Componentes Principales y Análisis Factorial

Matriz de Información: X

library(readr)
library(kableExtra)
url_link<-"http://halweb.uc3m.es/esp/Personal/personas/agrane/libro/ficheros_datos/capitulo_7/datos_prob_7_3.txt"
mat_X<-read_table2(url_link,col_names = FALSE)

mat_X %>% head() %>% 
  kable(caption ="Matriz de información:" ,align = "c",digits = 6) %>% 
  kable_material(html_font = "sans-serif")

Matriz de información:
X1	X2	X3	X4	X5	X6	X7	X8
30	41	670	3903	12	94	341	1.2
124	46	410	955	6	57	89	0.5
95	48	370	6	5	26	20	0.1
90	43	680	435	8	20	331	1.6
112	41	100	1293	2	51	22	0.1
73	51	390	6115	4	35	93	0.2

Cálculo de V(X): Cálculo “Manual”

library(dplyr)
library(kableExtra)
centrado<-function(x){
  x-mean(x)
}
Xcentrada<-apply(X = mat_X,MARGIN = 2,centrado)
Xcentrada %>% head() %>% 
  kable(caption ="Matriz de Variables centradas:",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif")

Matriz de Variables centradas:
X1	X2	X3	X4	X5	X6	X7	X8
-49.67	-0.67	303.89	1463.5	2.94	-60.17	196.72	0.71
44.33	4.33	43.89	-1484.5	-3.06	-97.17	-55.28	0.01
15.33	6.33	3.89	-2433.5	-4.06	-128.17	-124.28	-0.39
10.33	1.33	313.89	-2004.5	-1.06	-134.17	186.72	1.11
32.33	-0.67	-266.11	-1146.5	-7.06	-103.17	-122.28	-0.39
-6.67	9.33	23.89	3675.5	-5.06	-119.17	-51.28	-0.29

n_obs<-nrow(mat_X)
mat_V<-t(Xcentrada)%*%Xcentrada/(n_obs-1) 
mat_V %>% kable(caption ="Cálculo de V(X) forma manual:" ,
                align = "c",
                digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Cálculo de V(X) forma manual:
	X1	X2	X3	X4	X5	X6	X7	X8
X1	716.12	45.06	-2689.61	-16082.06	-121.63	-1019.06	-1844.37	-5.15
X2	45.06	46.94	-144.31	2756.71	-24.63	-938.41	-205.25	-0.42
X3	-2689.61	-144.31	36389.87	123889.71	740.82	838.33	17499.38	73.48
X4	-16082.06	2756.71	123889.71	5736372.38	3078.97	6672.44	140343.50	412.79
X5	-121.63	-24.63	740.82	3078.97	51.47	405.58	565.22	1.59
X6	-1019.06	-938.41	838.33	6672.44	405.58	26579.56	3149.77	-2.96
X7	-1844.37	-205.25	17499.38	140343.50	565.22	3149.77	16879.39	64.51
X8	-5.15	-0.42	73.48	412.79	1.59	-2.96	64.51	0.28

Cálculo con R base

library(dplyr)
library(kableExtra)
cov(mat_X) %>% 
  kable(caption="Cálculo de V(X) a través de R base",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Cálculo de V(X) a través de R base
	X1	X2	X3	X4	X5	X6	X7	X8
X1	716.12	45.06	-2689.61	-16082.06	-121.63	-1019.06	-1844.37	-5.15
X2	45.06	46.94	-144.31	2756.71	-24.63	-938.41	-205.25	-0.42
X3	-2689.61	-144.31	36389.87	123889.71	740.82	838.33	17499.38	73.48
X4	-16082.06	2756.71	123889.71	5736372.38	3078.97	6672.44	140343.50	412.79
X5	-121.63	-24.63	740.82	3078.97	51.47	405.58	565.22	1.59
X6	-1019.06	-938.41	838.33	6672.44	405.58	26579.56	3149.77	-2.96
X7	-1844.37	-205.25	17499.38	140343.50	565.22	3149.77	16879.39	64.51
X8	-5.15	-0.42	73.48	412.79	1.59	-2.96	64.51	0.28

Cálculo de R(X) Cálculo “Manual”

Zx<-scale(x = mat_X,center =TRUE)
Zx %>% head() %>% 
  kable(caption ="Matriz de Variables Estandarizadas:",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif")

Matriz de Variables Estandarizadas:
X1	X2	X3	X4	X5	X6	X7	X8
-1.86	-0.10	1.59	0.61	0.41	-0.37	1.51	1.34
1.66	0.63	0.23	-0.62	-0.43	-0.60	-0.43	0.02
0.57	0.92	0.02	-1.02	-0.57	-0.79	-0.96	-0.73
0.39	0.19	1.65	-0.84	-0.15	-0.82	1.44	2.09
1.21	-0.10	-1.39	-0.48	-0.98	-0.63	-0.94	-0.73
-0.25	1.36	0.13	1.53	-0.70	-0.73	-0.39	-0.54

n_obs<-nrow(mat_X)
mat_R<-t(Zx)%*%Zx/(n_obs-1) 
mat_R %>% kable(caption ="Cálculo de R(X) forma manual:" ,
                align = "c",
                digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Cálculo de R(X) forma manual:
	X1	X2	X3	X4	X5	X6	X7	X8
X1	1.00	0.25	-0.53	-0.25	-0.63	-0.23	-0.53	-0.36
X2	0.25	1.00	-0.11	0.17	-0.50	-0.84	-0.23	-0.12
X3	-0.53	-0.11	1.00	0.27	0.54	0.03	0.71	0.73
X4	-0.25	0.17	0.27	1.00	0.18	0.02	0.45	0.32
X5	-0.63	-0.50	0.54	0.18	1.00	0.35	0.61	0.42
X6	-0.23	-0.84	0.03	0.02	0.35	1.00	0.15	-0.03
X7	-0.53	-0.23	0.71	0.45	0.61	0.15	1.00	0.93
X8	-0.36	-0.12	0.73	0.32	0.42	-0.03	0.93	1.00

Cálculo usando R base

library(dplyr)
library(kableExtra)
cor(mat_X) %>% 
  kable(caption="Cálculo de R(X) a través de R base",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Cálculo de R(X) a través de R base
	X1	X2	X3	X4	X5	X6	X7	X8
X1	1.00	0.25	-0.53	-0.25	-0.63	-0.23	-0.53	-0.36
X2	0.25	1.00	-0.11	0.17	-0.50	-0.84	-0.23	-0.12
X3	-0.53	-0.11	1.00	0.27	0.54	0.03	0.71	0.73
X4	-0.25	0.17	0.27	1.00	0.18	0.02	0.45	0.32
X5	-0.63	-0.50	0.54	0.18	1.00	0.35	0.61	0.42
X6	-0.23	-0.84	0.03	0.02	0.35	1.00	0.15	-0.03
X7	-0.53	-0.23	0.71	0.45	0.61	0.15	1.00	0.93
X8	-0.36	-0.12	0.73	0.32	0.42	-0.03	0.93	1.00

Versiones gráficas de R(X)

Usando el paquete PerformanceAnalytics

library(PerformanceAnalytics)
chart.Correlation(as.matrix(mat_X),histogram = TRUE,pch=12)

Usando el paquete corrplot

Ejemplo de clases

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="upper",
         tl.col="black",
         tl.srt = 20,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         col = terrain.colors(100))

Ejemplo Anexo 1

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="lower",
         tl.col="black",
         tl.srt = 90,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         col = heat.colors(11))

Ejemplo anexo 2

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method = "color",
         type= "full",
         tl.col="black",
         tl.srt = 90,
         order = "hclust", addrect = 3,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         col = c("green","turquoise","gray","violet"))

Ejemplo anexo 3

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot.mixed(Mat_R$r,
         upper = "pie",     
         lower = "color",
         p.mat = Mat_R$r,
         tl.col="Black",
         tl.srt = 0,
         order = "hclust", addrect = 3,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         )

Componentes Principales y Análisis Factorial

RENE ERNESTO PEREIRA GARCIA PG15036

16/10/2020