ESTIMACIÓN DE LA MATRIZ DE CORRELACIÓN CON BOOTSTRAP Y JACKKNIFE (MATRIZ - MATRIZ)
Curso: EstadÃstica Computacional
Integrantes:
- Nestor Abel Lopez Lazaro 20180264
- Alvaro Cesar Tauma Salvador 20181160
1 Aplicación multivariada de Bootstrap
El archivo hatco.txt contiene datos que corresponden a 100 observaciones de 7 variables influyentes en la elección de distribuidor de una empresa .
se registran los siguientes atributos:
X1: Velocidad de entrega
X2: Nivel de precios
X3: Flexibilidad de precios
X4: Imagen del fabricante
X5: Servicio conjunto
X6: Imagen fuerza de ventas
X7: Calidad de producto
datos <- read.table(file = "hatco.txt", header = TRUE)
head(datos)## id x1 x2 x3 x4 x5 x6 x7
## 1 1 4.1 0.6 6.9 4.7 2.35 5.2 2.4
## 2 2 1.8 3.0 6.3 6.6 4.00 8.4 2.5
## 3 3 3.4 5.2 5.7 6.0 2.70 8.2 4.3
## 4 4 2.7 1.0 7.1 5.9 2.30 7.8 1.8
## 5 5 6.0 0.9 9.6 7.8 4.60 4.5 3.4
## 6 6 1.9 3.3 7.9 4.8 1.90 9.7 2.61.1 Función para hallar la matriz de correlaciones
corMatrix <- function(data) {
cor <- cor(data[,2:8])
return(cor)
}
corMatrix(datos)## x1 x2 x3 x4 x5 x6
## x1 1.00000000 -0.3492251 0.50929519 0.0504142 0.07742782 -0.4826309
## x2 -0.34922515 1.0000000 -0.48721259 0.2721868 0.18533024 0.4697458
## x3 0.50929519 -0.4872126 1.00000000 -0.1161041 -0.03479587 -0.4481120
## x4 0.05041420 0.2721868 -0.11610408 1.0000000 0.78813516 0.1999811
## x5 0.07742782 0.1853302 -0.03479587 0.7881352 1.00000000 0.1766130
## x6 -0.48263094 0.4697458 -0.44811201 0.1999811 0.17661305 1.0000000
## x7 0.61190069 0.5129808 0.06661728 0.2986774 0.24042771 -0.0551613
## x7
## x1 0.61190069
## x2 0.51298082
## x3 0.06661728
## x4 0.29867737
## x5 0.24042771
## x6 -0.05516130
## x7 1.00000000library(psych)
cor.plot(cor(datos[,-1]),
main="Mapa de Calor",
diag=F,
show.legend = TRUE) 
1.2 Función para estimar la matriz de correlaciones mediante Bootstrap
boot4<-function(datos,B,medida,...){ # Caso matriz -> matriz
n<-nrow(datos) # nro. de filas
p<-ncol(datos)-1 # nro. de columnas
esta<-array(data = rep(0,p*p*B),dim = c(p,p,B)) # crea B matrices de pxp
esboot<-matrix(0,p,p)
eeboot<-matrix(0,p,p)
cvboot <- matrix(0,p,p)
for(i in 1:B){
indices<- sample(n,n,T)
esta[,,i]<-medida(datos[indices,],...) # guardando la m. correlacion de la muestra "i"
}
for (i in 1:p) {
for (j in 1:p) {
esboot[i,j] <- mean(esta[i,j,]) # media de las "B" capas de matrices de correlacion
eeboot[i,j] <- sd(esta[i,j,]) # sd de las "B" capas de matrices de correlacion
cvboot[i,j] <- eeboot[i,j]*100/abs(esboot[i,j])
}
}
estimado<-medida(datos,...)
return(list(estimado=estimado,esboot=esboot,eeboot=eeboot,cvboot=cvboot))
}1.3 Bootstrap multivariado
RNGkind(sample.kind = "Rejection")
set.seed(11)
B <- boot4(datos,1000, corMatrix)
B## $estimado
## x1 x2 x3 x4 x5 x6
## x1 1.00000000 -0.3492251 0.50929519 0.0504142 0.07742782 -0.4826309
## x2 -0.34922515 1.0000000 -0.48721259 0.2721868 0.18533024 0.4697458
## x3 0.50929519 -0.4872126 1.00000000 -0.1161041 -0.03479587 -0.4481120
## x4 0.05041420 0.2721868 -0.11610408 1.0000000 0.78813516 0.1999811
## x5 0.07742782 0.1853302 -0.03479587 0.7881352 1.00000000 0.1766130
## x6 -0.48263094 0.4697458 -0.44811201 0.1999811 0.17661305 1.0000000
## x7 0.61190069 0.5129808 0.06661728 0.2986774 0.24042771 -0.0551613
## x7
## x1 0.61190069
## x2 0.51298082
## x3 0.06661728
## x4 0.29867737
## x5 0.24042771
## x6 -0.05516130
## x7 1.00000000
##
## $esboot
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.00000000 -0.3523156 0.51107898 0.04886231 0.07277115 -0.48296715
## [2,] -0.35231558 1.0000000 -0.48929555 0.27336517 0.18565602 0.46795581
## [3,] 0.51107898 -0.4892956 1.00000000 -0.11455090 -0.03487882 -0.44707589
## [4,] 0.04886231 0.2733652 -0.11455090 1.00000000 0.78391678 0.20101349
## [5,] 0.07277115 0.1856560 -0.03487882 0.78391678 1.00000000 0.17955747
## [6,] -0.48296715 0.4679558 -0.44707589 0.20101349 0.17955747 1.00000000
## [7,] 0.61114938 0.5066393 0.06880257 0.29791534 0.23654202 -0.05914982
## [,7]
## [1,] 0.61114938
## [2,] 0.50663935
## [3,] 0.06880257
## [4,] 0.29791534
## [5,] 0.23654202
## [6,] -0.05914982
## [7,] 1.00000000
##
## $eeboot
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00000000 0.07710370 0.05560500 0.09918620 0.10741643 0.07206883
## [2,] 0.07710370 0.00000000 0.07279446 0.09662679 0.09316906 0.06523080
## [3,] 0.05560500 0.07279446 0.00000000 0.10025403 0.10474332 0.06983001
## [4,] 0.09918620 0.09662679 0.10025403 0.00000000 0.03772650 0.10201428
## [5,] 0.10741643 0.09316906 0.10474332 0.03772650 0.00000000 0.10158881
## [6,] 0.07206883 0.06523080 0.06983001 0.10201428 0.10158881 0.00000000
## [7,] 0.06047968 0.07004007 0.10018446 0.09517001 0.08885541 0.10913816
## [,7]
## [1,] 0.06047968
## [2,] 0.07004007
## [3,] 0.10018446
## [4,] 0.09517001
## [5,] 0.08885541
## [6,] 0.10913816
## [7,] 0.00000000
##
## $cvboot
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.000000 21.88484 10.87992 202.991230 147.608532 14.92210 9.896055
## [2,] 21.884840 0.00000 14.87740 35.347147 50.183699 13.93952 13.824444
## [3,] 10.879923 14.87740 0.00000 87.519200 300.306417 15.61928 145.611520
## [4,] 202.991230 35.34715 87.51920 0.000000 4.812565 50.74997 31.945321
## [5,] 147.608532 50.18370 300.30642 4.812565 0.000000 56.57732 37.564324
## [6,] 14.922098 13.93952 15.61928 50.749967 56.577321 0.00000 184.511388
## [7,] 9.896055 13.82444 145.61152 31.945321 37.564324 184.51139 0.0000001.4 Matriz estimada vs Matriz Bootstrap
library(psych)
library(grid)
library(gridExtra)
estimado <- cor.plot(cor(datos[,-1]),
main="Matriz de correlaciones Estimado ",
diag=F,
show.legend = TRUE) 
bootstr <- cor.plot(r = B$esboot,
main="Matriz de correlaciones Bootstrap",
diag=F,
show.legend = TRUE) 
2 Función para estimar la matriz de correlaciones mediante Jackknife
jack4<-function(datos,medida,...){
n<-nrow(datos)
p<-ncol(datos)-1
esta<-array(data = rep(0,p*p*n),dim = c(p,p,n))#crea n matrices de px p
esjack<-matrix(0,p,p)
eejack<-matrix(0,p,p)
cvjack<-matrix(0,p,p)
for(i in 1:n){
esta[,,i]<-medida(datos[-i,],...) # se extrae muestras jackknife quitando un valor de la muestra
# aplicando a estas muestras la medida creada (matriz de correlacion)
# asignando estad superponiendo las n matrices de ceros con las n medidas (matrices de correlacion)
}
for (i in 1:p) {
for (j in 1:p) {
esjack[i,j] <- mean(esta[i,j,])# esta[i,j,] :# vector correlaciones de i con j de sacadas de todas las n matrices de correlaciones muestrajack # Se le agrega el valor mean(esta[i,j,]) a la posicion i,j de la matriz estimada jack
eejack[i,j] <- (n-1)*sd(esta[i,j,])/sqrt(n) # de la misma forma con el error
cvjack[i,j] <- eejack[i,j]*100/abs(esjack[i,j])
}
}
estimado<-medida(datos,...)
return(list(estimado=estimado,esjack=esjack,eejack=eejack,cvjack=cvjack))
}
jack4(datos,corMatrix)## $estimado
## x1 x2 x3 x4 x5 x6
## x1 1.00000000 -0.3492251 0.50929519 0.0504142 0.07742782 -0.4826309
## x2 -0.34922515 1.0000000 -0.48721259 0.2721868 0.18533024 0.4697458
## x3 0.50929519 -0.4872126 1.00000000 -0.1161041 -0.03479587 -0.4481120
## x4 0.05041420 0.2721868 -0.11610408 1.0000000 0.78813516 0.1999811
## x5 0.07742782 0.1853302 -0.03479587 0.7881352 1.00000000 0.1766130
## x6 -0.48263094 0.4697458 -0.44811201 0.1999811 0.17661305 1.0000000
## x7 0.61190069 0.5129808 0.06661728 0.2986774 0.24042771 -0.0551613
## x7
## x1 0.61190069
## x2 0.51298082
## x3 0.06661728
## x4 0.29867737
## x5 0.24042771
## x6 -0.05516130
## x7 1.00000000
##
## $esjack
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.00000000 -0.3492358 0.50929395 0.05041027 0.07740073 -0.48261561
## [2,] -0.34923584 1.0000000 -0.48719710 0.27216711 0.18533909 0.46974602
## [3,] 0.50929395 -0.4871971 1.00000000 -0.11608848 -0.03480093 -0.44810840
## [4,] 0.05041027 0.2721671 -0.11608848 1.00000000 0.78811407 0.20000242
## [5,] 0.07740073 0.1853391 -0.03480093 0.78811407 1.00000000 0.17664774
## [6,] -0.48261561 0.4697460 -0.44810840 0.20000242 0.17664774 1.00000000
## [7,] 0.61187793 0.5129521 0.06663315 0.29865280 0.24040993 -0.05515645
## [,7]
## [1,] 0.61187793
## [2,] 0.51295209
## [3,] 0.06663315
## [4,] 0.29865280
## [5,] 0.24040993
## [6,] -0.05515645
## [7,] 1.00000000
##
## $eejack
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00000000 0.07836248 0.05530565 0.10109332 0.10996978 0.07320655
## [2,] 0.07836248 0.00000000 0.07222304 0.10035536 0.09586711 0.06366594
## [3,] 0.05530565 0.07222304 0.00000000 0.10530581 0.10942184 0.07274459
## [4,] 0.10109332 0.10035536 0.10530581 0.00000000 0.03728309 0.10213815
## [5,] 0.10996978 0.09586711 0.10942184 0.03728309 0.00000000 0.10220987
## [6,] 0.07320655 0.06366594 0.07274459 0.10213815 0.10220987 0.00000000
## [7,] 0.06137925 0.07067541 0.10140261 0.09807979 0.09083831 0.11083325
## [,7]
## [1,] 0.06137925
## [2,] 0.07067541
## [3,] 0.10140261
## [4,] 0.09807979
## [5,] 0.09083831
## [6,] 0.11083325
## [7,] 0.00000000
##
## $cvjack
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.00000 22.43827 10.85928 200.541132 142.078481 15.16871 10.03129
## [2,] 22.43827 0.00000 14.82419 36.872701 51.725255 13.55327 13.77817
## [3,] 10.85928 14.82419 0.00000 90.711680 314.422209 16.23370 152.18042
## [4,] 200.54113 36.87270 90.71168 0.000000 4.730672 51.06846 32.84074
## [5,] 142.07848 51.72526 314.42221 4.730672 0.000000 57.86084 37.78476
## [6,] 15.16871 13.55327 16.23370 51.068459 57.860843 0.00000 200.94339
## [7,] 10.03129 13.77817 152.18042 32.840741 37.784757 200.94339 0.000002.1 RESULTADOS ESTIMADO , BOOTSTRAP y JACKKNIFE
RNGkind(sample.kind = "Rejection")
set.seed(11)
B <- boot4(datos,1000, corMatrix)
B$estimado## x1 x2 x3 x4 x5 x6
## x1 1.00000000 -0.3492251 0.50929519 0.0504142 0.07742782 -0.4826309
## x2 -0.34922515 1.0000000 -0.48721259 0.2721868 0.18533024 0.4697458
## x3 0.50929519 -0.4872126 1.00000000 -0.1161041 -0.03479587 -0.4481120
## x4 0.05041420 0.2721868 -0.11610408 1.0000000 0.78813516 0.1999811
## x5 0.07742782 0.1853302 -0.03479587 0.7881352 1.00000000 0.1766130
## x6 -0.48263094 0.4697458 -0.44811201 0.1999811 0.17661305 1.0000000
## x7 0.61190069 0.5129808 0.06661728 0.2986774 0.24042771 -0.0551613
## x7
## x1 0.61190069
## x2 0.51298082
## x3 0.06661728
## x4 0.29867737
## x5 0.24042771
## x6 -0.05516130
## x7 1.00000000B$esboot## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.00000000 -0.3523156 0.51107898 0.04886231 0.07277115 -0.48296715
## [2,] -0.35231558 1.0000000 -0.48929555 0.27336517 0.18565602 0.46795581
## [3,] 0.51107898 -0.4892956 1.00000000 -0.11455090 -0.03487882 -0.44707589
## [4,] 0.04886231 0.2733652 -0.11455090 1.00000000 0.78391678 0.20101349
## [5,] 0.07277115 0.1856560 -0.03487882 0.78391678 1.00000000 0.17955747
## [6,] -0.48296715 0.4679558 -0.44707589 0.20101349 0.17955747 1.00000000
## [7,] 0.61114938 0.5066393 0.06880257 0.29791534 0.23654202 -0.05914982
## [,7]
## [1,] 0.61114938
## [2,] 0.50663935
## [3,] 0.06880257
## [4,] 0.29791534
## [5,] 0.23654202
## [6,] -0.05914982
## [7,] 1.00000000J <- jack4(datos,corMatrix)
J$esjack## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.00000000 -0.3492358 0.50929395 0.05041027 0.07740073 -0.48261561
## [2,] -0.34923584 1.0000000 -0.48719710 0.27216711 0.18533909 0.46974602
## [3,] 0.50929395 -0.4871971 1.00000000 -0.11608848 -0.03480093 -0.44810840
## [4,] 0.05041027 0.2721671 -0.11608848 1.00000000 0.78811407 0.20000242
## [5,] 0.07740073 0.1853391 -0.03480093 0.78811407 1.00000000 0.17664774
## [6,] -0.48261561 0.4697460 -0.44810840 0.20000242 0.17664774 1.00000000
## [7,] 0.61187793 0.5129521 0.06663315 0.29865280 0.24040993 -0.05515645
## [,7]
## [1,] 0.61187793
## [2,] 0.51295209
## [3,] 0.06663315
## [4,] 0.29865280
## [5,] 0.24040993
## [6,] -0.05515645
## [7,] 1.00000000estimado <- cor.plot(cor(datos[,-1]),
main="Matriz de correlaciones Estimado ",
diag=F,
show.legend = TRUE)
bootest <- cor.plot(r = B$esboot,
main="Matriz de correlaciones Bootstrap",
diag=F,
show.legend = TRUE)
jackest<- cor.plot(r = J$esjack,
main="Matriz de correlaciones Jackknife",
diag=F,
show.legend = TRUE)