Practica Reduccion 1
Almada Jimenez Ayrton Pablo
6/3/2019
Reduccion
En el presente documento se mostrará y explicará qué hace la función PCA_FA; la cual, a grandes rasgos, realiza el análisis de componentes principales y de factores de un dataframe.
La función
PCA_FA<-function(direccion){
require(DataExplorer)
require(GPArotation)
require(psych)
require(naniar)
require(dplyr)
require(ggplot2)
require(lmtest)
require(corrplot)
require(ggcorrplot)
require(Amelia)
#Primero carga el arhivo y lo guarda en un dataframe, en este caso es la variable df
df<-read.csv(file=direccion, header=TRUE, sep=";")
#Es muy importante considerar el caso donde haya missing values en la base de datos, aquà es donde entra en juego el paquete "Amelia", su función principal, (i.e. amelia), nos permitirá lidiar con el problema de los Nan's.**IMPORTANTE: si hay observaciones cuyos valores sean todos Nan, entonces se procederá aplicando el método datos[complete.cases(datos),]
if(all(is.na(df))){
A<-amelia(df)
Data<-A$imputations$imp1
a<-which_na(A)
Data<-Data[complete.cases(Data),]
}
else{
Data<-df
}
#Mostraremos un reporte con toda la información necesaria de los datos conlos que vamos a trabajar
R<-create_report(df)
#Aplicamos la rutina de componentes principales de R a df, pedimos que scale=TRUE para estandarizar la información (de esa forma evitamos escalas distintas)
y1=prcomp(Data,scale=TRUE)
#Mostramos la desviación estandar, la proporción de varianza y la proporción de varianza acumulada de cada uno de los componentes principales que recientemente fueron obtenidos, dicha información ayuda a decidir cúantos componenetes principales vamos a ocupar, dicha información estáubicada en Importance
SUMM<-summary(y1)
Importance<-SUMM$importance
PC<-y1$rotation
Transformados<-y1$x
#Aquà preparamos los parámetros necesarios para las gráficas de los modelos de pca y de fa
#Nos fijamos que el último de los componenetes principales no tiene proporción acumulada de varianza menor que 1, (se quiere cocupar la menor cantidad de componentes).
if(Importance[3,ncol(Importance)-1]<1){
#Se puede notar que la distribución de las proporciones acumuladas de los componentes principales se asemeja a una exponencial(lambda*x).
#Por lo que esta distribución se puede linealizar si le aplicamos -log(1-x), (los valores están en (0,1))
#Importance[3,-ncol(Importance)]%>%plot()
Y<-Importance[3,-ncol(Importance)]%>%(function(x) -log(1-x))
#Importance[3,-ncol(Importance)]%>%(function(x) -log(1-x))%>%plot()
#Creamos el modelo lineal que mejor se ajusta a Y
modelo<-lm(Y~0+I(1:length(Y)))
#Obtenemos la lambda de la distribución a partir de la pendiente del modelo lineal
lambda<-modelo$coefficients[1]
#De igual manera se calcula para cuál componente por lo menos ya se acumula el 92.5% de la proporción acumulada de varianza, (ara estos fines eso es más que suficiente)
inflexion<- round(-log(0.075/lambda)/lambda)%>% as.numeric()
#Y estos son los conjuntos conlos que podremos plotear la gráfica de la distribución exponencial que más o menos se aproxima a la distribución real de la proporción de varianza de los PC
dominio<-seq(0,ncol(Importance),by=0.01)
imagen<-lambda*exp(-lambda*dominio)
}
#Ahora, preparamos la gráfica de codo de los componentes principales
Codo<-ggplot()+
#Ejes coordenados
aes(x=1:ncol(Importance),y=Importance[2,])+geom_point()+
#Tipo de trazo
geom_line(linetype=1)+
#Nombre de los ejes
ylab(label = "% of Var")+
xlab(label = "PC")+
#Estilo o tema
theme_light()+
#TÃtulo
ggtitle(label = "Screeplot for the PCA")
if(Importance[3,ncol(Importance)-1]<1){
Codo<-Codo+
#Le agregamos más detalles estéticos al plot
geom_line(aes(x=dominio,y=imagen),colour="red")+
#Agregamos también la ubicación del componente que acumule el 92.5%
annotate("pointrange",x=inflexion,y=Importance[2,inflexion],colour="darkblue",ymin = 0,ymax = Importance[2,inflexion])+
annotate("text",x=inflexion+0.1,y=Importance[2,inflexion]+0.05,label=paste0(colnames(Importance)[inflexion]),colour="darkblue")
}
#Seguimos con la composición de los componentes pricipales, o bien, la importancia relativa de cada componenete en términos de la variables originales
p<-plot_prcomp(Data)
Composicion<-p$page_1
#Luego, con la gráfica de colores que representa las correlaciones entre cada una de las variables
Corre<-ggcorrplot(cor(Data),hc.order=TRUE,type="lower")
#Finalmete, se muestra la lista que contiene la información necesaria, es decir: 1)El reporte de la información original; 2)El dataframe que contiene la sd, proporcion de varianza, proporción acumulada de cada componenete; 3)Los pesos de cada componente cra a cada variable; 4)Los datos transformados en términos de los componentes principales; 5)La gráfica de codo; 6)La composición; 7)Las correlaciones.
Output<-list(Report = R,Importance = Importance,Components = PC,
x = Transformados,Screeplot = Codo,CStructure = Composicion,
Correlations = Corre)
return(Output)
}##Ejemplo Ahora, llevaremos a cabo un ejemplo de todo lo que anteriormente mencionamos
a<-PCA_FA("Ejercicio_paises.csv");## Loading required package: DataExplorer## Loading required package: GPArotation## Loading required package: psych## Loading required package: naniar## Loading required package: dplyr##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: corrplot## corrplot 0.84 loaded## Loading required package: ggcorrplot## Loading required package: Amelia## Loading required package: Rcpp## ##
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.5, built: 2018-05-07)
## ## Copyright (C) 2005-2019 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ####
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## processing file: report.rmd##
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## label: plot_by_scatterplot## output file: /cloud/project/report.knit.md## /usr/lib/rstudio-server/bin/pandoc/pandoc +RTS -K512m -RTS /cloud/project/report.utf8.md --to html4 --from markdown+autolink_bare_uris+ascii_identifiers+tex_math_single_backslash+smart --output /cloud/project/report.html --email-obfuscation none --self-contained --standalone --section-divs --table-of-contents --toc-depth 6 --template /home/rstudio-user/R/x86_64-pc-linux-gnu-library/3.5/rmarkdown/rmd/h/default.html --no-highlight --variable highlightjs=1 --variable 'theme:cerulean' --include-in-header /tmp/RtmpBkFLTD/rmarkdown-str6da20409951.html --mathjax --variable 'mathjax-url:https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'##
## Output created: report.html##
##
## Report is generated at "/cloud/project/report.html".
##El dataframe que contiene la sd, proporcion de varianza, proporción acumulada de cada componenete
a$Importance## PC1 PC2 PC3 PC4 PC5
## Standard deviation 2.009546 1.390194 1.184621 1.039342 0.9291441
## Proportion of Variance 0.336520 0.161050 0.116940 0.090020 0.0719400
## Cumulative Proportion 0.336520 0.497580 0.614520 0.704540 0.7764800
## PC6 PC7 PC8 PC9 PC10
## Standard deviation 0.8619797 0.8132745 0.7556971 0.5704844 0.4080445
## Proportion of Variance 0.0619200 0.0551200 0.0475900 0.0271200 0.0138800
## Cumulative Proportion 0.8384000 0.8935200 0.9411100 0.9682300 0.9821000
## PC11 PC12
## Standard deviation 0.3820547 0.2622959
## Proportion of Variance 0.0121600 0.0057300
## Cumulative Proportion 0.9942700 1.0000000##Los pesos de cada componente cra a cada variable
a$Components## PC1 PC2 PC3 PC4 PC5
## PAIS 0.052645215 -0.05445434 -0.29020539 0.792603803 -0.04441202
## X1 0.313387887 -0.34386737 0.10492597 -0.129396768 0.47751452
## X2 0.391545693 0.04429061 0.16916686 0.077164191 0.12442861
## X3 -0.115735882 0.57694652 -0.20197274 0.116178700 -0.08499706
## X4 -0.296459155 0.18140951 0.50249973 0.150132217 0.26870949
## X5 -0.260381982 0.17931209 0.58150424 0.173935577 0.17453355
## X6 -0.445057717 0.02353114 -0.15357365 -0.032193528 -0.04480418
## X7 -0.093139472 -0.31516261 0.37474153 -0.001249501 -0.72974127
## X8 -0.008053745 0.46120102 -0.10843532 -0.365486879 0.02665443
## X9 0.241366294 0.16021138 0.07959544 -0.305680632 -0.26268627
## X10 -0.414150549 -0.23502149 -0.18312716 -0.140959964 0.09238293
## X11 -0.374208928 -0.29224721 -0.17047731 -0.186712651 0.17847928
## PC6 PC7 PC8 PC9 PC10
## PAIS 0.15587442 -0.499094558 -0.0310017303 0.047979054 -0.04509946
## X1 0.01760370 -0.317443743 0.1514888059 -0.081740043 0.50434318
## X2 -0.11672131 -0.007052855 0.6405070602 -0.329951264 -0.27006907
## X3 0.04808067 0.172535393 0.5361564627 0.051856060 0.22135046
## X4 0.12577965 -0.110609175 -0.1550291525 -0.445008830 -0.38402552
## X5 0.07374817 -0.066090232 0.1056264288 0.508367248 0.31216703
## X6 0.05766856 -0.053758203 -0.0043782747 -0.565837701 0.46225857
## X7 -0.23152729 -0.241232141 0.2275761896 -0.052279232 0.07189749
## X8 -0.39937308 -0.672900377 -0.1010751474 0.055747217 -0.08134798
## X9 0.82727556 -0.235035248 -0.0003185064 -0.007144679 -0.02341877
## X10 0.17041770 -0.126357299 0.2661862732 -0.046790122 -0.03858335
## X11 0.09133403 -0.136484567 0.3321212080 0.307792194 -0.38631590
## PC11 PC12
## PAIS -0.02233426 0.02574363
## X1 0.36267489 -0.10566147
## X2 -0.39657922 0.17796903
## X3 0.43682040 -0.17372922
## X4 0.33441465 -0.15007180
## X5 -0.32934271 0.12597572
## X6 -0.18970286 0.44571736
## X7 0.20627128 -0.07073559
## X8 -0.09415541 -0.00888659
## X9 -0.03546701 0.07622700
## X10 -0.36771333 -0.67568467
## X11 0.27515439 0.47097758##Los datos transformados
a$x## PC1 PC2 PC3 PC4 PC5
## [1,] 0.63450064 1.46834756 -0.340351488 -1.495974823 -0.024665313
## [2,] 2.47914718 0.75343638 0.439891223 -0.882805647 0.890488792
## [3,] -0.47971397 -3.59976195 0.930191991 -1.732317811 1.730376158
## [4,] 1.05330385 -1.29321531 0.582838262 -1.089160099 0.544844013
## [5,] -0.57309075 -0.44026945 1.226064774 -0.938343907 -0.610598361
## [6,] -3.52211506 -0.56196228 0.398610346 -1.272781059 0.087218564
## [7,] -2.23635897 0.88094243 -0.515773655 -1.409146684 0.067159223
## [8,] 2.31581295 0.75960751 0.633244682 -1.262123617 -0.496157564
## [9,] -2.94939235 -0.35020168 -0.055200325 -1.030089018 -0.626411230
## [10,] 2.26526119 1.54277535 0.042312441 -1.292871189 0.682752013
## [11,] -1.39161547 0.82458538 -0.972064370 -1.013065668 -0.221672093
## [12,] 1.66575945 0.78899225 0.125917967 -1.401818609 0.259966616
## [13,] -0.35219186 1.95716535 2.178886327 -0.959157659 1.041010311
## [14,] -2.51708389 1.08288554 1.242826748 -0.373824783 -1.927054139
## [15,] 1.74508364 0.73115420 -0.004119231 -1.189965445 0.720506512
## [16,] -5.51356407 0.27273622 2.407445406 -0.732952826 0.256575769
## [17,] 0.52253390 1.01814139 -0.058018480 -1.284473204 0.186552295
## [18,] 1.93715814 1.21984363 -0.158515347 -1.215034355 1.040516376
## [19,] -0.35715119 1.04308983 -0.547772984 -1.770300492 -0.101505871
## [20,] -2.33516807 1.41606406 0.616246718 -1.194568510 0.083355070
## [21,] 2.35473131 0.07885918 0.331330914 -0.985356619 0.950753967
## [22,] 1.03135424 -0.32875895 0.373301006 -1.499923720 -0.945575085
## [23,] 0.22908309 -0.05566990 0.078632953 -0.580397543 -1.297673350
## [24,] -0.13440141 -1.21575364 0.823881123 -0.345118770 -1.649285389
## [25,] -2.12244984 2.30491317 5.432222775 1.414996493 1.507017150
## [26,] -2.85506116 0.26501698 -1.164238426 -0.451229389 -0.186258363
## [27,] 1.47221651 -0.19377167 0.326885007 -1.103979222 -0.585798591
## [28,] 1.30995091 -0.24065089 0.316705867 -1.303023504 -0.340429932
## [29,] 1.05056973 -1.30668848 0.978392877 0.102868105 -0.428283506
## [30,] 1.39272452 -0.11959726 0.100966956 -0.483608033 -0.392278265
## [31,] -2.92995058 -6.24968322 -0.831251886 -2.390539452 2.463017302
## [32,] -1.27877447 1.00218555 -1.197879191 -0.629508599 -0.516512084
## [33,] -2.40019332 1.05468730 0.970189260 -0.384636808 -0.302457616
## [34,] 2.33783782 0.30447014 0.155624404 0.195107295 0.751502551
## [35,] 1.58912103 0.36176006 0.552283396 -0.884016248 -0.858139986
## [36,] -2.93843584 1.59975191 -1.568429279 -1.389776568 -0.330464797
## [37,] -4.97681987 1.92544597 3.958736306 1.171462028 1.414554292
## [38,] 1.56705688 1.38017690 -0.598947862 -1.103622930 0.954969466
## [39,] 1.99372378 1.58942947 -0.388248708 -0.445767704 0.507556838
## [40,] -1.74625906 0.43538441 -0.860838915 -0.655436468 -0.546541529
## [41,] 1.89783574 -0.17893879 0.076539640 -0.839455881 0.400238625
## [42,] 2.55113580 0.84533747 0.066483773 -0.458825003 -0.568962754
## [43,] -2.92888790 -0.29139408 -0.278006766 0.229932927 0.006136431
## [44,] 1.94556751 0.05201258 0.053598158 -0.844464825 0.112772947
## [45,] -1.25938832 0.35806196 -0.783555335 0.380125423 -1.078998418
## [46,] 0.44404817 0.34199116 2.620687177 0.905036740 0.523644742
## [47,] 1.01486979 1.66578073 0.037704182 -0.405470089 0.337806508
## [48,] 1.27686501 -4.23724434 3.437869285 0.316460923 -4.532346210
## [49,] 0.63883341 -2.07605175 1.205229311 0.202163019 -0.338293583
## [50,] -1.85433518 -0.85060204 -1.174428477 0.506988840 -0.101124719
## [51,] -2.71494087 -1.03067902 -1.638879785 0.078303766 -0.566158769
## [52,] -1.20526031 -0.96799621 -0.799808249 0.268629439 0.451527886
## [53,] 1.36317658 -2.49735028 0.019102967 0.395014435 1.623930436
## [54,] 1.73375594 0.18962955 -0.328023272 0.795956067 0.469380944
## [55,] -2.51557192 -1.97064902 -1.278577075 0.052402196 -0.486619758
## [56,] 0.94989498 -1.05738585 -0.235775156 0.346686917 0.199883775
## [57,] 0.62680781 -3.02384924 0.305639558 0.560680359 0.762495667
## [58,] 0.26506075 0.39512152 -0.245746646 -0.730034092 -0.586126151
## [59,] 0.97836287 -0.34888198 -0.204498032 0.976571536 0.259868164
## [60,] 0.02448431 -0.36407840 1.186973420 0.362346418 -0.230001498
## [61,] 2.19356950 1.19329202 -0.381343782 0.858970085 0.240206111
## [62,] 1.91594156 1.39312496 -0.404451211 0.260643304 0.090040257
## [63,] 2.22117325 0.76049606 -0.273161404 0.367957656 0.362684484
## [64,] 1.87280082 0.49904638 -0.309665926 -0.307993704 0.044636143
## [65,] 2.07463885 -0.08894215 -0.126662437 0.734954966 0.760538935
## [66,] -3.51433847 -0.03972563 -1.494532119 0.497142626 0.101603576
## [67,] -1.99768545 0.02739976 -1.408300830 0.343778016 -0.537028792
## [68,] 0.94348224 -2.82711846 -0.040130963 0.013844714 1.002231436
## [69,] 2.39486979 -1.79315625 1.930707232 0.443986596 -2.108090649
## [70,] 0.91262325 0.18307729 -0.366379233 -0.016978244 -0.959899635
## [71,] 1.93299086 0.01545290 -0.141229091 0.001082414 0.107078584
## [72,] 1.28777744 0.26449948 -0.317364890 0.250441084 0.192948186
## [73,] -1.32178761 0.71802427 -0.785747936 0.934457405 -0.168931432
## [74,] -1.50229803 0.67740414 -1.048498098 0.945211383 -1.166129073
## [75,] -4.34376582 0.96933475 1.795633588 2.231804714 1.542151895
## [76,] -2.01340602 0.52547486 -1.776574148 0.527032743 -0.298957952
## [77,] -0.72647845 0.34202520 -0.556746535 1.095644902 -1.664718500
## [78,] 1.83375211 0.69877393 -0.615656673 0.736212253 0.330343961
## [79,] -2.67144526 -1.51733128 -2.069261327 -0.226410695 0.482480002
## [80,] 0.30377747 -2.23273291 -0.479093212 2.106425706 1.268681686
## [81,] 1.06204924 0.24316171 -0.518174879 0.847401296 -0.887060755
## [82,] 2.10658505 -0.69349392 0.136272063 1.070792170 -0.373149422
## [83,] -3.21155946 1.61966892 -1.522066683 0.311524599 -0.088808099
## [84,] -2.49041475 0.36680096 -1.190049727 1.149875760 0.265746905
## [85,] -0.25043725 -0.84200479 0.152537311 1.801478165 0.877491601
## [86,] 0.83977341 1.18020243 -0.054022087 0.814842556 -1.127740793
## [87,] 2.24317690 1.23376823 -0.789324802 1.023021708 0.536368433
## [88,] 0.76029701 -1.25764618 -0.538657008 2.040439315 0.376387165
## [89,] 0.23137452 -0.09290639 -0.034761587 1.459555648 -0.028775550
## [90,] -1.94506728 0.30663367 -0.693391297 1.675781107 -0.576025331
## [91,] -0.06686614 0.02654301 -1.158907016 2.046217457 -0.488483246
## [92,] 0.24324471 0.03785076 -0.693730043 0.408262288 0.191463503
## [93,] 1.44217742 0.97701165 -0.759538614 1.349387063 -0.489923701
## [94,] 2.67068250 -1.42050453 0.031044133 1.671621370 1.057698320
## [95,] 2.41193510 1.13919327 -0.613308080 1.238061430 0.333039617
## [96,] 1.58740327 0.34860449 -0.889970951 1.486764094 0.387917648
## PC6 PC7 PC8 PC9 PC10
## [1,] -1.227590233 0.861222576 -0.66263185 0.460315341 -0.295565095
## [2,] -0.418582327 1.479599746 1.83807959 -0.734480546 0.004978460
## [3,] 0.260252676 0.330213157 -0.49577924 0.429092909 -0.105123243
## [4,] 0.292116647 1.510587181 -0.98650073 0.054504340 -0.056937658
## [5,] -0.567864047 0.810379952 -0.73039560 -0.334742978 -0.294182421
## [6,] 0.295930735 0.470877802 0.90345218 -0.234613552 0.200523840
## [7,] -0.711910781 0.466270394 -0.46957749 -0.547014863 0.110914748
## [8,] 2.032574156 1.328892595 0.66562561 -0.308995996 -0.127658160
## [9,] -0.148475692 0.917184793 0.24134950 -0.522204211 -0.151240636
## [10,] -0.409773458 0.432957422 1.19706696 -0.357196900 0.196587330
## [11,] -0.575839361 1.306409338 0.39514050 0.682953115 -0.318036341
## [12,] -0.451096089 0.254687500 0.08637092 -0.159119764 -0.128719988
## [13,] -0.672029943 -0.688883754 -0.83927764 -0.078946127 -0.655063556
## [14,] -0.835938047 0.744869868 0.79341539 1.330697902 0.799944543
## [15,] -0.697871962 0.319878831 -0.18525734 0.003384177 0.224839276
## [16,] -0.638317851 -1.186896864 1.49523148 0.481549492 0.877279160
## [17,] -0.599197284 0.061334783 -0.81702984 0.227359849 0.071120603
## [18,] -1.253848119 -0.133388987 0.86027173 -0.210293052 -0.002105563
## [19,] -1.467009602 -0.878505998 0.45679883 1.086903391 -0.486276552
## [20,] -0.724638223 -0.842737961 -0.53399002 -0.469527767 -0.076865459
## [21,] -0.353387681 0.224997703 0.24117403 -0.386054576 0.062526793
## [22,] 1.041376507 -0.140154803 -1.09817423 -0.094158082 0.626305815
## [23,] 0.074171618 1.100624085 -0.64744707 0.553188778 -0.099591998
## [24,] -0.780692884 0.728553666 -0.56658233 0.028209446 0.314878086
## [25,] 0.970820865 0.627315084 0.33467856 2.313215354 0.877902507
## [26,] 0.497962684 1.336729145 0.22663931 -0.733394636 0.344174622
## [27,] 1.126329717 0.261199261 -0.86185559 -0.028560967 -0.040204803
## [28,] -0.002107572 -0.484499798 -1.03047482 0.067357611 -0.115511503
## [29,] -0.418796527 1.153102127 -0.09675804 -0.125501119 0.039266775
## [30,] 1.182867541 1.109992119 -0.64344361 0.033097380 0.045455358
## [31,] 1.102716060 -1.534446370 1.74917815 0.862122781 -0.657527265
## [32,] -0.295053011 0.625328923 0.15469544 0.498560577 -0.196591228
## [33,] -0.506692126 -0.500694117 -0.99230043 -0.610157298 -0.546767025
## [34,] -0.364767679 1.201363545 1.20296654 -0.585334904 -0.184349493
## [35,] 1.358561444 -0.131743194 -0.29560691 0.069652077 0.111323877
## [36,] -0.726380284 -1.151671769 0.25289798 -0.338087040 0.355575160
## [37,] 0.941914846 -0.312784865 -0.57409203 -1.767697904 -0.642200501
## [38,] -1.063868419 -1.070057976 1.08843670 0.041812528 -0.381712786
## [39,] -0.020605035 0.045029466 0.94493440 -0.052411904 0.416839042
## [40,] -0.557494592 -0.237934092 -0.74122314 -0.402351169 0.173489281
## [41,] 0.246186307 -0.488692571 -1.08762010 0.016274323 0.007051703
## [42,] 3.030005078 0.844892191 0.49051488 -0.177493726 -0.076182997
## [43,] 0.448402534 0.707402643 -0.10783062 -0.904069732 -0.030038997
## [44,] 0.419664948 -0.686297563 -0.75691819 0.031353595 0.161734398
## [45,] -0.426269677 1.176893961 -0.13749252 0.449155922 -0.405886173
## [46,] 0.102709818 0.195390085 0.04043355 0.675196671 0.017576951
## [47,] -0.374743410 -0.708963449 -0.40710337 0.071134953 -0.516443345
## [48,] -1.980380629 -1.272281237 1.90941479 -0.958665148 -0.271271446
## [49,] -0.487753439 -0.269506288 -0.17632698 -0.079466698 0.209484099
## [50,] -0.294437895 1.309724589 -0.72494345 -0.020386928 -0.338601299
## [51,] 0.821590035 0.798025190 0.68016684 -0.771405059 0.967322992
## [52,] 0.268005460 0.515065416 0.02575599 -0.378585470 1.034047617
## [53,] -0.498115653 0.370227316 -0.97935254 -0.058124039 0.844112791
## [54,] 0.376681018 1.167117296 0.53351736 -0.033595052 0.538756481
## [55,] 0.831872155 0.764093373 -0.00460736 0.375427550 -1.181225700
## [56,] 0.317681222 0.516621367 -0.84676044 0.100495061 0.010783669
## [57,] -0.900089427 0.155134356 0.25791907 -0.026626030 -0.197130718
## [58,] 0.409504746 -1.543039550 -0.58652433 0.212431664 0.414366761
## [59,] -1.322091940 0.633692679 -0.19670500 -0.034982462 -0.093805844
## [60,] 0.496156662 -0.678351585 -0.47383471 0.067312818 -0.230906919
## [61,] -0.065811090 0.669789954 1.48344436 -0.430554775 -0.422229809
## [62,] -0.107384261 -0.304656455 0.46547093 -0.153460351 -0.442611954
## [63,] -0.221989834 -0.277800508 0.59805415 -0.269639729 -0.211936120
## [64,] 0.173163291 -1.235566873 -0.38473533 0.119813615 0.275961549
## [65,] 0.117276804 0.230364341 0.30046172 -0.195886193 -0.057147453
## [66,] -0.432276403 -0.140713543 0.67152317 0.033852742 0.161580765
## [67,] 0.132179425 -0.180372051 0.16191819 -0.320176573 0.578046250
## [68,] -0.160305923 -1.044422790 -1.28080575 0.180244874 0.466571677
## [69,] 1.303296728 -0.931840132 0.77167324 -0.552156666 -0.001120608
## [70,] 0.340185931 -1.039104844 -0.82175993 0.166774720 0.124105238
## [71,] 1.226613211 -0.861268110 -0.95794788 0.231569068 0.080638972
## [72,] -0.734859593 -1.125985966 -0.95819283 0.069204680 -0.356831741
## [73,] 0.060747571 0.117440926 0.14791554 1.030969889 -0.425612948
## [74,] -0.581036703 0.000158564 -0.50923095 -0.113716657 -0.018508574
## [75,] 0.755354375 0.100898624 -0.49212062 -1.174020578 -0.912032739
## [76,] 0.193956228 -0.154519018 0.41176034 0.960384297 -0.739646433
## [77,] -0.415152241 -0.008400968 0.16590968 0.585315112 -0.444268822
## [78,] -0.249771009 -0.628120945 0.19955931 0.046254203 0.173293489
## [79,] 2.700024563 -0.688753138 0.79495047 0.023084640 -0.159376314
## [80,] -2.528714828 0.747897955 -0.77760022 0.182449437 0.308061711
## [81,] 0.426694090 -0.273732055 -1.16086698 0.505621512 -0.152684216
## [82,] 0.115418119 -0.359687455 -0.18217910 -0.244284523 -0.421327348
## [83,] -0.146758104 -1.768968254 0.06209458 -0.659632383 0.824782888
## [84,] 0.085798610 -0.401695846 -0.61158381 -1.040430033 0.410618163
## [85,] -0.008456980 0.171502444 0.57854372 0.670203214 -0.019473494
## [86,] 1.948862221 -0.692612470 0.07049132 0.265021507 -0.181060874
## [87,] 0.150252958 -0.704909103 0.96855188 -0.102678295 0.275572368
## [88,] -1.073152098 0.614203548 -0.70949371 0.095652877 -0.017594073
## [89,] -0.216804286 -0.609326457 -0.23409752 -0.353767062 0.046213549
## [90,] 0.273693319 0.097766318 0.83551209 1.447930292 -0.413687124
## [91,] -0.048657842 0.937483262 -0.75764510 0.084324605 0.083077477
## [92,] 0.244986837 -1.893821603 -0.58878585 0.589822168 -0.076993358
## [93,] 0.617142258 -0.402302326 0.26239470 0.317454490 0.337701036
## [94,] -0.200346042 -0.443780814 0.55860585 -0.564079781 0.209204189
## [95,] -0.135096837 -1.032636569 1.25580421 -0.338360607 -0.260043455
## [96,] 0.288582952 -0.404856376 0.35069742 0.208382359 0.223320115
## PC11 PC12
## [1,] 0.033398278 -0.2633198970
## [2,] -0.144605691 0.0429970946
## [3,] -0.061210212 -0.0819468382
## [4,] -0.179018637 0.0742436434
## [5,] 0.251229586 -0.1632662036
## [6,] 0.546752631 0.2691201270
## [7,] -0.086332551 0.1779942451
## [8,] -0.048973082 0.1052047433
## [9,] -0.039118512 -0.1322678776
## [10,] 0.147210150 -0.1404102820
## [11,] 0.555015527 0.0903010757
## [12,] -0.261107520 0.0106172516
## [13,] -0.169646514 -0.1980116765
## [14,] -0.581896706 0.3994119676
## [15,] 0.120561864 -0.2060137995
## [16,] -0.392227234 -0.3650943774
## [17,] 0.025550907 -0.0688660941
## [18,] -0.027885153 -0.0886158394
## [19,] 0.911935434 0.2698991681
## [20,] 0.030528081 0.0718722375
## [21,] -0.296675802 0.0809992178
## [22,] 0.227303708 0.1247725528
## [23,] 0.471486097 -0.3144940038
## [24,] 0.590253579 -0.2122736425
## [25,] -0.607529978 0.1042679724
## [26,] 0.014911937 0.6270672081
## [27,] -0.228496139 0.2538679416
## [28,] -0.297040669 0.1201487585
## [29,] -0.109879821 0.0013212658
## [30,] -0.022629149 0.0336268641
## [31,] 0.536102721 0.2361980906
## [32,] 0.150872808 -0.3329714280
## [33,] 0.001130534 0.1291244270
## [34,] -0.356579884 0.0944658525
## [35,] 0.348080010 -0.1154517524
## [36,] -0.578825791 -0.3735258076
## [37,] 0.790081688 -0.3899520465
## [38,] 0.034588020 0.2379233721
## [39,] 0.545849004 -0.3016861628
## [40,] -0.368293542 0.7764383449
## [41,] -0.332789245 0.0995127918
## [42,] -0.041521219 0.1873414104
## [43,] 0.087128848 0.0786423940
## [44,] -0.099181931 0.0358289667
## [45,] 0.110204707 -0.1660916697
## [46,] -0.777310080 0.2236589811
## [47,] -0.028111496 -0.1796213255
## [48,] 0.150925489 -0.0119280020
## [49,] 0.133724133 -0.0749048560
## [50,] -0.430936361 0.4339666373
## [51,] -0.540650674 -1.0254140449
## [52,] 0.691009604 0.3003517474
## [53,] 0.284685884 -0.0918088354
## [54,] 0.668485674 -0.2939968079
## [55,] -1.448896669 -1.0813537713
## [56,] -0.114052318 0.0973910036
## [57,] -0.099778586 0.0590052534
## [58,] 0.424208895 -0.1668612859
## [59,] -0.026007570 -0.0891110558
## [60,] 0.115493729 -0.1121798667
## [61,] -0.338532144 0.0773177347
## [62,] -0.275395387 0.0009100605
## [63,] -0.299464283 0.0533298590
## [64,] 0.181771507 -0.1396669010
## [65,] -0.164261457 0.0739470024
## [66,] -0.057043257 0.3952856067
## [67,] -0.049213945 0.0182941110
## [68,] 0.008640030 -0.1987349360
## [69,] -0.140601264 0.2312255213
## [70,] 0.108743856 0.0442865221
## [71,] -0.341857109 0.1489762830
## [72,] -0.443793144 0.0667329242
## [73,] 0.221330400 0.0781885156
## [74,] 0.052981736 0.2637707388
## [75,] 0.707680153 0.0689844709
## [76,] 0.155978462 0.1820535338
## [77,] 0.210691625 -0.0663161559
## [78,] 0.250317571 -0.1633131819
## [79,] -0.251058582 -0.0234850908
## [80,] 0.224941968 -0.2156523507
## [81,] 0.171267855 -0.1496767444
## [82,] -0.568606093 0.1956997194
## [83,] -0.737389425 -0.0981765311
## [84,] -0.266988068 0.3947392963
## [85,] -0.057855450 0.1363807394
## [86,] 0.459808645 -0.1268157794
## [87,] 0.362969697 -0.1819447033
## [88,] -0.040820906 -0.0728483600
## [89,] -0.149290281 0.2547674906
## [90,] 0.255368881 0.1333002026
## [91,] 0.049464138 0.1385197933
## [92,] -0.101637475 -0.0495181169
## [93,] 0.771059873 -0.3341883353
## [94,] -0.265727385 0.1583280235
## [95,] -0.318098508 0.0711713706
## [96,] 0.473116975 -0.1720156905##La gráfica de codo
a$Screeplot
##La composición
a$CStructure
a$Correlations