002575 8.5595975 8.5871391
## SUCR TOLI VALL ARAU CASA PUTU SANA
## ANTI 2.0593189 0.1792242 0.5126695 2.2171754 0.5573754 0.6719950 1.0786998
## ATLA 2.2962842 0.5933242 0.7705803 2.2690581 0.8471959 0.9235669 1.0431797
## BOGO 2.9885331 1.1548557 0.5478206 3.0217423 1.3812312 1.4801885 0.9637775
## BOLI 1.2880667 1.4076050 1.9622373 1.1224549 1.2361666 1.1849008 1.9271380
## BOYA 2.0533948 0.2896671 0.5679767 2.3050280 0.5979486 0.6759125 1.1743405
## CALD 2.1641269 0.4069567 0.4834276 2.4293067 0.7451026 0.8069343 1.1828244
## CAQU 1.0529479 1.2350248 1.8613262 1.2958632 1.1193938 1.0932687 2.0413056
## CAUC 1.5686314 0.5293530 1.0856978 1.7864188 0.4276073 0.2909506 1.2732107
## CESA 1.1400199 1.3254734 1.9651942 1.3000701 1.1535869 1.1553682 2.1112592
## CORDO 0.8867113 2.4040223 2.9726173 0.6454577 2.0672452 2.1620924 3.0293081
## CUND 2.6690362 0.8110871 0.2461407 2.7228298 1.0621201 1.1668907 0.8579337
## CHOC 4.2307385 5.0726982 5.5496241 4.3025388 4.9384817 4.5864839 5.1099356
## HUIL 1.8083008 0.2800644 0.7799342 2.1004771 0.5070444 0.6033300 1.3203871
## GUAJ 4.6570093 6.0364177 6.6626686 4.5547554 5.7703284 5.7607786 6.6192784
## MAGD 1.0590370 1.5901750 2.2201450 1.1582203 1.4035713 1.3583438 2.2854319
## META 1.9081902 0.3583680 0.7351630 1.9499149 0.3884232 0.6065738 1.0636868
## NARI 1.5737198 0.8625494 1.4112761 1.8339877 0.7644745 0.3619060 1.3999840
## NDES 1.4165152 0.7646228 1.4105098 1.6338272 0.6745633 0.6923779 1.6592247
## QUIN 2.4333341 0.5678093 0.1825102 2.6026851 0.9208218 1.0167267 1.0619736
## RISA 2.2365239 0.3310391 0.4096261 2.4451556 0.7701843 0.8303500 1.1272812
## SANT 2.2318564 0.3829358 0.3507549 2.3688081 0.6744603 0.8085709 1.0082483
## SUCR 0.0000000 1.9421453 2.5633848 1.1369538 1.6881391 1.7304088 2.7928431
## TOLI 1.9421453 0.0000000 0.6610719 2.1251541 0.4737439 0.5846960 1.1648662
## VALL 2.5633848 0.6610719 0.0000000 2.6743055 1.0043844 1.0887130 0.9508277
## ARAU 1.1369538 2.1251541 2.6743055 0.0000000 1.7695343 1.9305822 2.6851272
## CASA 1.6881391 0.4737439 1.0043844 1.7695343 0.0000000 0.5062300 1.2740681
## PUTU 1.7304088 0.5846960 1.0887130 1.9305822 0.5062300 0.0000000 1.1476651
## SANA 2.7928431 1.1648662 0.9508277 2.6851272 1.2740681 1.1476651 0.0000000
## AMAZ 2.1946696 2.3834559 2.8890566 2.0391370 2.1678668 1.9496348 2.5324980
## GUAI 4.2084594 5.5665042 6.1545081 4.0025428 5.3064712 5.1815139 5.9029338
## GUAV 0.9785128 1.5035609 2.0714308 1.0459408 1.2684698 1.1832610 2.0524101
## VAUP 5.9769459 7.0420832 7.5616548 5.5837827 6.8050290 6.6579603 7.1587241
## VICH 6.9643157 8.2741238 8.8360735 6.5637426 8.0065550 7.9648915 8.5924088
## AMAZ GUAI GUAV VAUP VICH
## ANTI 2.5104287 5.6911725 1.5946368 7.1537257 8.3938950
## ATLA 2.3215252 5.5866170 1.7274080 6.9429106 8.2082128
## BOGO 3.2351285 6.5489030 2.4736382 7.9132145 9.2142061
## BOLI 1.6181668 4.2920328 0.5091677 5.7662926 6.9880807
## BOYA 2.5668826 5.7556873 1.6637684 7.2498212 8.4877405
## CALD 2.7123971 5.8932619 1.7770648 7.3851260 8.6276417
## CAQU 1.7766467 4.4595435 0.6741195 6.0233076 7.1792729
## CAUC 2.0905348 5.1821645 1.0547338 6.6931508 7.9508983
## CESA 1.5369250 4.3344596 0.8685716 5.8872312 7.0297542
## CORDO 2.2954796 3.8644792 1.1435277 5.5704191 6.5096494
## CUND 2.9519161 6.2399080 2.1561092 7.6299909 8.9150731
## CHOC 3.1943165 2.6776416 3.9391904 3.4753734 5.3482523
## HUIL 2.4761144 5.5753639 1.4523994 7.1018318 8.3151075
## GUAJ 4.2801310 2.2310968 4.9905276 3.3839231 3.3504730
## MAGD 1.4368275 4.0405591 0.7349300 5.6026340 6.7583184
## META 2.3737708 5.4968679 1.3793832 6.9534260 8.1833823
## NARI 1.6614754 4.8737147 1.0170341 6.3622972 7.6861595
## NDES 1.8125815 4.8721157 1.0504478 6.3923201 7.5817143
## QUIN 2.8723902 6.1014073 1.9907498 7.5452354 8.8002575
## RISA 2.6336639 5.8566529 1.8049308 7.3109621 8.5595975
## SANT 2.6695662 5.8864493 1.7755174 7.3393559 8.5871391
## SUCR 2.1946696 4.2084594 0.9785128 5.9769459 6.9643157
## TOLI 2.3834559 5.5665042 1.5035609 7.0420832 8.2741238
## VALL 2.8890566 6.1545081 2.0714308 7.5616548 8.8360735
## ARAU 2.0391370 4.0025428 1.0459408 5.5837827 6.5637426
## CASA 2.1678668 5.3064712 1.2684698 6.8050290 8.0065550
## PUTU 1.9496348 5.1815139 1.1832610 6.6579603 7.9648915
## SANA 2.5324980 5.9029338 2.0524101 7.1587241 8.5924088
## AMAZ 0.0000000 3.6246540 1.7229372 4.9280748 6.3736935
## GUAI 3.6246540 0.0000000 4.2409500 2.0021932 3.0574389
## GUAV 1.7229372 4.2409500 0.0000000 5.8039236 7.0142834
## VAUP 4.9280748 2.0021932 5.8039236 0.0000000 2.2010942
## VICH 6.3736935 3.0574389 7.0142834 2.2010942 0.0000000m<-as.matrix(diseuclidea)
eucl<-as.dist(m)
eucl## ANTI ATLA BOGO BOLI BOYA CALD CAQU
## ATLA 0.6214865
## BOGO 0.9997844 1.2089113
## BOLI 1.5099682 1.4631114 2.3926166
## BOYA 0.2375173 0.8108277 1.0140573 1.6354478
## CALD 0.3053430 0.8741195 0.9266148 1.7507244 0.1635319
## CAQU 1.3709305 1.4014567 2.3486669 0.5255618 1.4514571 1.5683759
## CAUC 0.6115467 0.9537897 1.5032973 1.0812857 0.6388315 0.7594123 0.9628862
## CESA 1.4799795 1.4333684 2.4394705 0.6917018 1.5480957 1.6868613 0.4000148
## CORDO 2.4937076 2.6617080 3.3300215 1.4264280 2.5400639 2.6535135 1.5030705
## CUND 0.6567852 0.9043398 0.3475979 2.0648549 0.6974978 0.6266055 2.0039350
## CHOC 5.1740104 5.1001553 5.9041573 4.0170708 5.2151836 5.3194541 4.2062816
## HUIL 0.3252863 0.8685499 1.2416073 1.4434001 0.2669883 0.3650614 1.2286314
## GUAJ 6.1910157 6.0525327 7.0891990 4.9811726 6.2312114 6.3810957 4.9754461
## MAGD 1.7329489 1.6872208 2.6865846 0.5816885 1.8097958 1.9432412 0.4636307
## META 0.3253518 0.6912691 1.1325457 1.3060978 0.4809481 0.5734397 1.2470028
## NARI 0.9804132 1.1179938 1.8243028 1.0263532 0.9881462 1.1186913 0.9194974
## NDES 0.9297581 0.9536147 1.8932838 0.9040404 0.9881997 1.1287713 0.6104554
## QUIN 0.4184727 0.8165087 0.6588458 1.9119158 0.4263881 0.3182943 1.7762202
## RISA 0.2576068 0.6333509 0.9374168 1.7011656 0.2947532 0.2819190 1.5255108
## SANT 0.2283505 0.7236117 0.7895867 1.7067458 0.2780964 0.2651173 1.5868860
## SUCR 2.0593189 2.2962842 2.9885331 1.2880667 2.0533948 2.1641269 1.0529479
## TOLI 0.1792242 0.5933242 1.1548557 1.4076050 0.2896671 0.4069567 1.2350248
## VALL 0.5126695 0.7705803 0.5478206 1.9622373 0.5679767 0.4834276 1.8613262
## ARAU 2.2171754 2.2690581 3.0217423 1.1224549 2.3050280 2.4293067 1.2958632
## CASA 0.5573754 0.8471959 1.3812312 1.2361666 0.5979486 0.7451026 1.1193938
## PUTU 0.6719950 0.9235669 1.4801885 1.1849008 0.6759125 0.8069343 1.0932687
## SANA 1.0786998 1.0431797 0.9637775 1.9271380 1.1743405 1.1828244 2.0413056
## AMAZ 2.5104287 2.3215252 3.2351285 1.6181668 2.5668826 2.7123971 1.7766467
## GUAI 5.6911725 5.5866170 6.5489030 4.2920328 5.7556873 5.8932619 4.4595435
## GUAV 1.5946368 1.7274080 2.4736382 0.5091677 1.6637684 1.7770648 0.6741195
## VAUP 7.1537257 6.9429106 7.9132145 5.7662926 7.2498212 7.3851260 6.0233076
## VICH 8.3938950 8.2082128 9.2142061 6.9880807 8.4877405 8.6276417 7.1792729
## CAUC CESA CORDO CUND CHOC HUIL GUAJ
## ATLA
## BOGO
## BOLI
## BOYA
## CALD
## CAQU
## CAUC
## CESA 1.0994023
## CORDO 1.9987113 1.5744658
## CUND 1.1776418 2.0974941 3.0311016
## CHOC 4.6618589 4.1815685 4.1570666 5.6341975
## HUIL 0.4703063 1.3593480 2.3116171 0.9164873 5.0774437
## GUAJ 5.7609771 4.7410752 4.4942931 6.7686843 4.3966781 6.0555086
## MAGD 1.2933682 0.3446246 1.3886949 2.3459104 3.9086830 1.6091378 4.5477332
## META 0.4909319 1.3614599 2.2497683 0.8031941 5.0486265 0.4461932 6.0412034
## NARI 0.5095682 0.9495654 2.0351903 1.5090018 4.2607819 0.8756343 5.4695474
## NDES 0.6476392 0.5765797 1.9170394 1.5505487 4.5401392 0.8226022 5.2842608
## QUIN 0.9893911 1.8897469 2.8729399 0.3600493 5.5149726 0.6364335 6.5945707
## RISA 0.8155694 1.6198592 2.7183682 0.6147700 5.2953267 0.4674370 6.3205752
## SANT 0.7723258 1.6897052 2.6475263 0.4541192 5.3462655 0.4675877 6.3856108
## SUCR 1.5686314 1.1400199 0.8867113 2.6690362 4.2307385 1.8083008 4.6570093
## TOLI 0.5293530 1.3254734 2.4040223 0.8110871 5.0726982 0.2800644 6.0364177
## VALL 1.0856978 1.9651942 2.9726173 0.2461407 5.5496241 0.7799342 6.6626686
## ARAU 1.7864188 1.3000701 0.6454577 2.7228298 4.3025388 2.1004771 4.5547554
## CASA 0.4276073 1.1535869 2.0672452 1.0621201 4.9384817 0.5070444 5.7703284
## PUTU 0.2909506 1.1553682 2.1620924 1.1668907 4.5864839 0.6033300 5.7607786
## SANA 1.2732107 2.1112592 3.0293081 0.8579337 5.1099356 1.3203871 6.6192784
## AMAZ 2.0905348 1.5369250 2.2954796 2.9519161 3.1943165 2.4761144 4.2801310
## GUAI 5.1821645 4.3344596 3.8644792 6.2399080 2.6776416 5.5753639 2.2310968
## GUAV 1.0547338 0.8685716 1.1435277 2.1561092 3.9391904 1.4523994 4.9905276
## VAUP 6.6931508 5.8872312 5.5704191 7.6299909 3.4753734 7.1018318 3.3839231
## VICH 7.9508983 7.0297542 6.5096494 8.9150731 5.3482523 8.3151075 3.3504730
## MAGD META NARI NDES QUIN RISA SANT
## ATLA
## BOGO
## BOLI
## BOYA
## CALD
## CAQU
## CAUC
## CESA
## CORDO
## CUND
## CHOC
## HUIL
## GUAJ
## MAGD
## META 1.5852399
## NARI 1.1143724 0.9136024
## NDES 0.8748345 0.8691212 0.6209975
## QUIN 2.1478543 0.6727669 1.3408383 1.3302360
## RISA 1.8887640 0.5786615 1.1144847 1.0550428 0.3162423
## SANT 1.9438935 0.4393562 1.1454470 1.1370332 0.2531001 0.2948725
## SUCR 1.0590370 1.9081902 1.5737198 1.4165152 2.4333341 2.2365239 2.2318564
## TOLI 1.5901750 0.3583680 0.8625494 0.7646228 0.5678093 0.3310391 0.3829358
## VALL 2.2201450 0.7351630 1.4112761 1.4105098 0.1825102 0.4096261 0.3507549
## ARAU 1.1582203 1.9499149 1.8339877 1.6338272 2.6026851 2.4451556 2.3688081
## CASA 1.4035713 0.3884232 0.7644745 0.6745633 0.9208218 0.7701843 0.6744603
## PUTU 1.3583438 0.6065738 0.3619060 0.6923779 1.0167267 0.8303500 0.8085709
## SANA 2.2854319 1.0636868 1.3999840 1.6592247 1.0619736 1.1272812 1.0082483
## AMAZ 1.4368275 2.3737708 1.6614754 1.8125815 2.8723902 2.6336639 2.6695662
## GUAI 4.0405591 5.4968679 4.8737147 4.8721157 6.1014073 5.8566529 5.8864493
## GUAV 0.7349300 1.3793832 1.0170341 1.0504478 1.9907498 1.8049308 1.7755174
## VAUP 5.6026340 6.9534260 6.3622972 6.3923201 7.5452354 7.3109621 7.3393559
## VICH 6.7583184 8.1833823 7.6861595 7.5817143 8.8002575 8.5595975 8.5871391
## SUCR TOLI VALL ARAU CASA PUTU SANA
## ATLA
## BOGO
## BOLI
## BOYA
## CALD
## CAQU
## CAUC
## CESA
## CORDO
## CUND
## CHOC
## HUIL
## GUAJ
## MAGD
## META
## NARI
## NDES
## QUIN
## RISA
## SANT
## SUCR
## TOLI 1.9421453
## VALL 2.5633848 0.6610719
## ARAU 1.1369538 2.1251541 2.6743055
## CASA 1.6881391 0.4737439 1.0043844 1.7695343
## PUTU 1.7304088 0.5846960 1.0887130 1.9305822 0.5062300
## SANA 2.7928431 1.1648662 0.9508277 2.6851272 1.2740681 1.1476651
## AMAZ 2.1946696 2.3834559 2.8890566 2.0391370 2.1678668 1.9496348 2.5324980
## GUAI 4.2084594 5.5665042 6.1545081 4.0025428 5.3064712 5.1815139 5.9029338
## GUAV 0.9785128 1.5035609 2.0714308 1.0459408 1.2684698 1.1832610 2.0524101
## VAUP 5.9769459 7.0420832 7.5616548 5.5837827 6.8050290 6.6579603 7.1587241
## VICH 6.9643157 8.2741238 8.8360735 6.5637426 8.0065550 7.9648915 8.5924088
## AMAZ GUAI GUAV VAUP
## ATLA
## BOGO
## BOLI
## BOYA
## CALD
## CAQU
## CAUC
## CESA
## CORDO
## CUND
## CHOC
## HUIL
## GUAJ
## MAGD
## META
## NARI
## NDES
## QUIN
## RISA
## SANT
## SUCR
## TOLI
## VALL
## ARAU
## CASA
## PUTU
## SANA
## AMAZ
## GUAI 3.6246540
## GUAV 1.7229372 4.2409500
## VAUP 4.9280748 2.0021932 5.8039236
## VICH 6.3736935 3.0574389 7.0142834 2.2010942Modelo.
ama<-mds(delta=eucl,ndim=2,type="ratio")
ama##
## Call:
## mds(delta = eucl, ndim = 2, type = "ratio")
##
## Model: Symmetric SMACOF
## Number of objects: 33
## Stress-1 value: 0.038
## Number of iterations: 21Stress.
print(ama$stress)## [1] 0.03808881Stress por puntos.
print(ama$spp)#stress por punto## ANTI ATLA BOGO BOLI BOYA CALD CAQU CAUC
## 0.3418225 5.3620552 1.1389363 3.6612973 0.6441090 0.6128697 2.7221439 1.5844691
## CESA CORDO CUND CHOC HUIL GUAJ MAGD META
## 4.8258118 6.8802692 0.8723051 7.2736495 0.8106177 8.2037755 2.8317174 1.9999833
## NARI NDES QUIN RISA SANT SUCR TOLI VALL
## 2.5828026 2.7384482 0.2676887 1.2995721 0.5267713 6.4278308 0.7345125 0.4843912
## ARAU CASA PUTU SANA AMAZ GUAI GUAV VAUP
## 8.1874953 1.7794892 2.1156280 3.2095956 5.1953994 1.3287025 7.2250168 2.6519834
## VICH
## 3.4788399RSQ.
dis<-cbind(ama$dhat)
dia<-cbind(ama$confdist)
summary(lm(dis~dia))##
## Call:
## lm(formula = dis ~ dia)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.153112 -0.017170 -0.005431 0.009585 0.182201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.024069 0.002250 10.7 <2e-16 ***
## dia 0.982094 0.002252 436.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03459 on 526 degrees of freedom
## Multiple R-squared: 0.9972, Adjusted R-squared: 0.9972
## F-statistic: 1.902e+05 on 1 and 526 DF, p-value: < 2.2e-16Mapa perceptual.
plot(ama$conf,pch=1,xlim=range(ama$conf,repel=T))
text(ama$conf,pos=1, labels = row.names(datos), cex=0.7)
print(ama$conf)## D1 D2
## ANTI -0.420916589 0.004764313
## ATLA -0.376502876 -0.160420114
## BOGO -0.679123463 -0.097683511
## BOLI 0.016664405 -0.035546694
## BOYA -0.440940934 0.052934550
## CALD -0.480786822 0.057911892
## CAQU -0.042448805 0.096430882
## CAUC -0.262700028 0.000840934
## CESA -0.006557104 0.094331609
## CORDO 0.199860149 0.373329973
## CUND -0.585195629 -0.076241818
## CHOC 0.869034475 -0.743172482
## HUIL -0.383610929 0.084222245
## GUAJ 1.299054442 0.534960032
## MAGD 0.083561607 0.063827675
## META -0.358477768 -0.002716068
## NARI -0.170413172 -0.103305994
## NDES -0.169165876 0.061977401
## QUIN -0.541215277 0.003197534
## RISA -0.467664256 -0.017798179
## SANT -0.479683012 0.006654432
## SUCR 0.042011521 0.355272602
## TOLI -0.383985880 0.020365513
## VALL -0.557661863 -0.042026748
## ARAU 0.162550439 0.281271128
## CASA -0.302875452 0.076646158
## PUTU -0.261467556 -0.069264622
## SANA -0.467413811 -0.295526596
## AMAZ 0.243936296 -0.292885482
## GUAI 1.224168027 -0.065004120
## GUAV 0.040708772 0.012702451
## VAUP 1.635416982 -0.337838023
## VICH 2.021839987 0.157789128—|—|—|
O.M.F.
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