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):

calculo 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)

calculo 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 clase

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))

ejemplos adicionales

# ejemplo 1 

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="red",
         tl.srt = 20,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         col = cm.colors(150),
         method="pie")

# ejemplo 2 

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

# ejemplo 3

library(corrplot)
library(grDevices)
library(Hmisc)
col4 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "#7FFF7F",
                           "cyan", "#007FFF", "blue", "#00007F"))
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="lower",
         tl.col="black",
         tl.srt = 20,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         col = col4(50),
         method="square")

# ejemplo 4 

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="red",
         tl.srt = 20,
         pch.col = "red",
         insig = "p-value",
         sig.level = -1,
         col =  gray.colors(100),
         method="ellipse")

# ejemplo 5

library(corrplot)
library(grDevices)
library(Hmisc)
col3 <- colorRampPalette(c("red", "white", "blue"))
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="lower",
         tl.col="yellow",
         tl.srt = 20,
         pch.col = "yellow",
         insig = "p-value",
         sig.level = -1,
         col = col3(100) ,
         method="circle")

# ejemplo 6 

library(corrplot)
library(grDevices)
library(Hmisc)
whiteblack <- c("white", "black")
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="full",
         order = "hclust",
         addrect = 5,
         tl.col="blue",
         tl.srt = 10,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         method="circle",
         col = whiteblack,
         bg = "gold2")

Extracción de los Componentes

Ejemplo de extracción.

Cálculo “manual” de los componentes

Siguiendo el ejemplo de los datos de “Desarrollo”, se encontraran todos los componentes de la batería de indicadores (dataframe):

library(kableExtra)
library(dplyr)
library(Hmisc)
Rx<-mat_X %>% as.matrix() %>% rcorr()
Rx$r %>% kable(caption="Matriz R(X)",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Matriz R(X)
	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

Rx$P %>% kable(caption="p-values de R(X)",
        align = "c",
        digits = 2) %>% 
  kable_classic_2(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

p-values de R(X)
	X1	X2	X3	X4	X5	X6	X7	X8
X1	NA	0.33	0.02	0.32	0.00	0.35	0.02	0.14
X2	0.33	NA	0.66	0.51	0.03	0.00	0.36	0.65
X3	0.02	0.66	NA	0.28	0.02	0.92	0.00	0.00
X4	0.32	0.51	0.28	NA	0.48	0.95	0.06	0.19
X5	0.00	0.03	0.02	0.48	NA	0.16	0.01	0.08
X6	0.35	0.00	0.92	0.95	0.16	NA	0.56	0.89
X7	0.02	0.36	0.00	0.06	0.01	0.56	NA	0.00
X8	0.14	0.65	0.00	0.19	0.08	0.89	0.00	NA

Descomposición de autovalores y autovectores

library(stargazer)
descomposicion<-eigen(Rx$r)
t(descomposicion$values) %>% kable(caption="Autovalores de R(X)",
        align = "c",
        digits = 2) %>% 
  kable_classic_2(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Autovalores de R(X)
3.75	1.93	0.84	0.72	0.34	0.31	0.1	0.01

descomposicion$vectors %>% kable(caption="Autovectores de R(X)",
        align = "c",
        digits = 2) %>% 
  kable_classic_2(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Autovectores de R(X)
-0.37	-0.05	-0.03	0.71	-0.42	0.41	0.12	0.06
-0.22	-0.61	0.05	-0.24	0.05	0.01	0.70	-0.15
0.41	-0.20	-0.27	-0.02	0.36	0.75	-0.05	0.11
0.22	-0.29	0.88	0.04	-0.08	0.16	-0.23	-0.06
0.41	0.18	-0.09	-0.35	-0.75	0.18	0.19	-0.18
0.18	0.61	0.30	0.21	0.32	0.09	0.57	-0.18
0.47	-0.17	-0.01	0.28	-0.09	-0.34	0.26	0.69
0.41	-0.27	-0.21	0.45	0.04	-0.29	-0.07	-0.65

calculo usando R

library(dplyr)
library(factoextra)
library(kableExtra)
library(stargazer)
library(ggplot2)
options(scipen = 99999)
PC<-princomp(x = mat_X,cor = TRUE,fix_sign = FALSE)
factoextra::get_eig(PC) %>% kable(caption="Resumen de PCA",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("hover"))

Resumen de PCA
	eigenvalue	variance.percent	cumulative.variance.percent
Dim.1	3.75	46.92	46.92
Dim.2	1.93	24.11	71.03
Dim.3	0.84	10.45	81.48
Dim.4	0.72	9.04	90.52
Dim.5	0.34	4.26	94.77
Dim.6	0.31	3.81	98.59
Dim.7	0.10	1.24	99.83
Dim.8	0.01	0.17	100.00

library(factoextra)
library(ggplot2)
fviz_eig(PC,
         choice = "eigenvalue",
         barcolor = "red",
         barfill = "red",
         addlabels = TRUE, 
       )+labs(title = "Gráfico de Sedimentación",subtitle = "Usando princomp, con Autovalores")+
  xlab(label = "Componentes")+
  ylab(label = "Autovalores")+geom_hline(yintercept = 1)

library(factoextra)
library(ggplot2)
fviz_eig(PC,
         choice = "variance",
         barcolor = "green",
         barfill = "green",
         addlabels = TRUE,
       )+labs(title = "Gráfico de Sedimentación",
              subtitle = "Usando princomp, con %Varianza Explicada")+ xlab(label = "Componentes")+ ylab(label = "%Varianza")

Correlación de los componentes con las variables: rij=aj⋅λ−−√j

library(dplyr)
library(kableExtra)
raiz_lambda<-as.matrix(sqrt(descomposicion$values))
autovectores<-descomposicion$vectors
corr_componentes_coordenadas<-vector(mode = "list")
for(j in 1:8){raiz_lambda[j]*autovectores[,j]->corr_componentes_coordenadas[[j]]}
corr_componentes_coordenadas %>% bind_cols()->corr_componentes_coordenadas
names(corr_componentes_coordenadas)<-paste0("Comp",1:8)
corr_componentes_coordenadas %>% as.data.frame() %>% 
  kable(caption="Correlación de X con las componentes",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Correlación de X con las componentes
Comp1	Comp2	Comp3	Comp4	Comp5	Comp6	Comp7	Comp8
-0.72	-0.06	-0.03	0.60	-0.25	0.22	0.04	0.01
-0.43	-0.85	0.04	-0.20	0.03	0.01	0.22	-0.02
0.80	-0.28	-0.25	-0.02	0.21	0.42	-0.02	0.01
0.42	-0.40	0.81	0.03	-0.05	0.09	-0.07	-0.01
0.80	0.25	-0.08	-0.29	-0.44	0.10	0.06	-0.02
0.34	0.84	0.27	0.18	0.19	0.05	0.18	-0.02
0.91	-0.23	-0.01	0.24	-0.05	-0.19	0.08	0.08
0.80	-0.38	-0.20	0.38	0.02	-0.16	-0.02	-0.08

Usando Facto Extra

library(dplyr)
library(factoextra)
library(kableExtra)
variables_pca<-get_pca_var(PC)
variables_pca$coord%>% 
  kable(caption="Correlación de X con las componentes, usando factoextra",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))

Correlación de X con las componentes, usando factoextra
	Dim.1	Dim.2	Dim.3	Dim.4	Dim.5	Dim.6	Dim.7	Dim.8
X1	-0.72	-0.06	-0.03	0.60	0.25	0.22	0.04	0.01
X2	-0.43	-0.85	0.04	-0.20	-0.03	0.01	0.22	-0.02
X3	0.80	-0.28	-0.25	-0.02	-0.21	0.42	-0.02	0.01
X4	0.42	-0.40	0.81	0.03	0.05	0.09	-0.07	-0.01
X5	0.80	0.25	-0.08	-0.29	0.44	0.10	0.06	-0.02
X6	0.34	0.84	0.27	0.18	-0.19	0.05	0.18	-0.02
X7	0.91	-0.23	-0.01	0.24	0.05	-0.19	0.08	0.08
X8	0.80	-0.38	-0.20	0.38	-0.02	-0.16	-0.02	-0.08

Representación Gráfica de las correlaciones en los ejes de los componentes

fviz_pca_var(PC,repel = TRUE,axes = c(1,2))

fviz_pca_var(PC,repel = TRUE,axes = c(3,4))

fviz_pca_var(PC,repel = TRUE,axes = c(5,6))

fviz_pca_var(PC,repel = TRUE,axes = c(7,8))

Representación alternativa:

library(corrplot)
corrplot(variables_pca$coord,is.corr = FALSE,method = "square",addCoef.col="black",number.cex = 0.75)

Análisis Factorial en R

library(psych)
library(corrplot)
library(dplyr)
#Modelo de 2 Factores (sin rotar)
numero_de_factores<-2
modelo_2_factores<-principal(r = Rx$r,
                             nfactors = numero_de_factores,
                             covar = FALSE,
                             rotate = "none")
modelo_2_factores

## Principal Components Analysis
## Call: principal(r = Rx$r, nfactors = numero_de_factores, rotate = "none", 
##     covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##      PC1   PC2   h2    u2 com
## X1 -0.72  0.06 0.53 0.472 1.0
## X2 -0.43  0.85 0.91 0.093 1.5
## X3  0.80  0.28 0.72 0.280 1.2
## X4  0.42  0.40 0.33 0.668 2.0
## X5  0.80 -0.25 0.70 0.302 1.2
## X6  0.34 -0.84 0.82 0.176 1.3
## X7  0.91  0.23 0.89 0.108 1.1
## X8  0.80  0.38 0.78 0.217 1.4
## 
##                        PC1  PC2
## SS loadings           3.75 1.93
## Proportion Var        0.47 0.24
## Cumulative Var        0.47 0.71
## Proportion Explained  0.66 0.34
## Cumulative Proportion 0.66 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 2 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.09 
## 
## Fit based upon off diagonal values = 0.96

correlaciones_modelo<-variables_pca$coord


corrplot(correlaciones_modelo[,1:numero_de_factores],
         is.corr = FALSE,
         method = "square",addCoef.col="black",number.cex = 0.75)

modelo 3 factores

library(psych)
library(corrplot)
library(dplyr)
#Modelo de 3 Factores (sin rotar)
numero_de_factores<-3
modelo_3_factores<-principal(r = Rx$r,
                             nfactors = numero_de_factores,
                             covar = FALSE,
                             rotate = "none")
modelo_3_factores

## Principal Components Analysis
## Call: principal(r = Rx$r, nfactors = numero_de_factores, rotate = "none", 
##     covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##      PC1   PC2   PC3   h2    u2 com
## X1 -0.72  0.06 -0.03 0.53 0.472 1.0
## X2 -0.43  0.85  0.04 0.91 0.092 1.5
## X3  0.80  0.28 -0.25 0.78 0.219 1.4
## X4  0.42  0.40  0.81 0.98 0.017 2.0
## X5  0.80 -0.25 -0.08 0.71 0.295 1.2
## X6  0.34 -0.84  0.27 0.90 0.101 1.6
## X7  0.91  0.23 -0.01 0.89 0.108 1.1
## X8  0.80  0.38 -0.20 0.82 0.179 1.6
## 
##                        PC1  PC2  PC3
## SS loadings           3.75 1.93 0.84
## Proportion Var        0.47 0.24 0.10
## Cumulative Var        0.47 0.71 0.81
## Proportion Explained  0.58 0.30 0.13
## Cumulative Proportion 0.58 0.87 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 3 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.08 
## 
## Fit based upon off diagonal values = 0.97

correlaciones_modelo<-variables_pca$coord


corrplot(correlaciones_modelo[,1:numero_de_factores],
         is.corr = FALSE,
         method = "square",addCoef.col="black",number.cex = 0.75)

modelo 4 factores

library(psych)
library(corrplot)
library(dplyr)
#Modelo de 4 Factores (sin rotar)
numero_de_factores<-4
modelo_4_factores<-principal(r = Rx$r,
                             nfactors = numero_de_factores,
                             covar = FALSE,
                             rotate = "none")
modelo_4_factores

## Principal Components Analysis
## Call: principal(r = Rx$r, nfactors = numero_de_factores, rotate = "none", 
##     covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##      PC1   PC2   PC3   PC4   h2    u2 com
## X1 -0.72  0.06 -0.03  0.60 0.89 0.112 2.0
## X2 -0.43  0.85  0.04 -0.20 0.95 0.050 1.6
## X3  0.80  0.28 -0.25 -0.02 0.78 0.219 1.4
## X4  0.42  0.40  0.81  0.03 0.98 0.016 2.0
## X5  0.80 -0.25 -0.08 -0.29 0.79 0.208 1.5
## X6  0.34 -0.84  0.27  0.18 0.93 0.070 1.7
## X7  0.91  0.23 -0.01  0.24 0.95 0.052 1.3
## X8  0.80  0.38 -0.20  0.38 0.97 0.032 2.1
## 
##                        PC1  PC2  PC3  PC4
## SS loadings           3.75 1.93 0.84 0.72
## Proportion Var        0.47 0.24 0.10 0.09
## Cumulative Var        0.47 0.71 0.81 0.91
## Proportion Explained  0.52 0.27 0.12 0.10
## Cumulative Proportion 0.52 0.78 0.90 1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 4 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.04 
## 
## Fit based upon off diagonal values = 0.99

correlaciones_modelo<-variables_pca$coord


corrplot(correlaciones_modelo[,1:numero_de_factores],
         is.corr = FALSE,
         method = "square",addCoef.col="black",number.cex = 0.75)

Componentes Principales y Análisis Factorial (Uso de libreria corrplot)

KATHYA ELIZABETH HERNANDEZ MENJIVAR-HM17039

16/10/2020

Matriz de Información: X

Cálculo de V(X):

calculo manual

Cálculo con R base

Cálculo de R(X)

calculo manual

Cálculo usando R base

Versiones gráficas de R(X)

Usando el paquete PerformanceAnalytics

Usando el paquete corrplot

ejemplo clase

ejemplos adicionales

Extracción de los Componentes

Ejemplo de extracción.

Cálculo “manual” de los componentes

Siguiendo el ejemplo de los datos de “Desarrollo”, se encontraran todos los componentes de la batería de indicadores (dataframe):

Descomposición de autovalores y autovectores

calculo usando R

Correlación de los componentes con las variables: rij=aj⋅λ−−√j

Usando Facto Extra

Representación Gráfica de las correlaciones en los ejes de los componentes

Representación alternativa:

Análisis Factorial en R

modelo 3 factores

modelo 4 factores