A.Factorial sobre coches.sav
IMLE
30/11/2022
#carga de datos #correlaciones,valores y vectores propios #gráfico de correlaciones #valores y vectores propios #componentes principales (procedimientos)#procedimiento prcomp : #procedimiento princomp :
| #autovalores #cargas_factoriales #gráfico de sedimentación #graf.variables individuos en el plano F1F2 #puntuaciones factoriales ( no tipificadas) |
| #A.F. por máxima verosimilitud #principales resultados #forma alternativa para principales resultados #gráfico de las variables sobre el plano F1-F2 # puntuaciones factoriales ML |
| #A.F. por el método de ejes principales |
Nota: En todos los casos, las puntuaciones factoriales que se ofrecen sólo son las de los primeros y los últimos individuos ( No aparecen las 2181 para no sobrecargar la lectura )
Algunas cuestiones a reseñar:
Observar en el gráfico de correlaciones que aparecen varios "paquetes" de variables altamente correlacionasdas ( positiva o negativamente) es un buen presagio de que el análisis factorial será fructífero. Igualmente el determinante de correlación debería ser bajo.
Tanto el procedimiento prcomp como el princomp dan como resultado las componentes principales sin tipificar . Por lo tanto para poder interpretar los factores es necesario obtener la matriz de estructura ( correlaciones entre variables y factores ) . Y para obtener la puntuiaciones tipificadas es necesario tipificar.
El atributo $rotation ( a pesar del nombre) del procedimiento prcomp nos ofrece los coeficientes de la solución sin rotar, al igual que la función loadings() del procediemto princomp. Para obtener la solución rotada es necesario aplicar la función varimax() .
CARGA DE DATOS
library(haven)
coches <- read_sav("http://www.uv.es/mlejarza/actuariales/tam/coches.sav")
#View(coches)
datafact<-coches
#si tuviéramos una primera fila de identificación de cada póliza (variable "numpoliza" de otras versiones)
# la eliminaríamos de la matriz de datos y asignaríamos esta variable como nombre de las
# filas :
#datafact <- (coches[,-1])
#row.names(datafact)<-coches$numpoliza####CUESTIONES PREVIAS : CORRELACIONES Y VALORES Y VECTORES PROPIOS
library(corrplot)## corrplot 0.90 loadedmatriz_correlaciones <- cor(datafact, use = "pairwise.complete.obs")
matriz_correlaciones## sexo edad grupedad naños tipovehiculo
## sexo 1.000000000 -0.09826418 -0.05442932 -0.063553281 -0.028315438
## edad -0.098264182 1.00000000 0.91935195 0.665079187 0.197086162
## grupedad -0.054429324 0.91935195 1.00000000 0.600850571 0.226046472
## naños -0.063553281 0.66507919 0.60085057 1.000000000 0.003944353
## tipovehiculo -0.028315438 0.19708616 0.22604647 0.003944353 1.000000000
## antigvehiculo 0.089155644 -0.36166036 -0.38451376 -0.392211160 -0.048944522
## nsiniest -0.014689769 0.30249288 0.31544855 0.427200477 -0.061216618
## costetotal 0.003035431 0.15573491 0.17193046 0.201950134 0.031804395
## costemedio 0.040873708 0.20963740 0.21344428 0.273662201 0.006823645
## costemanual -0.002592670 -0.06415031 -0.03030591 -0.070379422 -0.030502377
## sinisetropaño -0.024758400 -0.06751720 -0.03147783 -0.057969038 -0.119811863
## edadvehiculo 0.078168779 -0.28609899 -0.34583057 -0.314146682 -0.044253524
## antigcarnet -0.096886356 0.99473353 0.91685257 0.672969530 0.196388393
## kilometros 0.079029442 -0.28281248 -0.34240478 -0.313347992 -0.044477731
## nsinultaño -0.021957312 -0.13448097 -0.10253556 -0.159942628 -0.106505601
## sinisetro -0.008853640 0.37994989 0.38907057 0.557956783 -0.086016916
## sin 0.001232326 0.41722106 0.41606528 0.613683619 -0.090894347
## antigvehiculo nsiniest costetotal costemedio costemanual
## sexo 0.089155644 -0.01468977 0.003035431 0.040873708 -0.00259267
## edad -0.361660364 0.30249288 0.155734909 0.209637402 -0.06415031
## grupedad -0.384513757 0.31544855 0.171930457 0.213444278 -0.03030591
## naños -0.392211160 0.42720048 0.201950134 0.273662201 -0.07037942
## tipovehiculo -0.048944522 -0.06121662 0.031804395 0.006823645 -0.03050238
## antigvehiculo 1.000000000 -0.12203376 0.033519943 -0.018410084 0.03999578
## nsiniest -0.122033756 1.00000000 0.703542595 0.450817887 0.41813702
## costetotal 0.033519943 0.70354260 1.000000000 0.751516509 0.63697576
## costemedio -0.018410084 0.45081789 0.751516509 1.000000000 0.46393010
## costemanual 0.039995776 0.41813702 0.636975764 0.463930102 1.00000000
## sinisetropaño -0.035075912 0.54311772 0.422803920 0.268364913 0.75634942
## edadvehiculo 0.937135920 -0.07643555 0.061535718 0.018994019 0.04543813
## antigcarnet -0.343829922 0.29826434 0.153140525 0.205524837 -0.06493618
## kilometros 0.935171672 -0.07598638 0.060066920 0.016273786 0.04441843
## nsinultaño 0.003902536 0.42132633 0.365055209 0.181366696 0.73993224
## sinisetro -0.180868316 0.88248421 0.627989411 0.581961459 0.37950074
## sin -0.235329508 0.72785639 0.524279399 0.644487985 0.30373669
## sinisetropaño edadvehiculo antigcarnet kilometros
## sexo -0.02475840 0.0781687794 -0.09688636 0.0790294416
## edad -0.06751720 -0.2860989933 0.99473353 -0.2828124829
## grupedad -0.03147783 -0.3458305657 0.91685257 -0.3424047798
## naños -0.05796904 -0.3141466819 0.67296953 -0.3133479923
## tipovehiculo -0.11981186 -0.0442535237 0.19638839 -0.0444777306
## antigvehiculo -0.03507591 0.9371359199 -0.34382992 0.9351716724
## nsiniest 0.54311772 -0.0764355479 0.29826434 -0.0759863818
## costetotal 0.42280392 0.0615357179 0.15314052 0.0600669196
## costemedio 0.26836491 0.0189940187 0.20552484 0.0162737859
## costemanual 0.75634942 0.0454381302 -0.06493618 0.0444184258
## sinisetropaño 1.00000000 -0.0257480150 -0.06842462 -0.0250980644
## edadvehiculo -0.02574801 1.0000000000 -0.27083199 0.9987755681
## antigcarnet -0.06842462 -0.2708319945 1.00000000 -0.2677239662
## kilometros -0.02509806 0.9987755681 -0.26772397 1.0000000000
## nsinultaño 0.95662256 0.0002470139 -0.13488979 0.0006832635
## sinisetro 0.48705722 -0.1166018674 0.37318714 -0.1162790152
## sin 0.39354327 -0.1626636911 0.40633015 -0.1628929505
## nsinultaño sinisetro sin
## sexo -0.0219573124 -0.00885364 0.001232326
## edad -0.1344809741 0.37994989 0.417221060
## grupedad -0.1025355604 0.38907057 0.416065282
## naños -0.1599426282 0.55795678 0.613683619
## tipovehiculo -0.1065056008 -0.08601692 -0.090894347
## antigvehiculo 0.0039025356 -0.18086832 -0.235329508
## nsiniest 0.4213263288 0.88248421 0.727856389
## costetotal 0.3650552085 0.62798941 0.524279399
## costemedio 0.1813666962 0.58196146 0.644487985
## costemanual 0.7399322444 0.37950074 0.303736693
## sinisetropaño 0.9566225567 0.48705722 0.393543273
## edadvehiculo 0.0002470139 -0.11660187 -0.162663691
## antigcarnet -0.1348897941 0.37318714 0.406330146
## kilometros 0.0006832635 -0.11627902 -0.162892951
## nsinultaño 1.0000000000 0.33387356 0.242461606
## sinisetro 0.3338735584 1.00000000 0.920667775
## sin 0.2424616063 0.92066778 1.000000000#Gráfico de las correlaciones
corrplot(cor(datafact), order = "hclust", tl.col='black', tl.cex=1) 
# Se puede conocer la presencia de multicolinealidad al evaluar el
# Determinante de la matriz de correlaciones
# Un determinante bajo, es decir, cercano a 0,
# indica alta multicolinealidad entre las variables.
det(matriz_correlaciones)## [1] 1.782036e-12# Obtener los valores propios y los vectores propios de la matriz de correlación
# puede hacerse a partir de la función << eigen >> que nos devuelve (todos los) valores y vectore propios
ev <- eigen(cor(datafact)) # get eigenvalues
ev## eigen() decomposition
## $values
## [1] 5.714748117 3.933756104 2.280357168 1.249369410 1.031639831 0.945264345
## [7] 0.666634318 0.397978531 0.315105528 0.168275870 0.101870093 0.067738302
## [13] 0.061577897 0.034657105 0.025253181 0.004584621 0.001189581
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.02953041 -0.04617373 -0.04684445 -0.25817166 -0.52748429 0.803498296
## [2,] -0.28603757 0.25890476 -0.22782042 0.24963907 0.10282571 0.143244583
## [3,] -0.28826431 0.24979685 -0.17784865 0.25790992 0.03024411 0.165983858
## [4,] -0.29109946 0.19143839 -0.15835568 -0.20051016 0.14651262 0.013162343
## [5,] -0.01900949 0.10526202 -0.09630895 0.53128513 -0.55602218 -0.195536431
## [6,] 0.19770294 -0.28052294 -0.41694244 0.07671822 0.08443694 0.042509092
## [7,] -0.32536955 -0.18755022 -0.04082251 -0.11827810 0.08879636 0.007961672
## [8,] -0.26161899 -0.26460408 -0.08426527 -0.03118665 -0.30319816 -0.252969305
## [9,] -0.25191958 -0.18207968 -0.13381392 -0.17538391 -0.37834498 -0.288434707
## [10,] -0.17221801 -0.34691414 0.16818439 0.26114380 -0.11913960 -0.001632044
## [11,] -0.18568608 -0.34056181 0.26227201 0.24395021 0.18766924 0.204608009
## [12,] 0.17152380 -0.27958860 -0.46267493 0.07420969 0.11524612 0.046399751
## [13,] -0.28307815 0.25692015 -0.23676724 0.25445340 0.10914757 0.148632316
## [14,] 0.17108386 -0.27859608 -0.46303921 0.07607924 0.11743335 0.050168553
## [15,] -0.13422190 -0.34057061 0.28998947 0.31465440 0.17799847 0.222129162
## [16,] -0.35746553 -0.14572686 -0.07777262 -0.22401130 0.08366266 -0.010839721
## [17,] -0.35141898 -0.09122833 -0.08752088 -0.27838205 0.04975041 -0.027699838
## [,7] [,8] [,9] [,10] [,11]
## [1,] 0.004750906 0.0237981745 -0.04380849 -0.019327065 0.03315174
## [2,] -0.182434665 0.0393271366 0.06758344 -0.048516001 0.34371447
## [3,] -0.157047138 0.1017723020 0.22869667 0.185812801 -0.63967799
## [4,] 0.133434472 -0.2721914742 -0.76715489 -0.247953190 -0.20704800
## [5,] 0.568164441 -0.1553283546 -0.04296885 -0.012024737 0.01689316
## [6,] 0.008207580 0.0062322886 0.01608193 0.021120015 -0.49066099
## [7,] 0.361029468 0.5451463823 0.02819038 -0.066924426 0.02890022
## [8,] -0.204800941 0.4914164210 -0.16930883 -0.195944463 -0.01104562
## [9,] -0.390885118 -0.3595489513 0.24624902 -0.322948797 -0.04771865
## [10,] -0.314077245 -0.0634018095 -0.40505813 0.646476772 0.07262148
## [11,] 0.087013483 -0.1628081981 0.08621021 -0.200723524 -0.03432759
## [12,] 0.026038904 -0.0594718664 -0.03732161 -0.008632365 0.18992563
## [13,] -0.184694801 0.0358850047 0.02992182 -0.079679947 0.30484011
## [14,] 0.026372081 -0.0571818037 -0.03574187 -0.007587087 0.19731362
## [15,] 0.024528084 -0.1357963057 0.02593418 -0.384478485 -0.06417460
## [16,] 0.305435948 -0.0004508411 0.16393463 0.256191142 0.04478121
## [17,] 0.201685640 -0.4052947382 0.24054867 0.274490552 0.06267967
## [,12] [,13] [,14] [,15] [,16]
## [1,] -0.005922215 0.014097804 -0.0066323958 6.211167e-03 1.289870e-03
## [2,] -0.166360640 0.150707785 0.0183111988 -4.732575e-03 7.035712e-01
## [3,] 0.362721791 -0.253994731 0.0196719658 -1.910640e-02 -5.277299e-05
## [4,] 0.018681593 -0.066912447 -0.0240228444 1.896368e-02 3.405425e-02
## [5,] -0.018547077 0.008015686 0.0009277217 1.454635e-07 -1.416128e-04
## [6,] -0.533902123 0.406006440 0.0084335131 3.276255e-02 2.878848e-02
## [7,] -0.301841460 -0.386928085 0.3937197594 -7.638071e-02 -6.619247e-03
## [8,] 0.367523271 0.425602522 -0.0685966735 1.612442e-01 -3.245519e-03
## [9,] -0.236775823 -0.341250844 -0.0151213286 -7.895100e-02 1.066681e-02
## [10,] -0.150478367 -0.122745318 0.0730969133 -7.934046e-02 -4.389080e-03
## [11,] -0.024563257 -0.106103508 -0.1351154750 7.280778e-01 3.066591e-02
## [12,] 0.260246988 -0.197909879 0.0072843661 -1.589252e-02 -1.979909e-02
## [13,] -0.209275734 0.133190367 -0.0410339060 3.165306e-02 -7.064293e-01
## [14,] 0.278485495 -0.208115148 0.0008851182 -1.081123e-02 8.314445e-03
## [15,] 0.132187508 0.174187834 0.0628034061 -6.150296e-01 -1.371395e-02
## [16,] -0.037574536 0.028556757 -0.7479948144 -1.946164e-01 1.494543e-02
## [17,] 0.203768517 0.371736709 0.4998577285 7.857183e-02 -4.421149e-02
## [,17]
## [1,] 0.0010044789
## [2,] 0.0137144296
## [3,] 0.0046733790
## [4,] -0.0006915200
## [5,] -0.0009647844
## [6,] -0.0114908044
## [7,] -0.0022057919
## [8,] 0.0015832666
## [9,] -0.0030831644
## [10,] -0.0016070636
## [11,] 0.0047221990
## [12,] 0.7127772976
## [13,] -0.0145967160
## [14,] -0.7009478341
## [15,] -0.0021128801
## [16,] 0.0028037778
## [17,] -0.0030208773EL procedimiento general para Componentes principales en R es << prcomp >> que, sin embargo, tiene algunos inconvenientes” (Existe otro procedimiento: la función << princomp >> #el procedimiento princomp sólo puede usarse cuando hay más individuos que variables.EN ESTE CASO SE PODRÍA y lo haremos luego)”
#procedimiento prcomp
mod1<-prcomp(datafact,scale. = TRUE) # scale=TRUE PARA A.FACTORIAL SOBRE CORRELACIONES
summary(mod1) # desvtipica, prop.de varianza, y proporc acumulada de var explicada## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.3906 1.9834 1.5101 1.11775 1.01570 0.9722 0.81648
## Proportion of Variance 0.3362 0.2314 0.1341 0.07349 0.06068 0.0556 0.03921
## Cumulative Proportion 0.3362 0.5676 0.7017 0.77519 0.83587 0.8915 0.93069
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.63086 0.56134 0.4102 0.31917 0.26027 0.24815 0.18616
## Proportion of Variance 0.02341 0.01854 0.0099 0.00599 0.00398 0.00362 0.00204
## Cumulative Proportion 0.95410 0.97264 0.9825 0.98853 0.99251 0.99614 0.99817
## PC15 PC16 PC17
## Standard deviation 0.15891 0.06771 0.03449
## Proportion of Variance 0.00149 0.00027 0.00007
## Cumulative Proportion 0.99966 0.99993 1.00000# para obtener los valores propios debemos elevar al cuadrado las desv.típicas
vpropios<-(mod1$sdev)^2 # valores propios ( cuadrado de desvtipica)
vpropios## [1] 5.714748117 3.933756104 2.280357168 1.249369410 1.031639831 0.945264345
## [7] 0.666634318 0.397978531 0.315105528 0.168275870 0.101870093 0.067738302
## [13] 0.061577897 0.034657105 0.025253181 0.004584621 0.001189581# este procedimeinto de R no da las cargas factoriales para las COMPONENTES PRINCIPALES TIPIFICADAS
# SINO LA MATRIZ T ( TRANSFORMACIÓN Z=TP )
mod1$rotation #matriz T (¡¡ OJO !!)### PC1 PC2 PC3 PC4 PC5
## sexo -0.02953041 0.04617373 0.04684445 0.25817166 0.52748429
## edad 0.28603757 -0.25890476 0.22782042 -0.24963907 -0.10282571
## grupedad 0.28826431 -0.24979685 0.17784865 -0.25790992 -0.03024411
## naños 0.29109946 -0.19143839 0.15835568 0.20051016 -0.14651262
## tipovehiculo 0.01900949 -0.10526202 0.09630895 -0.53128513 0.55602218
## antigvehiculo -0.19770294 0.28052294 0.41694244 -0.07671822 -0.08443694
## nsiniest 0.32536955 0.18755022 0.04082251 0.11827810 -0.08879636
## costetotal 0.26161899 0.26460408 0.08426527 0.03118665 0.30319816
## costemedio 0.25191958 0.18207968 0.13381392 0.17538391 0.37834498
## costemanual 0.17221801 0.34691414 -0.16818439 -0.26114380 0.11913960
## sinisetropaño 0.18568608 0.34056181 -0.26227201 -0.24395021 -0.18766924
## edadvehiculo -0.17152380 0.27958860 0.46267493 -0.07420969 -0.11524612
## antigcarnet 0.28307815 -0.25692015 0.23676724 -0.25445340 -0.10914757
## kilometros -0.17108386 0.27859608 0.46303921 -0.07607924 -0.11743335
## nsinultaño 0.13422190 0.34057061 -0.28998947 -0.31465440 -0.17799847
## sinisetro 0.35746553 0.14572686 0.07777262 0.22401130 -0.08366266
## sin 0.35141898 0.09122833 0.08752088 0.27838205 -0.04975041
## PC6 PC7 PC8 PC9 PC10
## sexo 0.803498296 -0.004750906 -0.0237981745 0.04380849 -0.019327065
## edad 0.143244583 0.182434665 -0.0393271366 -0.06758344 -0.048516001
## grupedad 0.165983858 0.157047138 -0.1017723020 -0.22869667 0.185812801
## naños 0.013162343 -0.133434472 0.2721914742 0.76715489 -0.247953190
## tipovehiculo -0.195536431 -0.568164441 0.1553283546 0.04296885 -0.012024737
## antigvehiculo 0.042509092 -0.008207580 -0.0062322886 -0.01608193 0.021120015
## nsiniest 0.007961672 -0.361029468 -0.5451463823 -0.02819038 -0.066924426
## costetotal -0.252969305 0.204800941 -0.4914164210 0.16930883 -0.195944463
## costemedio -0.288434707 0.390885118 0.3595489513 -0.24624902 -0.322948797
## costemanual -0.001632044 0.314077245 0.0634018095 0.40505813 0.646476772
## sinisetropaño 0.204608009 -0.087013483 0.1628081981 -0.08621021 -0.200723524
## edadvehiculo 0.046399751 -0.026038904 0.0594718664 0.03732161 -0.008632365
## antigcarnet 0.148632316 0.184694801 -0.0358850047 -0.02992182 -0.079679947
## kilometros 0.050168553 -0.026372081 0.0571818037 0.03574187 -0.007587087
## nsinultaño 0.222129162 -0.024528084 0.1357963057 -0.02593418 -0.384478485
## sinisetro -0.010839721 -0.305435948 0.0004508411 -0.16393463 0.256191142
## sin -0.027699838 -0.201685640 0.4052947382 -0.24054867 0.274490552
## PC11 PC12 PC13 PC14 PC15
## sexo 0.03315174 -0.005922215 -0.014097804 0.0066323958 -6.211167e-03
## edad 0.34371447 -0.166360640 -0.150707785 -0.0183111988 4.732575e-03
## grupedad -0.63967799 0.362721791 0.253994731 -0.0196719658 1.910640e-02
## naños -0.20704800 0.018681593 0.066912447 0.0240228444 -1.896368e-02
## tipovehiculo 0.01689316 -0.018547077 -0.008015686 -0.0009277217 -1.454635e-07
## antigvehiculo -0.49066099 -0.533902123 -0.406006440 -0.0084335131 -3.276255e-02
## nsiniest 0.02890022 -0.301841460 0.386928085 -0.3937197594 7.638071e-02
## costetotal -0.01104562 0.367523271 -0.425602522 0.0685966735 -1.612442e-01
## costemedio -0.04771865 -0.236775823 0.341250844 0.0151213286 7.895100e-02
## costemanual 0.07262148 -0.150478367 0.122745318 -0.0730969133 7.934046e-02
## sinisetropaño -0.03432759 -0.024563257 0.106103508 0.1351154750 -7.280778e-01
## edadvehiculo 0.18992563 0.260246988 0.197909879 -0.0072843661 1.589252e-02
## antigcarnet 0.30484011 -0.209275734 -0.133190367 0.0410339060 -3.165306e-02
## kilometros 0.19731362 0.278485495 0.208115148 -0.0008851182 1.081123e-02
## nsinultaño -0.06417460 0.132187508 -0.174187834 -0.0628034061 6.150296e-01
## sinisetro 0.04478121 -0.037574536 -0.028556757 0.7479948144 1.946164e-01
## sin 0.06267967 0.203768517 -0.371736709 -0.4998577285 -7.857183e-02
## PC16 PC17
## sexo 1.289870e-03 -0.0010044789
## edad 7.035712e-01 -0.0137144296
## grupedad -5.277299e-05 -0.0046733790
## naños 3.405425e-02 0.0006915200
## tipovehiculo -1.416128e-04 0.0009647844
## antigvehiculo 2.878848e-02 0.0114908044
## nsiniest -6.619247e-03 0.0022057919
## costetotal -3.245519e-03 -0.0015832666
## costemedio 1.066681e-02 0.0030831644
## costemanual -4.389080e-03 0.0016070636
## sinisetropaño 3.066591e-02 -0.0047221990
## edadvehiculo -1.979909e-02 -0.7127772976
## antigcarnet -7.064293e-01 0.0145967160
## kilometros 8.314445e-03 0.7009478341
## nsinultaño -1.371395e-02 0.0021128801
## sinisetro 1.494543e-02 -0.0028037778
## sin -4.421149e-02 0.0030208773
#puntuaciones
mod1$x### PC1 PC2 PC3 PC4 PC5
## [1,] 0.62892960 -2.532871534 -0.537298517 -1.143296063 0.9176979430
## [2,] -0.04600583 -1.975593165 -1.156131505 -1.005263305 0.0346239114
## [3,] -0.23928876 -1.749544675 -1.113299540 -0.392218845 1.1218893311
## [4,] 0.57503444 -2.466228989 -0.495374488 -1.127778282 0.9122446394
## [5,] -0.10301313 -1.791501254 -1.183422416 -0.367723943 -0.6708650591
## [6,] -0.13826863 -1.829150868 -0.972732040 -0.503523136 1.0669592713
## [7,] -0.18408269 -1.684463220 -1.133947579 0.178061916 0.4001925059
## [8,] -0.08608143 -1.910299432 -1.047857592 -1.022831013 0.0074212438
## [9,] -0.11580998 -1.883022905 -1.071269180 -0.996661421 0.0184417916
## [10,] -0.11626724 -1.769911534 -1.147586669 -0.373569364 -0.6799042740
## [11,] -0.15030088 -1.735616725 -1.159390427 -0.349255882 -0.6717684819
## [12,] -0.26974639 -1.699921846 -1.031007003 -0.405575550 1.1012089538
## [13,] -0.09742931 -1.891817062 -1.017162851 -1.027852908 -0.0003386349
## [14,] -0.14732259 -1.740479341 -1.167379681 -0.348026454 -0.6698386473
## [15,] -0.15608708 -1.726195184 -1.143725491 -0.351835007 -0.6757474815
## [16,] -0.10572073 -1.878305771 -0.994774998 -1.031469751 -0.0059452397
## [17,] -0.09765734 -1.891450038 -1.016521497 -1.027986449 -0.0005338939
## [18,] -0.11086880 -1.869919517 -0.980858866 -1.033736282 -0.0094514796
## [19,] 0.53596671 -2.402581037 -0.389802867 -1.144931709 0.8856929122
## [20,] -0.45814139 -1.434371072 -0.583830279 -1.019422574 -0.0673374796
## [21,] -0.12191660 -1.760722494 -1.132237586 -0.376160012 -0.6838765801
## [22,] -0.17044033 -1.815182047 -1.027361618 -0.981462248 0.0124938787
## [23,] -0.12484192 -1.755955860 -1.124337030 -0.377438512 -0.6858575933
## [24,] -0.25402519 -1.591669231 -1.048702109 0.186590696 0.3839014647
## [25,] 0.09292066 -1.803698304 -0.902604694 0.562545002 0.2042755820
## [26,] -2.00187218 -0.028987559 -1.744839981 0.395665162 -0.2439481967
## [27,] -1.17781929 -0.671807941 -1.034815310 0.407666436 0.5534393824
## [28,] -1.08829207 -0.792636283 -1.107081230 -0.134490699 -0.5119722524
## [29,] -1.17614627 -0.674539792 -1.039301280 0.408354536 0.5545204104
## [30,] -1.17654599 -0.673888364 -1.038222378 0.408180682 0.5542507378
## [31,] -1.12235393 -0.758300668 -1.118779663 -0.110228224 -0.5039021825
## [32,] -2.05670718 0.077639868 -1.558862835 0.874654000 0.7826447927
## [33,] -0.45076118 -1.386465391 -0.359788947 -0.590500718 0.9401980274
## [34,] 0.94744031 -2.469623436 -0.404991841 -0.074246714 -1.7710344491
## [35,] -1.09781039 -0.777133481 -1.081336806 -0.138700908 -0.5184785946
## [36,] -1.09965114 -0.774138507 -1.076340465 -0.139538504 -0.5197650422
## [37,] -0.38339641 -1.471181222 -0.372200309 -1.142342983 -0.1402208458
## [38,] -1.11190984 -0.754168625 -1.043205034 -0.144932999 -0.5281110223
## [39,] -1.10207870 -0.973764016 -0.810906012 -1.426441766 0.8433953618
## [40,] -2.43224403 0.400365879 -1.769329643 0.990514316 0.9197355548
## [41,] 0.30220286 -2.226955655 0.281574418 -2.682291102 0.4156198243
## [42,] -1.19787353 -0.617984922 -0.876848555 0.359600880 0.5085391311
## [43,] -2.50726087 0.592471610 -1.851001833 1.658777851 0.2326045611
## [44,] -0.44709701 -1.371299002 -0.265829433 -0.628266919 0.9112793898
## [45,] -1.15994161 -0.862204134 -0.616743640 -0.948786353 1.8679257066
## [46,] -1.12768264 -0.932045352 -0.741748099 -1.437642603 0.8260435610
## [47,] -1.19205948 -0.644729479 -0.930467124 -0.140766277 -0.5511950449
## [48,] -2.03108500 0.039750223 -1.562089725 0.343532524 -0.2951281693
## [49,] -0.08861593 -1.580291088 -0.217080614 -0.756467671 -1.5090340743
## [50,] -2.09601226 0.215593331 -1.671750823 1.016851252 -0.9747334065
##
##
##
## [2177,] -3.96202031 2.802165952 2.108714350 0.341282358 -0.0106402691
## [2178,] -2.03528022 1.195726077 3.484907788 -0.601282772 -0.6942286510
## [2179,] -1.95091825 1.083311116 3.426609313 -1.145720461 -1.7631660135
## [2180,] -3.26607377 2.139512609 2.568855492 -0.751956709 -1.3129404386
## [2181,] -1.95354356 1.087586221 3.433714729 -1.146887910 -1.7649680484
## PC6 PC7 PC8 PC9 PC10
## [1,] 1.183079773 3.919312e-01 -0.2264418237 7.118150e-02 -1.045506e-01
## [2,] -0.824690472 -3.406247e-02 0.0023611553 3.467988e-01 -2.325707e-01
## [3,] 0.726691721 -1.219568e-01 -0.0240794334 4.580402e-01 -2.454853e-01
## [4,] 1.174717815 3.690317e-01 -0.2144149142 7.948157e-02 -9.743387e-02
## [5,] -0.575179476 6.583534e-01 -0.1768525210 3.012423e-01 -2.194139e-01
## [6,] 0.791514392 -4.864190e-02 -0.0339166563 4.414954e-01 -2.727974e-01
## [7,] 1.014362546 6.308269e-01 -0.2232900225 3.903412e-01 -2.494306e-01
## [8,] -0.813417177 -4.019079e-02 0.0160187832 3.553538e-01 -2.344739e-01
##
##
##
## [2178,] 1.492941690 4.196268e-01 0.1667769415 5.948686e-01 -2.375086e-01
## [2179,] -0.097346986 4.476383e-01 0.2119937079 5.049983e-01 -2.072883e-01
## [2180,] -0.565306951 1.795843e-01 -0.0531376601 -4.108845e-01 6.526624e-02
## [2181,] -0.096577140 4.472337e-01 0.2128711725 5.055468e-01 -2.074047e-01
## PC11 PC12 PC13 PC14 PC15
## [1,] -0.0255665797 0.222635878 0.195536008 0.0546416433 -7.310491e-03
## [2,] 0.3533585504 -0.013965924 0.062508138 0.0533673260 -3.581869e-03
## [3,] 0.3048005685 0.078567434 0.113014188 0.0616852591 -9.263753e-03
## [4,] -0.0291487997 0.283466209 0.238745381 0.0499779078 -2.252649e-03
## [5,] 0.3705754790 0.061514092 0.112117930 0.0536248685 -8.953561e-04
## [6,] 0.4571602311 0.026337212 0.073629135 0.0658156180 -1.339630e-02
## [7,] 0.3973188148 0.060518820 0.089436189 0.0630354896 -1.078359e-02
## [8,] 0.3986091938 0.048941332 0.109939759 0.0523747634 -4.290731e-04
## [9,] 0.3675178091 0.071304323 0.124244831 0.0481297990 2.869567e-03
## [10,] 0.3856760526 0.082643204 0.127988437 0.0534059292 6.099309e-05##
##
#### [2178,] 0.1567791189 0.211614202 0.191508571 0.0066923795 -2.382056e-02
## [2179,] 0.1266818169 0.208314235 0.210788190 -0.0023420998 -1.442408e-02
## [2180,] 0.8250468090 -0.007364540 -0.017212896 -0.0375702166 1.515323e-02
## [2181,] 0.1297096283 0.212587643 0.213981753 -0.0023556821 -1.425818e-02
## PC16 PC17
## [1,] -5.596159e-02 -5.922693e-02
## [2,] -5.373283e-02 -3.049208e-02
## [3,] -4.948464e-02 6.721697e-03
## [4,] 1.713794e-02 -2.347669e-02
## [5,] -5.503344e-02 -5.024020e-02
## [6,] -5.237001e-02 -3.885743e-02
## [7,] 2.193636e-02 -4.226395e-03
## [8,] -5.523877e-02 -4.005420e-02
## [9,] 1.797823e-02 -3.831727e-02
## [10,] -5.505065e-02 -2.921035e-02
##
##
##
## [2179,] -2.011421e-04 2.792149e-04
## [2180,] 2.075369e-02 1.090367e-02
## [2181,] -7.355554e-05 1.103538e-02
# Estas puntuaciones no estan tipificadas podemos comprobarlo calculando
# la desviación típica de alguina de ellas :
sd(mod1$x[,1])## [1] 2.390554############################################################################
#########Reducimos la dimensión
#por ejemplo con 5 CP explicaríamos un 83,59% de la variabilidad original
#SI NOS QUEDÁRAMOS CON SÓLO 5 COMP.PRINCIPALES podríamos usar el argumento rank : rank=5
mod2<-prcomp(datafact,scale. = TRUE, rank=5)
summary(mod2)## Importance of first k=5 (out of 17) components:
## PC1 PC2 PC3 PC4 PC5
## Standard deviation 2.3906 1.9834 1.5101 1.11775 1.01570
## Proportion of Variance 0.3362 0.2314 0.1341 0.07349 0.06068
## Cumulative Proportion 0.3362 0.5676 0.7017 0.77519 0.83587vpropios2<-(mod2$sdev)^2 # valores propios ( cuadrado de desvtipica)
vpropios2 # salen todos## [1] 5.714748117 3.933756104 2.280357168 1.249369410 1.031639831 0.945264345
## [7] 0.666634318 0.397978531 0.315105528 0.168275870 0.101870093 0.067738302
## [13] 0.061577897 0.034657105 0.025253181 0.004584621 0.001189581mod2$rotation # SÓLO SALEN LOS CINCO PRIMERAS COLUMNAS de la matriz T ( ¡¡ OJO !!)## PC1 PC2 PC3 PC4 PC5
## sexo -0.02953041 0.04617373 0.04684445 0.25817166 0.52748429
## edad 0.28603757 -0.25890476 0.22782042 -0.24963907 -0.10282571
## grupedad 0.28826431 -0.24979685 0.17784865 -0.25790992 -0.03024411
## naños 0.29109946 -0.19143839 0.15835568 0.20051016 -0.14651262
## tipovehiculo 0.01900949 -0.10526202 0.09630895 -0.53128513 0.55602218
## antigvehiculo -0.19770294 0.28052294 0.41694244 -0.07671822 -0.08443694
## nsiniest 0.32536955 0.18755022 0.04082251 0.11827810 -0.08879636
## costetotal 0.26161899 0.26460408 0.08426527 0.03118665 0.30319816
## costemedio 0.25191958 0.18207968 0.13381392 0.17538391 0.37834498
## costemanual 0.17221801 0.34691414 -0.16818439 -0.26114380 0.11913960
## sinisetropaño 0.18568608 0.34056181 -0.26227201 -0.24395021 -0.18766924
## edadvehiculo -0.17152380 0.27958860 0.46267493 -0.07420969 -0.11524612
## antigcarnet 0.28307815 -0.25692015 0.23676724 -0.25445340 -0.10914757
## kilometros -0.17108386 0.27859608 0.46303921 -0.07607924 -0.11743335
## nsinultaño 0.13422190 0.34057061 -0.28998947 -0.31465440 -0.17799847
## sinisetro 0.35746553 0.14572686 0.07777262 0.22401130 -0.08366266
## sin 0.35141898 0.09122833 0.08752088 0.27838205 -0.04975041mod2$x # puntuaciones de la 5 primera comp.principales sin tipificar (¡¡ OJO !! ) (NO ROTADAS) ## PC1 PC2 PC3 PC4 PC5
## [1,] 0.62892960 -2.532871534 -0.537298517 -1.143296063 0.9176979430
## [2,] -0.04600583 -1.975593165 -1.156131505 -1.005263305 0.0346239114
## [3,] -0.23928876 -1.749544675 -1.113299540 -0.392218845 1.1218893311
## [4,] 0.57503444 -2.466228989 -0.495374488 -1.127778282 0.9122446394
## [5,] -0.10301313 -1.791501254 -1.183422416 -0.367723943 -0.6708650591
## [6,] -0.13826863 -1.829150868 -0.972732040 -0.503523136 1.0669592713
## [7,] -0.18408269 -1.684463220 -1.133947579 0.178061916 0.4001925059
## [8,] -0.08608143 -1.910299432 -1.047857592 -1.022831013 0.0074212438
## [9,] -0.11580998 -1.883022905 -1.071269180 -0.996661421 0.0184417916##
#### [2175,] -3.78540142 2.539447312 1.801121054 -0.162659436 -1.0168903263
## [2176,] -3.14566876 1.964505750 2.347251512 -0.738335511 -1.2623612837
## [2177,] -3.96202031 2.802165952 2.108714350 0.341282358 -0.0106402691
## [2178,] -2.03528022 1.195726077 3.484907788 -0.601282772 -0.6942286510
## [2179,] -1.95091825 1.083311116 3.426609313 -1.145720461 -1.7631660135
## [2180,] -3.26607377 2.139512609 2.568855492 -0.751956709 -1.3129404386
## [2181,] -1.95354356 1.087586221 3.433714729 -1.146887910 -1.7649680484
# PARA INTERPRETARLAS tendremos que obtener
# o bien la matriz factorial para cp tipificadas A multiplicando por la matriz D^1/2
# o bien obteniendo las correlaciones ( que es equivalente)
matriz_correlaciones<-cor(datafact,mod2$x)
matriz_correlaciones## PC1 PC2 PC3 PC4 PC5
## sexo -0.07059403 0.09157958 0.07073911 0.28857187 0.53576407
## edad 0.68378825 -0.51350390 0.34402823 -0.27903455 -0.10443974
## grupedad 0.68911137 -0.49543955 0.26856661 -0.28827932 -0.03071884
## naños 0.69588897 -0.37969313 0.23913057 0.22412062 -0.14881239
## tipovehiculo 0.04544320 -0.20877351 0.14543472 -0.59384499 0.56474990
## antigvehiculo -0.47261955 0.55638075 0.62961859 -0.08575194 -0.08576232
## nsiniest 0.77781345 0.37198145 0.06164546 0.13220558 -0.09019017
## costetotal 0.62541432 0.52480777 0.12724773 0.03485894 0.30795738
## costemedio 0.60222735 0.36113135 0.20207041 0.19603571 0.38428376
## costemanual 0.41169645 0.68805907 -0.25397275 -0.29189399 0.12100970
## sinisetropaño 0.44389259 0.67546003 -0.39605306 -0.27267582 -0.19061503
## edadvehiculo -0.41003690 0.55452762 0.69867854 -0.08294802 -0.11705511
## antigcarnet 0.67671358 -0.50956770 0.35753869 -0.28441579 -0.11086083
## kilometros -0.40898519 0.55255907 0.69922863 -0.08503772 -0.11927667
## nsinultaño 0.32086470 0.67547750 -0.43790879 -0.35170557 -0.18079246
## sinisetro 0.85454063 0.28903027 0.11744328 0.25038907 -0.08497589
## sin 0.84008601 0.18093952 0.13216398 0.31116207 -0.05053133#podemos obtener las puntuaciones TIPIFICADAS tipificando las columnas de mod2$x
puntuaciones<-as.array(scale(mod2$x),dimnames=c(F1,F2,F3,F4,F5))
sd(puntuaciones[,1])#lo comprobamos## [1] 1#representacion gráfica de variables originales e individuos en el plano
#de las dos primeras componentes principales
biplot(x = mod2, scale = 0, cex = 0.6, col = c("blue4", "brown3"))
####### ROTACIÓN VARIMAX
#solucion rotada varimax
sol.rotada<-varimax(mod2$rotation)# aplicamos la función varimax a la solución obtenida
sol.rotadaSe obtienen: las cargas factoriales ( no tipificadas) .- aparecen sólo las de mayor relevancia
las sumas de cuadrados de las cargas % explicado y % explicado acumulado para cada factor
la matriz de rotación
## $loadings
##
## Loadings:
## PC1 PC2 PC3 PC4 PC5
## sexo -0.232 0.206 0.497
## edad -0.518
## grupedad -0.493
## naños 0.346 -0.192 -0.212
## tipovehiculo -0.509 0.102 -0.351 0.468
## antigvehiculo 0.551
## nsiniest 0.368 0.142
## costetotal 0.159 0.137 0.438
## costemedio 0.201 0.496
## costemanual 0.465 0.209
## sinisetropaño 0.547
## edadvehiculo 0.583
## antigcarnet -0.522
## kilometros 0.584
## nsinultaño 0.582
## sinisetro 0.447
## sin 0.452 0.114
##
## PC1 PC2 PC3 PC4 PC5
## SS loadings 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.059 0.059 0.059 0.059 0.059
## Cumulative Var 0.059 0.118 0.176 0.235 0.294
##
## $rotmat
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.6719957 0.2874979 -0.3078408 -0.53188902 0.29680790
## [2,] 0.2246790 0.6270628 0.4966515 0.48629708 0.27048850
## [3,] 0.1391818 -0.4290417 0.7751445 -0.40354226 0.18126330
## [4,] 0.5965457 -0.5584766 -0.1370167 0.55782799 0.04786909
## [5,] -0.3502896 -0.1678224 -0.1973546 0.08118368 0.89643360sol.rotada$loadings # de nuevo son los coeficientes de T ( CP no tipificadas)###
## Loadings:
## PC1 PC2 PC3 PC4 PC5
## sexo -0.232 0.206 0.497
## edad -0.518
## grupedad -0.493
## naños 0.346 -0.192 -0.212
## tipovehiculo -0.509 0.102 -0.351 0.468
## antigvehiculo 0.551
## nsiniest 0.368 0.142
## costetotal 0.159 0.137 0.438
## costemedio 0.201 0.496
## costemanual 0.465 0.209
## sinisetropaño 0.547
## edadvehiculo 0.583
## antigcarnet -0.522
## kilometros 0.584
## nsinultaño 0.582
## sinisetro 0.447
## sin 0.452 0.114
##
## PC1 PC2 PC3 PC4 PC5
## SS loadings 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.059 0.059 0.059 0.059 0.059
## Cumulative Var 0.059 0.118 0.176 0.235 0.294
sol.rotada$rotmat # matriz de rotación de la solución## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.6719957 0.2874979 -0.3078408 -0.53188902 0.29680790
## [2,] 0.2246790 0.6270628 0.4966515 0.48629708 0.27048850
## [3,] 0.1391818 -0.4290417 0.7751445 -0.40354226 0.18126330
## [4,] 0.5965457 -0.5584766 -0.1370167 0.55782799 0.04786909
## [5,] -0.3502896 -0.1678224 -0.1973546 0.08118368 0.89643360#para obtener las puntuaciones rotadas tendremos que multiplicar matricialmente
# la matriz de puntuaciones tipificadas (sin rotar) por la matriza de rotación que antes hay que
# definir como matriz
mat.rotacion<-as.array(sol.rotada$rotmat)
punt.rotadas<-as.array(puntuaciones%*%mat.rotacion,dimnames=C(FR1,FR2,FR3,FR4,FR5))
punt.rotadas## [,1] [,2] [,3] [,4] [,5]
## [1,] -1.086324971 -0.152890549 -1.0292073386 -1.114604617 0.429142553
## [2,] -0.891740371 0.194891796 -0.9657356546 -0.664121185 -0.426409620
## [3,] -0.964307508 -0.255005762 -1.1486646065 -0.184286761 0.571415156
## [4,] -1.079899147 -0.157066130 -0.9849017410 -1.090168202 0.432423545
## [5,] -0.305864585 0.052017518 -0.8673765961 -0.337224419 -1.007004354
## [6,] -0.972431524 -0.243274269 -1.0851353077 -0.323784130 0.536727251
## [7,] -0.390063746 -0.387615262 -1.0797530045 0.051826207 -0.027865537
## [8,] -0.885624187 0.193225152 -0.8812075298 -0.679071187 -0.434244921
## [9,] -0.882882877 0.190028913 -0.8879157315 -0.645571406 -0.426179007
## [10,] -0.303844045 0.051481935 -0.8393957603 -0.342198072 -1.009632216
## [11,] -0.300443726 0.048092899 -0.8370456623 -0.310278499 -1.002375845
## [12,] -0.959659511 -0.256270130 -1.0844191956 -0.195653117 0.565454945
## [13,] -0.883895337 0.192774195 -0.8572387393 -0.683343763 -0.436512601
## [14,] -0.300903118 0.048250464 -0.8432734867 -0.309230620 -1.001872325
## [15,] -0.299563379 0.047871148 -0.8248110334 -0.312472396 -1.003551255
## [16,] -0.882628797 0.192421490 -0.8397629891 -0.686422058 -0.438115249
##
##
#### [2169,] -1.036757097 -0.206131489 1.6759236528 0.932646446 0.773769660
## [2170,] -0.446396768 -0.347778421 1.8808556059 1.208380717 0.175851792
## [2171,] -0.445769961 -0.347938148 1.8895597714 1.206822927 0.175019730
## [2172,] -0.444279346 -0.348317995 1.9102592297 1.203118331 0.173040997
## [2173,] -0.498877120 -0.283378410 2.0786496596 0.499941402 0.006108534
## [2174,] -0.927663116 0.226755099 2.2324971026 0.482657464 -0.237359974
## [2175,] -0.346525723 0.085185639 2.2654206146 0.821104896 -0.811920208
## [2176,] -0.404070323 0.153374811 2.4376689889 0.084936689 -0.986648333
## [2177,] -0.416139876 -0.358439094 2.2545490995 1.174545609 0.148580237
## [2178,] -0.196957941 -0.441720292 2.5589527805 -0.540824850 -0.309778147
## [2179,] -0.113267320 -0.001908495 2.7644522822 -0.928726139 -1.288371640
## [2180,] -0.387492966 0.146425925 2.6222465153 0.084575668 -0.996353754
## [2181,] -0.112867714 -0.002010325 2.7700014197 -0.929719272 -1.288902101
###### #MATRIZ DE ESTRUCTURA / INTERPERETACIÓN DE LOS FACTORES
#para obtener la matriz de estructura e intentar explicar la solución rotada
matriz.correlaciones.rotada<-as.array(cor(datafact,punt.rotadas),dimnames=c(FR1,FR2,FR3,FR4,FR5))
matriz.correlaciones.rotada## [,1] [,2] [,3] [,4] [,5]
## sexo -0.03254353 -0.244293358 -0.023226797 0.25800562 0.51073135
## edad 0.26213895 -0.099652392 -0.140014729 -0.91637692 0.01943613
## grupedad 0.22793327 -0.061627381 -0.204457841 -0.87914370 0.07786720
## naños 0.60143355 -0.240813887 -0.218776881 -0.53833903 0.02451634
## tipovehiculo -0.54820923 0.056623974 -0.035033322 -0.46980063 0.46121301
## antigvehiculo -0.12607308 0.005159270 0.938539293 0.21307244 0.04335903
## nsiniest 0.72530295 0.371729204 -0.007228362 -0.19126749 0.26813101
## costetotal 0.46882024 0.383148098 0.101200823 -0.08434195 0.62837973
## costemedio 0.49629098 0.138921731 0.047899700 -0.08569317 0.66692459
## costemanual 0.17938570 0.801490822 0.034235547 0.06511041 0.35677535
## sinisetropaño 0.29903905 0.905369847 -0.033198467 0.08461576 0.05873865
## edadvehiculo -0.06218808 -0.003954274 0.977676475 0.15003928 0.04603315
## antigcarnet 0.25918868 -0.100931756 -0.123404824 -0.91967496 0.01483628
## kilometros -0.06231548 -0.003582447 0.977526193 0.14695455 0.04382104
## nsinultaño 0.15995761 0.930456208 -0.018871155 0.12366442 0.01966302
## sinisetro 0.83466729 0.250955129 -0.046016744 -0.22858415 0.28891259
## sin 0.82690529 0.132983104 -0.098964494 -0.24270332 0.29183978######### PROCEDIMIENTO << PRINCOMP>>
#la función princomp sólo se puede usar cuanda haya más individuos que variables # en este caso se puede
mod3 <- princomp(datafact, cor=TRUE)
summary(mod3) # desviación típica y % de varianza explicada## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 2.3905539 1.9833699 1.5100852 1.11775194 1.0156967
## Proportion of Variance 0.3361617 0.2313974 0.1341387 0.07349232 0.0606847
## Cumulative Proportion 0.3361617 0.5675591 0.7016977 0.77519005 0.8358747
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## Standard deviation 0.97224706 0.81647677 0.6308554 0.56134261 0.410214419
## Proportion of Variance 0.05560378 0.03921378 0.0234105 0.01853562 0.009898581
## Cumulative Proportion 0.89147853 0.93069231 0.9541028 0.97263843 0.982537013
## Comp.11 Comp.12 Comp.13 Comp.14
## Standard deviation 0.319170947 0.260265829 0.248148940 0.186164189
## Proportion of Variance 0.005992358 0.003984606 0.003622229 0.002038653
## Cumulative Proportion 0.988529371 0.992513977 0.996136207 0.998174860
## Comp.15 Comp.16 Comp.17
## Standard deviation 0.158912495 0.0677098273 3.449030e-02
## Proportion of Variance 0.001485481 0.0002696836 6.997535e-05
## Cumulative Proportion 0.999660341 0.9999300246 1.000000e+00autovalores<- mod3$sdev^2
cat("\nAutovalores (Varianzas de las componentes):\n")##
## Autovalores (Varianzas de las componentes):autovalores### Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## 5.714748117 3.933756104 2.280357168 1.249369410 1.031639831 0.945264345
## Comp.7 Comp.8 Comp.9 Comp.10 Comp.11 Comp.12
## 0.666634318 0.397978531 0.315105528 0.168275870 0.101870093 0.067738302
## Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
## 0.061577897 0.034657105 0.025253181 0.004584621 0.001189581
cat("\nCargas factoriales:\n")####Cargas factoriales:
loadings(mod3) # CARGAS FACTORIALES ,de nuevo de la obtención de COMP Princi NO TIPIFICADAS##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## sexo 0.258 0.527 0.803
## edad -0.286 -0.259 0.228 -0.250 -0.103 0.143 -0.182
## grupedad -0.288 -0.250 0.178 -0.258 0.166 -0.157 0.102 -0.229
## naños -0.291 -0.191 0.158 0.201 -0.147 0.133 -0.272 0.767
## tipovehiculo -0.105 -0.531 0.556 -0.196 0.568 -0.155
## antigvehiculo 0.198 0.281 0.417
## nsiniest -0.325 0.188 0.118 0.361 0.545
## costetotal -0.262 0.265 0.303 -0.253 -0.205 0.491 0.169
## costemedio -0.252 0.182 0.134 0.175 0.378 -0.288 -0.391 -0.360 -0.246
## costemanual -0.172 0.347 -0.168 -0.261 0.119 -0.314 0.405
## sinisetropaño -0.186 0.341 -0.262 -0.244 -0.188 0.205 -0.163
## edadvehiculo 0.172 0.280 0.463 -0.115
## antigcarnet -0.283 -0.257 0.237 -0.254 -0.109 0.149 -0.185
## kilometros 0.171 0.279 0.463 -0.117
## nsinultaño -0.134 0.341 -0.290 -0.315 -0.178 0.222 -0.136
## sinisetro -0.357 0.146 0.224 0.305 -0.164
## sin -0.351 0.278 0.202 -0.405 -0.241
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
## sexo
## edad 0.344 0.166 0.151 0.704
## grupedad -0.186 -0.640 -0.363 -0.254
## naños 0.248 -0.207
## tipovehiculo
## antigvehiculo -0.491 0.534 0.406
## nsiniest 0.302 -0.387 -0.394
## costetotal 0.196 -0.368 0.426 0.161
## costemedio 0.323 0.237 -0.341
## costemanual -0.646 0.150 -0.123
## sinisetropaño 0.201 -0.106 0.135 0.728
## edadvehiculo 0.190 -0.260 -0.198 0.713
## antigcarnet 0.305 0.209 0.133 -0.706
## kilometros 0.197 -0.278 -0.208 -0.701
## nsinultaño 0.384 -0.132 0.174 -0.615
## sinisetro -0.256 0.748 -0.195
## sin -0.274 -0.204 0.372 -0.500
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059
## Cumulative Var 0.059 0.118 0.176 0.235 0.294 0.353 0.412 0.471 0.529
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059
## Cumulative Var 0.588 0.647 0.706 0.765 0.824 0.882 0.941 1.000plot(mod3,type="lines",main = "Gráfico de sedimentación") # grafico de sedimentación
biplot(mod3,main="variables e individuos en el plano Comp1,Comp2") 
print("Puntuaciones factoriales")## [1] "Puntuaciones factoriales"mod3$scores # componentes principales ( sin tipificar)## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## [1,] -0.62907383 -2.533452401 -0.537421737 -1.143558257 0.9179084000
## [2,] 0.04601638 -1.976046231 -1.156396643 -1.005493843 0.0346318517
## [3,] 0.23934364 -1.749945900 -1.113554854 -0.392308794 1.1221466157
## [4,] -0.57516631 -2.466794573 -0.495488093 -1.128036917 0.9124538459
## [5,] 0.10303676 -1.791912101 -1.183693812 -0.367808273 -0.6710189096
## [6,] 0.13830034 -1.829570350 -0.972955118 -0.503638609 1.0672039587
## [7,] 0.18412491 -1.684849521 -1.134207629 0.178102751 0.4002842827
## [8,] 0.08610117 -1.910737524 -1.048097898 -1.023065580 0.0074229457
## [9,] 0.11583654 -1.883454742 -1.071514856 -0.996889987 0.0184460209
## [10,] 0.11629390 -1.770317430 -1.147849847 -0.373655035 -0.6800601974
##
#### [2170,] 3.75282658 2.481670917 1.645250659 0.394330223 0.1008593349
## [2171,] 3.75694549 2.488378221 1.656398500 0.392498587 0.0980320835
## [2172,] 3.76674070 2.504328924 1.682909285 0.388142756 0.0913085701
## [2173,] 3.15794625 1.958736218 2.209398849 -0.162087583 -0.1441191821
## [2174,] 3.76029067 2.406474670 1.912673318 -0.813957767 -0.3325046402
## [2175,] 3.78626953 2.540029687 1.801534108 -0.162696739 -1.0171235313
## [2176,] 3.14639016 1.964956273 2.347789811 -0.738504835 -1.2626507829
## [2177,] 3.96292892 2.802808577 2.109197944 0.341360625 -0.0106427092
## [2178,] 2.03574697 1.196000294 3.485706987 -0.601420665 -0.6943878595
## [2179,] 1.95136566 1.083559553 3.427395142 -1.145983211 -1.7635703631
## [2180,] 3.26682278 2.140003267 2.569444612 -0.752129157 -1.3132415372
## [2181,] 1.95399157 1.087835638 3.434502188 -1.147150928 -1.7653728112
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## [1,] 1.183351091 -3.920211e-01 0.2264937539 7.119782e-02 1.045746e-01
## [2,] -0.824879599 3.407028e-02 -0.0023616968 3.468783e-01 2.326240e-01
## [3,] 0.726858374 1.219847e-01 0.0240849556 4.581453e-01 2.455416e-01
## [4,] 1.174987215 -3.691164e-01 0.2144640862 7.949979e-02 9.745622e-02
## [5,] -0.575311383 -6.585044e-01 0.1768930788 3.013114e-01 2.194642e-01
## [6,] 0.791695912 4.865305e-02 0.0339244344 4.415966e-01 2.728599e-01
## [7,] 1.014595172 -6.309715e-01 0.2233412300 3.904307e-01 2.494878e-01
## [8,] -0.813603719 4.020000e-02 -0.0160224568 3.554353e-01 2.345276e-01
## [9,] -0.828876799 5.939711e-02 -0.0198745768 3.586190e-01 2.262902e-01
## [10,] -0.571515506 -6.564703e-01 0.1724117226 3.041159e-01 2.200763e-01
##
#### [2171,] 0.672900558 1.993982e-01 0.0823801920 -2.554604e-01 -1.729206e-01
## [2172,] 0.675772901 2.009081e-01 0.0791063126 -2.534140e-01 -1.724862e-01
## [2173,] 0.994543303 -1.958048e-01 0.1579858322 -3.591990e-01 -3.459587e-02
## [2174,] -1.150303763 9.007330e-01 -0.1851837130 -2.720250e-01 -1.927472e-01
## [2175,] -0.909407090 2.034177e-01 0.0046831462 -3.242415e-01 -2.073970e-01
## [2176,] -0.575755023 -2.126999e-01 0.0878682244 -4.334938e-01 -6.133031e-02
## [2177,] 0.707305683 2.455572e-01 0.0185180384 -2.146907e-01 -1.728143e-01
## [2178,] 1.493284069 -4.197230e-01 -0.1668151887 5.950050e-01 2.375630e-01
## [2179,] -0.097369310 -4.477410e-01 -0.2120423247 5.051141e-01 2.073358e-01
## [2180,] -0.565436594 -1.796254e-01 0.0531498462 -4.109787e-01 -6.528121e-02
## [2181,] -0.096599289 -4.473362e-01 -0.2129199905 5.056627e-01 2.074522e-01
## Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## [1,] -0.0255724429 -0.222686936 -0.195580850 0.0546541743 7.312167e-03
## [2,] 0.3534395866 0.013969127 -0.062522473 0.0533795648 3.582691e-03
## [3,] 0.3048704689 -0.078585452 -0.113040106 0.0616994054 9.265878e-03
## [4,] -0.0291554844 -0.283531217 -0.238800133 0.0499893693 2.253165e-03
## [5,] 0.3706604636 -0.061528199 -0.112143642 0.0536371664 8.955614e-04
## [6,] 0.4572650723 -0.026343251 -0.073646020 0.0658307116 1.339937e-02
## [7,] 0.3974099325 -0.060532699 -0.089456700 0.0630499456 1.078606e-02
## [8,] 0.3987006074 -0.048952556 -0.109964972 0.0523867746 4.291715e-04
## [9,] 0.3676020925 -0.071320675 -0.124273324 0.0481408367 -2.870225e-03
## [10,] 0.3857645003 -0.082662157 -0.128017788 0.0534181768 -6.100708e-05## [2171,] -0.0244509079 -0.092584305 -0.042228184 -0.0418285246 -1.579709e-02
## [2172,] -0.0131539399 -0.108528677 -0.054143581 -0.0418792011 -1.641608e-02
## [2173,] 0.7019064677 0.282862299 0.244202387 -0.0201602950 1.047382e-02
## [2174,] 0.0268621456 -0.216385865 -0.162149571 -0.0583196501 -3.493708e-02
## [2175,] 0.0091555130 -0.243450865 -0.175198031 -0.0571940134 -3.510376e-02
## [2176,] 0.7537667461 0.172483950 0.139086028 -0.0312150911 -4.823570e-03
## [2177,] 0.1436594518 -0.392095440 -0.265409734 -0.0502763481 -3.283314e-02
## [2178,] 0.1568150733 -0.211662732 -0.191552490 0.0066939142 2.382603e-02
## [2179,] 0.1267108690 -0.208362008 -0.210836531 -0.0023426370 1.442738e-02
## [2180,] 0.8252360182 0.007366228 0.017216843 -0.0375788327 -1.515670e-02
## [2181,] 0.1297393748 -0.212636396 -0.214030826 -0.0023562224 1.426145e-02
## Comp.16 Comp.17
## [1,] -5.597442e-02 5.924052e-02
## [2,] -5.374515e-02 3.049907e-02
## [3,] -4.949598e-02 -6.723239e-03
## [4,] 1.714187e-02 2.348207e-02
## [5,] -5.504606e-02 5.025172e-02
## [6,] -5.238202e-02 3.886634e-02
## [7,] 2.194139e-02 4.227364e-03
## [8,] -5.525144e-02 4.006339e-02
## [9,] 1.798235e-02 3.832606e-02
## [10,] -5.506328e-02 2.921705e-02
##
#### [2171,] -3.657538e-02 2.741726e-02
## [2172,] -3.609935e-02 -1.271471e-02
## [2173,] 2.961558e-02 -4.726068e-02
## [2174,] -4.238112e-02 3.608877e-02
## [2175,] -4.207917e-02 2.647894e-02
## [2176,] -4.963241e-02 -2.370783e-03
## [2177,] 3.075365e-02 3.159899e-02
## [2178,] 7.536653e-02 1.968591e-02
## [2179,] -2.011883e-04 -2.792789e-04
## [2180,] 2.075845e-02 -1.090617e-02
## [2181,] -7.357241e-05 -1.103791e-02
#estas puntuaciones tampoco están tipificadas deberíamos tipificarlas como en el caso anterior
# podemos añadir las 5 primeras COMp.principales a la base de datos
#estas estan sin tipificar
datafact <<- within(datafact, {
pc5 <- mod3$scores[,5]
pc4 <- mod3$scores[,4]
PC3 <- mod3$scores[,3]
PC2 <- mod3$scores[,2]
PC1 <- mod3$scores[,1]
})
#también podríamos añadir las puntuaciones tipificadas
# ( MÁS ARRIBA, LAS HEMOS LLAMADO puntuaciones )
datafact <<- within(datafact, {
F5 <- puntuaciones[,5]
F4 <- puntuaciones[,4]
F3 <- puntuaciones[,3]
F2 <- puntuaciones[,2]
F1 <- puntuaciones[,1]
})
# y las puntuaciones de las componentes rotadas
# ( MÁS ARRIBA, LAS HEMOS LLAMADO punt.rotadas )
datafact <<- within(datafact, {
FR5 <- punt.rotadas[,5]
FR4 <- punt.rotadas[,4]
FR3 <- punt.rotadas[,3]
FR2 <- punt.rotadas[,2]
FR1 <- punt.rotadas[,1]
})Maximum Likelihood Factor Analysis.
procedimiento: << factanal >>
factanal( formula, factors= numero de factores, rotation= método de rotación, scores= método estimación puntuaciones, data= base de datos)
fa <- factanal(~antigcarnet+costemanual+costemedio+costetotal+edad+edadvehiculo+kilometros+naños+nsiniest+nsinultaño+sinisetropaño,
factors=3, rotation="varimax", scores="regression", data=datafact)
fa #vemos los (principales) resultados
unicidades ( las comunalidades pueden obtenerse restando de 1 ) las cargas factorialessólo las más relevantes
suma de cuadrados , % de varianza explicada y % de varianza explicada acumulada ##
## Call:
## factanal(x = ~antigcarnet + costemanual + costemedio + costetotal + edad + edadvehiculo + kilometros + naños + nsiniest + nsinultaño + sinisetropaño, factors = 3, data = datafact, scores = "regression", rotation = "varimax")
##
## Uniquenesses:
## antigcarnet costemanual costemedio costetotal edad
## 0.005 0.418 0.867 0.766 0.005
## edadvehiculo kilometros naños nsiniest nsinultaño
## 0.005 0.005 0.531 0.590 0.076
## sinisetropaño
## 0.005
##
## Loadings:
## Factor1 Factor2 Factor3
## antigcarnet 0.992
## costemanual 0.756
## costemedio 0.301 0.202
## costetotal 0.455 0.145
## edad 0.990 -0.115
## edadvehiculo -0.176 0.983
## kilometros -0.173 0.983
## naños 0.654 -0.203
## nsiniest 0.578 0.273
## nsinultaño 0.942 -0.185
## sinisetropaño 0.988 -0.122
##
## Factor1 Factor2 Factor3
## SS loadings 3.071 2.646 2.014
## Proportion Var 0.279 0.241 0.183
## Cumulative Var 0.279 0.520 0.703
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 6593.26 on 25 degrees of freedom.
## The p-value is 0print(fa, digits=2, cutoff=.3, sort=TRUE) #Alternativa para ver los resultados,##
## Call:
## factanal(x = ~antigcarnet + costemanual + costemedio + costetotal + edad + edadvehiculo + kilometros + naños + nsiniest + nsinultaño + sinisetropaño, factors = 3, data = datafact, scores = "regression", rotation = "varimax")
##
## Uniquenesses:
## antigcarnet costemanual costemedio costetotal edad
## 0.00 0.42 0.87 0.77 0.01
## edadvehiculo kilometros naños nsiniest nsinultaño
## 0.00 0.00 0.53 0.59 0.08
## sinisetropaño
## 0.00
##
## Loadings:
## Factor1 Factor2 Factor3
## costemanual 0.76
## nsiniest 0.58
## nsinultaño 0.94
## sinisetropaño 0.99
## antigcarnet 0.99
## edad 0.99
## naños 0.65
## edadvehiculo 0.98
## kilometros 0.98
## costemedio 0.30
## costetotal 0.45
##
## Factor1 Factor2 Factor3
## SS loadings 3.07 2.65 2.01
## Proportion Var 0.28 0.24 0.18
## Cumulative Var 0.28 0.52 0.70
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 6593.26 on 25 degrees of freedom.
## The p-value is 0## 2 decimales, tres factores,ordenadas las correlaciones
#gráfico de las variables sobre el plano de los dos primeros factores
load <- fa$loadings[,1:2] #cargas de las variables en los dos primeros fractores
plot(load,type="n") # set up plot
text(load,labels=names(datafact),cex=.7) # añadimos nombres de lasvariables
#listamos las puntuaciones factoriales
print("puntuaciones factoriales Max.Veros.")## [1] "puntuaciones factoriales Max.Veros."fa$scores## Factor1 Factor2 Factor3
## 1 -0.2087468101 1.0081370203 -0.7840278702
## 2 -0.2942091745 0.3781910702 -0.8955547372
## 3 -0.3187778595 0.1735203497 -0.8818377618
## 4 -0.2104753981 0.9611922381 -0.7198971564
## 5 -0.2864656377 0.3886654538 -0.7941833655
## 6 -0.2865614419 0.3885388721 -0.7955546433
## 7 -0.2955313206 0.3317947306 -0.8260512731
## 8 -0.2849812144 0.3906765312 -0.7748734338
## 9 -0.2923088674 0.3361461930 -0.7835768505
## 10-0.2833927938 0.3928291049 -0.7542340925
##
##
## 2171 -0.3082738970 -1.1884853741 1.9419044918
## 2172 -0.3059822450 -1.1853740851 1.9714587546
## 2173 -0.1549512883 -0.0827155711 2.1884549520
## 2174 -0.2885238827 -1.1617613773 2.2001068863
## 2175 -0.2879074790 -1.1609245094 2.2080563294
## 2176 -0.1298632469 -0.0041620872 2.4296864607
## 2177 -0.2749960924 -1.1880673081 2.4638771320
## 2178 -0.0177786843 0.7076539717 2.8040430595
## 2179 -0.0094147999 0.7635915505 2.8260951065
## 2180 -0.1162868291 -0.0304019985 2.6940838292
## 2181 -0.0088004509 0.7644256289 2.8340180514Analisis factorial por el método de Ejes Principales
#creamos un nuevo conjunto de datos con las variables a utilizar
datafact2 <- subset(coches, select=c(antigcarnet,costemanual,
costemedio,costetotal,edad,edadvehiculo,kilometros,naños,nsiniest,
nsinultaño,sinisetropaño))
# extraemos 3 factores por el método de ejes princpales
library(psych) # cargamos el paquete necesario para ello
#la función fa de esta librería permite diversos métodos de análisis factorial
#por defecto es el metodo minres, con el argumento fm='pa' aplicaremos ejes principales
# (rotate, por defecto es oblimin, si no queremos ninguna o queremos variamax hay que especificarlo)
ep<-fa(datafact2,nfactors=3,rotate = 'none', fm = 'pa', max.iter = 50)
ep## Factor Analysis using method = pa
## Call: fa(r = datafact2, nfactors = 3, rotate = "none", max.iter = 50,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 h2 u2 com
## antigcarnet 0.38 -0.76 0.34 0.83 0.172 1.9
## costemanual 0.73 0.44 -0.10 0.73 0.267 1.7
## costemedio 0.59 0.02 0.24 0.40 0.600 1.3
## costetotal 0.76 0.15 0.24 0.65 0.352 1.3
## edad 0.38 -0.76 0.33 0.83 0.171 1.9
## edadvehiculo -0.20 0.63 0.73 0.97 0.032 2.1
## kilometros -0.20 0.62 0.73 0.96 0.039 2.1
## naños 0.37 -0.63 0.22 0.59 0.414 1.9
## nsiniest 0.75 -0.03 0.14 0.59 0.410 1.1
## nsinultaño 0.65 0.49 -0.30 0.75 0.247 2.3
## sinisetropaño 0.75 0.44 -0.26 0.82 0.181 1.9
##
## PA1 PA2 PA3
## SS loadings 3.50 2.98 1.63
## Proportion Var 0.32 0.27 0.15
## Cumulative Var 0.32 0.59 0.74
## Proportion Explained 0.43 0.37 0.20
## Cumulative Proportion 0.43 0.80 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 55 and the objective function was 18.01 with Chi Square of 39176.1
## The degrees of freedom for the model are 25 and the objective function was 8.19
##
## The root mean square of the residuals (RMSR) is 0.08
## The df corrected root mean square of the residuals is 0.11
##
## The harmonic number of observations is 2181 with the empirical chi square 1404.48 with prob < 4.2e-281
## The total number of observations was 2181 with Likelihood Chi Square = 17799.61 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0
## RMSEA index = 0.571 and the 90 % confidence intervals are 0.564 0.578
## BIC = 17607.42
## Fit based upon off diagonal values = 0.96
## Measures of factor score adequacy
## PA1 PA2 PA3
## Correlation of (regression) scores with factors 0.97 0.98 0.97
## Multiple R square of scores with factors 0.94 0.95 0.94
## Minimum correlation of possible factor scores 0.87 0.90 0.89