Prudential Life Insurance
Grupo 11
Preprocesamiento de datos.
Para la reducción de la dimensionalidad de la base de datos, se hace uso del Análisis de componentes principales, se usa el paquete PCAmixdata implementado en R; este paquete será de gran ayuda pues realiza un ACP mixto, es decir, trabaja con variables numéricas y variables categóricas.
Se va a trabajar con todas la variables excepto Ind que es código único del cliente y la variable Response que es la variable sobre la cual se basa el estudio.
Análisis de componentes principales
ACP
El procedimiento realizado por PCAmix, determina la matriz X de dimensiones n × k, que contiene los valores estandarizados de las componentes, la varianza de cada componente y una matriz de dimensiones n × k de las cargas al cuadrado. Estas cargas están definidas como las correlaciones al cuadrado de las variables cuantitativas con las componentes PCAMIX y como el coeficiente de correlación para las variables cualitativas.
Este procedimiento se lleva a cabo en los siguientes pasos: - Se construye la matriz real Z = \([Z_{1}\), \(Z_{2}]\) de dimensión \(n × (p_{1} + m)\) donde: * \(Z_{1}\) es la versión estandarizada de \(X_{1}\) (ACP). * \(Z_{2}\) es la versión centrada de la matriz de indicadores G de \(X_{2}\) (ACM).
Se construye la matriz diagonal N de los pesos de las filas de Z. Las n filas a menudo se ponderan con \(\frac{1}{n}\).
Se construye la matriz diagonal M de los pesos de las columnas, de manera que Las primeras columnas \(p_{1}\) (correspondientes a las variables numéricas) están ponderadas por 1 (como en PCA estándar) y las últimas m columnas (correspondientes a los niveles de las variables categóricas) están ponderadas por “\(\frac{n}{n_{s}}\)” (como en el ACM estándar), donde \(n_{s}\), s = 1,. . . , m denota el número de observaciones que pertenecen al nivel s.
Posterior a esto se tiene que la inercia total de Z con esta distancia y los pesos \(\frac{1}{n}\), es igual a \(p_{1} + m - p_{2}\).
En primera instancia, se divide las variables cualitativas y cuantitativas, mediante la función Splitmix, para poder hacer el Analisis de componentes principales usando la función PCAmix. Esta función nos entrega una lista con la siguiente información:
split <- splitmix(BACP)
res.pcamix <- PCAmix(X.quanti=split$X.quanti , X.quali=split$X.quali,rename.level=TRUE,
graph=FALSE)
rm(split)
varianza<-as.data.frame(res.pcamix$eig)
show(res.pcamix)##
## Call:
## PCAmix(X.quanti = split$X.quanti, X.quali = split$X.quali, rename.level = TRUE, graph = FALSE)
##
## Method = Principal Component of mixed data (PCAmix)
##
##
## "name" "description"
## "$eig" "eigenvalues of the principal components (PC) "
## "$ind" "results for the individuals (coord,contrib,cos2)"
## "$quanti" "results for the quantitative variables (coord,contrib,cos2)"
## "$levels" "results for the levels of the qualitative variables (coord,contrib,cos2)"
## "$quali" "results for the qualitative variables (contrib,relative contrib)"
## "$sqload" "squared loadings"
## "$coef" "coef of the linear combinations defining the PC"#write.csv(varianza,"varianza.csv")Esta función realiza un ACP a las variables numéricas y un MCA a las variables categóricas.
Para realizar el cálculo del ACP, se utilizan las variables originales estandarizadas, es decir, variables conmedia 0 y varianza 1. Esto equivale a tomar los componentes principales, no de la matriz de covarianzas sino de la matriz de correlaciones (en las variables estandarizadas coinciden lascovarianzas y las correlaciones).
Los datos de la base, no son dimensionalmente homogéneos, es decir, la magnitud de las variables no es el mismo. Por lo tanto, se aplica la matriz de correlaciones. Al tener variables numéricas y categóricas se utiliza el paquete PCAmix, el cual analiza la base de datos que comprende: n observaciones descritas por \(p_{1}\)=14 variables numéricas y \(p_{2}\)=56 variables categóricas, representada de la siguiente manera: - \(X_{1}\): Matriz cuantitativa (n x \(p_{1}\)) - \(X_{2}\): Matriz cualitativa (n x \(p_{2}\)), con m = número total de niveles de las variables categóricas \(p_{2}\).
Varianza
Debido a que se está trabajando con todas las variables, la mayor parte de las variables están incorreladas, por tanto, el ACP no va a reducir el número de variables; únicamente mostrará las variables de mayor a menor varianza. En nuestro caso el número de dimensiones es mucho mayor al número de variables originales, debido a que las variables categóricas tienen diferentes nieveles.
A continuación se muestra, los componentes con su respectiva variabilidad que recogen.
library(kableExtra)
library(DT)
datatable(round(varianza,2), options = list(pageLength = 13,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))Siguiendo el criterio de Kaiser, hay que conservar los componentes principales cuyos valores propios son mayores a 1. Sin embargo el criterio más usado suele ser el observar el porcentaje de varianza total explicada por cada componente y cuando este llega a un porcentaje alto, normalmente cerca del 90%, significa que el número de componentes es suficiente. En nuestro análisis, es preciso señalar que usando el Criterio de Kaiser solo conservaríamos hasta la componente 40, pero apenas explica el 62.48% de la variabilidad. Por otro lado, si mantenemos el criterio de mayor representación no estaríamos reduciendo la dimensión de nuestros datos.
Si analizamos las primera y la segunda componente, podemos ver en la proporción acumulada,que apenas representan el 9,76 % de la variabilidad de los datos, siendo 5.33% para el primer componente y 4.43% el segundo componente.
En la siguinete figura observamos la información de los componentes con su porcentaje de variabilidad:
aux<-data.frame(x=c(1:110),y=c(1,1))
ggplot(varianza, aes(c(1:length(varianza[,1])),Proportion)) +
geom_col()+geom_point()+geom_line(color='blue')+
xlab('Dimensión')+ylab('Porcentaje')+
geom_line(data = aux,
mapping = aes(x,y),color="red")
Gráficos
Ahora, podemos obtener los siguinetes gráficos:
plot(res.pcamix,choice="levels",xlim=c(-1.5,2.5), main="Levels")
plot(res.pcamix,choice="cor",xlim=c(-1.5,2.5), main="Correlación")
plot(res.pcamix,choice="sqload",coloring.var=T, leg=TRUE,
posleg="topright", main="Todas las variables" )
rm(varianza,res.pcamix)La grafica de todas las variables (categóricas y númericas) tiene como coordenadas las correlaciones al cuadrado para las variables numéricasy para las variables categóricas son coeficientes de correlación. En ambos casos, miden el vínculo entre las variables y las componentes principales. Se observa que todas las variables númericas y las variables categóricas, Insurence_History, Product_Inf Y Employment_info, están vinculadas a la primera componente. Por otro lado, las variables Medical_History son ortogonales a estas variables y están, en su mayoria, asociada a la segunda componente. En el grafico de las variables numericas por ejemplo podemos ver que las variables Employment_info 6 está negativamente correlacionada con la variable Product_Info2.
Análisis de componentes principales por grupos
Ahora, se consideran los siguientes grupos:
- Product_Info
- Num (variables numéricas estandarizadas)
- Employment_Info
- InsuredInfo
- Insurance_History
- Medical_History
Realizamos el ACP de esta manera porque nos interesa conocer las componentes que mejor representaen las variables en cada grupo.
Grupo 1
El grupo Product_Info consta de 7 variables categoricas y numéricas. Al realilzar el ACP obtenemos lo siguiente:
datatable(round(data.frame(res.mfamix$separate.analyses$Product_Info$eig),2), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v1 <- data.frame(res.mfamix$separate.analyses$Product_Info$eig)
ggplot(v1, aes(c(1:length(Proportion)),Proportion)) +
geom_col(color="dodgerblue1",fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+
geom_text(aes(y=0.1*max(Proportion)+
Proportion,label = paste0(as.character(round(Proportion,2)),"%")), size = 4)+
ggtitle('Grupo 1')
Podemos observar que las primeras 7 componentes recogen el 90% de la variabilidad.
El summary del grupo es el siguinete:
summary(res.mfamix$separate.analyses$Product_Info)##
## Call:
## PCAmix(X.quanti = base.qt, X.quali = base.ql, ndim = ndim, rename.level = rename.level, graph = FALSE)
##
## Method = Factor Analysis of mixed data (FAmix)
##
## Data:
## number of observations: 79146
## number of variables: 7
## number of numerical variables: 3
## number of categorical variables: 4
##
## Squared loadings :
## dim 1 dim 2 dim 3 dim 4 dim 5 dim 6 dim 7 dim 8
## Product_Info_2 0.39 0.24 0.00 0.02 0.01 0.02 0.00 0.31
## Product_Info_3 0.04 0.04 0.05 0.57 0.28 0.01 0.00 0.01
## Product_Info_4 0.53 0.07 0.00 0.01 0.01 0.01 0.01 0.37
## Product_Info_1 0.11 0.28 0.00 0.04 0.00 0.00 0.57 0.00
## Product_Info_5 0.07 0.23 0.00 0.00 0.00 0.57 0.12 0.00
## Product_Info_6 0.12 0.23 0.00 0.03 0.02 0.35 0.21 0.04
## Product_Info_7 0.07 0.01 0.94 0.33 0.65 0.00 0.01 0.00Grupo 2
El grupo 2 abarca las variables numéricas estandarizadas. Los resulatdos del análisis son los siguinetes:
datatable(round(data.frame(res.mfamix$separate.analyses$Num$eig),2), options = list(pageLength =5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v2 <- data.frame(res.mfamix$separate.analyses$Num$eig)
ggplot(v2, aes(c(1:length(Proportion)),Proportion)) +
geom_col(color="dodgerblue1",fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+
geom_text(aes(y=0.1*max(Proportion)+
Proportion,label = paste0(as.character(round(Proportion,2)),"%")), size = 4)+
ggtitle('Grupo 2')
En este grupo las dos primeras componentes, con valor propio mayor a uno, representan el 78.78% de la variabilidad y las 3 primeras componentes representan el 99.85%
Se tiene también el summary:
summary(res.mfamix$separate.analyses$Num)##
## Call:
## PCAmix(X.quanti = base.qt, X.quali = base.ql, ndim = ndim, rename.level = rename.level, graph = FALSE)
##
## Method = Principal Component Analysis (PCA)
##
## Data:
## number of observations: 79146
## number of variables: 4
##
## Squared loadings :
## dim 1 dim 2 dim 3 dim 4
## Ins_Age 0.04 0.78 0.19 0
## Ht 0.40 0.20 0.41 0
## Wt 0.99 0.00 0.00 0
## BMI 0.71 0.04 0.24 0Grupo 3
El grupo 3 tiene las variables Employment_Info, este conjunto tiene variables mixtas.Al realizar el ACP obtenemos:
datatable(round(data.frame(res.mfamix$separate.analyses$Employment_Info$eig),2), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v3 <- data.frame(res.mfamix$separate.analyses$Employment_Info$eig)
ggplot(v3, aes(c(1:length(Proportion)),Proportion)) +
geom_col(color="dodgerblue1",fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+
geom_text(aes(y=0.1*max(Proportion)+
Proportion,label = paste0(as.character(round(Proportion,2)),"%")), size = 4)+
ggtitle('Grupo 3')
Se observa que las dos primeras componentes tienen valor propio mayor a uno pero solamente logran explicar el 57% de la variabilidad de los datos.Por otr aprate las primeras 5 componentes explican el 96.19%.
Se presenta el summary del análisis:
summary(res.mfamix$separate.analyses$Employment_Info)##
## Call:
## PCAmix(X.quanti = base.qt, X.quali = base.ql, ndim = ndim, rename.level = rename.level, graph = FALSE)
##
## Method = Factor Analysis of mixed data (FAmix)
##
## Data:
## number of observations: 79146
## number of variables: 6
## number of numerical variables: 4
## number of categorical variables: 2
##
## Squared loadings :
## dim 1 dim 2 dim 3 dim 4 dim 5 dim 6
## Employment_Info_1 0.20 0.41 0.10 0.00 0.28 0.00
## Employment_Info_2 0.73 0.04 0.03 0.08 0.01 0.11
## Employment_Info_4 0.03 0.23 0.73 0.00 0.02 0.00
## Employment_Info_6 0.01 0.67 0.03 0.04 0.25 0.00
## Employment_Info_3 0.79 0.03 0.02 0.04 0.00 0.12
## Employment_Info_5 0.28 0.01 0.01 0.68 0.02 0.00Grupo 4
El grupo 4 contiene las variables InsuredInfo.Al realizar el ACP obtenemos:
datatable(round(data.frame(res.mfamix$separate.analyses$InsuredInfo$eig
),2), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v4 <- data.frame(res.mfamix$separate.analyses$InsuredInfo$eig)
ggplot(v4, aes(c(1:length(Proportion)),Proportion)) +
geom_col(color="dodgerblue1",fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+
geom_text(aes(y=0.1*max(Proportion)+
Proportion,label = paste0(as.character(round(Proportion,2)),"%")), size = 4)+
ggtitle('Grupo 4')
Notemos que las primeras 8 variables explican más del 90% de la variabilidad, pero no todas tiene sus valores propios mayores a uno.
Se presenta el summary del análisis:
summary(res.mfamix$separate.analyses$InsuredInfo)##
## Call:
## PCAmix(X.quanti = base.qt, X.quali = base.ql, ndim = ndim, rename.level = rename.level, graph = FALSE)
##
## Method = Factor Analysis of mixed data (FAmix)
##
## Data:
## number of observations: 79146
## number of variables: 7
## number of numerical variables: 1
## number of categorical variables: 6
##
## Squared loadings :
## dim 1 dim 2 dim 3 dim 4 dim 5 dim 6 dim 7 dim 8
## InsuredInfo_3 0.00 0.06 0.39 0.41 0.13 0.00 0.00 0.00
## InsuredInfo_1 0.01 0.28 0.55 0.50 0.64 0.00 0.02 0.00
## InsuredInfo_2 0.64 0.06 0.00 0.01 0.00 0.06 0.00 0.23
## InsuredInfo_4 0.06 0.31 0.02 0.06 0.14 0.00 0.41 0.00
## InsuredInfo_5 0.22 0.01 0.01 0.00 0.00 0.71 0.05 0.00
## InsuredInfo_6 0.04 0.38 0.03 0.02 0.03 0.10 0.40 0.00
## InsuredInfo_7 0.67 0.04 0.00 0.00 0.00 0.03 0.00 0.25Grupo 5
EL grupo 5 abarca las variables Insurance_History, de igual manera es un conjunto de datos mixto.Al realizar el ACP se obtiene lo siguiente:
datatable(round(data.frame(res.mfamix$separate.analyses$Insurance_History$eig),2), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v5 <- data.frame(res.mfamix$separate.analyses$Insurance_History$eig)
ggplot(v5, aes(c(1:length(Proportion)),Proportion)) +
geom_col(color="dodgerblue1",fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+ggtitle('Grupo 5')
las primeras 7 componentes con valor propio mayor a uno representan el 82.61% y las primeras 9 componentes de 15, logran representar más del 90% de variabilidad.
Grupo 6
El grupo 6 esta compuesto de las variables Medical_history, este conjunto de datos tiene variables en su mayoría categóricas. Al realizar el Análisis tenemos lo siguinete:
datatable(round(data.frame(res.mfamix$separate.analyses$Medical_History$eig),2), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))v6 <- data.frame(res.mfamix$separate.analyses$Medical_History$eig)
ggplot(v6, aes(c(1:length(Proportion)),Proportion)) +
geom_col(fill="dodgerblue1")+geom_point()+geom_line(size=1)+
xlab('Dimensión')+ylab('Porcentaje')+
ggtitle('Grupo 6')
Este grupo es muy similar al análisis inicial (de toda la base) debido a que este grupo contiene muchas variables categóricas lo que hace que se aumenten más componentes dando de resultado más componentes nuevas que variables. No se tiene reducción de los datos.
Se obtiene lo siguinete al realizar un summary:
summary(res.mfamix$separate.analyses$Medical_History)##
## Call:
## PCAmix(X.quanti = base.qt, X.quali = base.ql, ndim = ndim, rename.level = rename.level, graph = FALSE)
##
## Method = Factor Analysis of mixed data (FAmix)
##
## Data:
## number of observations: 79146
## number of variables: 38
## number of numerical variables: 2
## number of categorical variables: 36
##
## Squared loadings :
## dim 1 dim 2 dim 3 dim 4 dim 5 dim 6 dim 7 dim 8 dim 9 dim 10
## Medical_History_1 0.00 0.00 0.00 0.00 0.08 0.00 0.01 0.00 0.00 0.01
## Medical_History_2 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00
## Medical_History_3 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.05
## Medical_History_4 0.00 0.00 0.02 0.00 0.04 0.00 0.06 0.00 0.00 0.17
## Medical_History_5 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.83 0.00 0.00
## Medical_History_6 0.00 0.00 0.01 0.00 0.10 0.00 0.00 0.00 0.00 0.00
## Medical_History_7 0.01 0.00 0.39 0.58 0.02 0.00 0.00 0.00 0.00 0.00
## Medical_History_8 0.01 0.00 0.40 0.59 0.11 0.00 0.02 0.00 0.00 0.02
## Medical_History_9 0.00 0.09 0.01 0.00 0.15 0.26 0.02 0.00 0.00 0.03
## Medical_History_11 0.00 0.00 0.00 0.03 0.01 0.00 0.00 0.00 0.00 0.00
## Medical_History_12 0.00 0.00 0.00 0.01 0.08 0.00 0.01 0.00 0.00 0.01
## Medical_History_13 0.77 0.00 0.02 0.01 0.10 0.00 0.04 0.00 0.10 0.00
## Medical_History_14 0.00 0.00 0.36 0.61 0.01 0.00 0.00 0.00 0.00 0.00
## Medical_History_16 0.00 0.00 0.02 0.01 0.20 0.00 0.03 0.00 0.00 0.00
## Medical_History_17 0.00 0.00 0.00 0.00 0.03 0.00 0.03 0.83 0.00 0.00
## Medical_History_18 0.09 0.00 0.00 0.00 0.05 0.00 0.00 0.00 0.36 0.01
## Medical_History_19 0.75 0.00 0.00 0.00 0.03 0.00 0.01 0.00 0.03 0.02
## Medical_History_20 0.00 0.37 0.00 0.00 0.03 0.30 0.00 0.00 0.00 0.01
## Medical_History_21 0.84 0.00 0.01 0.00 0.12 0.00 0.02 0.00 0.03 0.03
## Medical_History_22 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.00 0.00
## Medical_History_23 0.06 0.00 0.01 0.00 0.22 0.00 0.03 0.00 0.61 0.00
## Medical_History_25 0.00 0.00 0.62 0.31 0.06 0.00 0.01 0.00 0.00 0.00
## Medical_History_26 0.00 0.00 0.62 0.31 0.06 0.00 0.00 0.00 0.00 0.00
## Medical_History_27 0.28 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.26 0.00
## Medical_History_28 0.00 0.61 0.00 0.00 0.06 0.04 0.01 0.00 0.00 0.00
## Medical_History_29 0.00 0.22 0.02 0.00 0.15 0.36 0.01 0.00 0.00 0.04
## Medical_History_30 0.61 0.00 0.01 0.00 0.04 0.00 0.00 0.00 0.04 0.02
## Medical_History_31 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_33 0.00 0.56 0.01 0.00 0.02 0.36 0.13 0.00 0.00 0.30
## Medical_History_34 0.00 0.61 0.01 0.00 0.04 0.03 0.02 0.00 0.00 0.00
## Medical_History_35 0.83 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.00
## Medical_History_36 0.00 0.00 0.62 0.31 0.07 0.00 0.02 0.00 0.00 0.01
## Medical_History_37 0.00 0.00 0.00 0.00 0.02 0.00 0.02 0.00 0.00 0.00
## Medical_History_38 0.00 0.56 0.00 0.00 0.01 0.36 0.06 0.00 0.00 0.24
## Medical_History_39 0.77 0.00 0.00 0.00 0.22 0.00 0.49 0.01 0.10 0.08
## Medical_History_40 0.00 0.78 0.00 0.00 0.01 0.04 0.08 0.00 0.00 0.25
## Medical_History_41 0.00 0.24 0.03 0.01 0.17 0.45 0.02 0.00 0.00 0.05
## Medical_Keyword_3 0.00 0.00 0.00 0.00 0.19 0.00 0.52 0.01 0.00 0.11
## dim 11 dim 12 dim 13 dim 14 dim 15 dim 16 dim 17 dim 18
## Medical_History_1 0.01 0.00 0.08 0.05 0.01 0.02 0.09 0.00
## Medical_History_2 0.08 0.02 0.00 0.06 0.00 0.02 0.01 0.00
## Medical_History_3 0.08 0.14 0.02 0.02 0.01 0.03 0.02 0.06
## Medical_History_4 0.05 0.03 0.00 0.05 0.02 0.00 0.01 0.00
## Medical_History_5 0.01 0.00 0.03 0.01 0.11 0.12 0.02 0.01
## Medical_History_6 0.02 0.10 0.00 0.01 0.05 0.03 0.02 0.03
## Medical_History_7 0.02 0.04 0.00 0.03 0.04 0.03 0.01 0.09
## Medical_History_8 0.00 0.00 0.03 0.02 0.00 0.03 0.00 0.00
## Medical_History_9 0.00 0.03 0.01 0.01 0.00 0.01 0.00 0.00
## Medical_History_11 0.01 0.03 0.01 0.24 0.00 0.35 0.29 0.04
## Medical_History_12 0.00 0.00 0.08 0.01 0.01 0.00 0.03 0.02
## Medical_History_13 0.06 0.00 0.01 0.01 0.00 0.01 0.02 0.00
## Medical_History_14 0.04 0.03 0.05 0.04 0.02 0.03 0.01 0.04
## Medical_History_16 0.01 0.03 0.00 0.01 0.01 0.00 0.01 0.03
## Medical_History_17 0.00 0.00 0.06 0.02 0.06 0.00 0.01 0.06
## Medical_History_18 0.01 0.00 0.01 0.00 0.04 0.01 0.00 0.07
## Medical_History_19 0.14 0.04 0.04 0.03 0.00 0.03 0.00 0.08
## Medical_History_20 0.07 0.00 0.00 0.05 0.01 0.00 0.05 0.00
## Medical_History_21 0.00 0.03 0.05 0.00 0.01 0.00 0.00 0.01
## Medical_History_22 0.01 0.04 0.09 0.05 0.08 0.02 0.04 0.03
## Medical_History_23 0.11 0.02 0.00 0.00 0.00 0.00 0.01 0.00
## Medical_History_25 0.02 0.00 0.02 0.05 0.00 0.02 0.07 0.01
## Medical_History_26 0.00 0.01 0.00 0.01 0.11 0.00 0.00 0.00
## Medical_History_27 0.02 0.08 0.01 0.02 0.02 0.03 0.00 0.04
## Medical_History_28 0.09 0.12 0.11 0.01 0.03 0.00 0.02 0.00
## Medical_History_29 0.01 0.06 0.07 0.00 0.00 0.01 0.00 0.02
## Medical_History_30 0.10 0.00 0.02 0.00 0.01 0.02 0.00 0.00
## Medical_History_31 0.01 0.03 0.03 0.12 0.05 0.19 0.05 0.14
## Medical_History_33 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00
## Medical_History_34 0.01 0.00 0.16 0.01 0.02 0.00 0.03 0.00
## Medical_History_35 0.00 0.00 0.00 0.01 0.02 0.01 0.00 0.00
## Medical_History_36 0.04 0.05 0.00 0.00 0.06 0.00 0.09 0.07
## Medical_History_37 0.07 0.00 0.00 0.02 0.18 0.02 0.05 0.12
## Medical_History_38 0.01 0.05 0.00 0.05 0.01 0.00 0.00 0.00
## Medical_History_39 0.03 0.01 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_40 0.00 0.02 0.00 0.03 0.00 0.00 0.01 0.01
## Medical_History_41 0.00 0.06 0.04 0.00 0.01 0.00 0.00 0.00
## Medical_Keyword_3 0.02 0.01 0.00 0.00 0.00 0.00 0.00 0.00
## dim 19 dim 20 dim 21 dim 22 dim 23 dim 24 dim 25 dim 26
## Medical_History_1 0.04 0.01 0.04 0.00 0.01 0.00 0.00 0.02
## Medical_History_2 0.02 0.00 0.04 0.02 0.02 0.00 0.00 0.00
## Medical_History_3 0.01 0.12 0.02 0.09 0.16 0.21 0.06 0.05
## Medical_History_4 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00
## Medical_History_5 0.02 0.01 0.01 0.17 0.05 0.00 0.02 0.03
## Medical_History_6 0.03 0.08 0.35 0.01 0.02 0.05 0.04 0.04
## Medical_History_7 0.01 0.07 0.01 0.00 0.01 0.00 0.00 0.03
## Medical_History_8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_9 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_11 0.11 0.07 0.02 0.03 0.01 0.01 0.00 0.12
## Medical_History_12 0.04 0.04 0.06 0.01 0.01 0.42 0.04 0.37
## Medical_History_13 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00
## Medical_History_14 0.01 0.03 0.02 0.00 0.00 0.00 0.01 0.00
## Medical_History_16 0.10 0.01 0.01 0.19 0.02 0.05 0.42 0.00
## Medical_History_17 0.06 0.03 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_18 0.06 0.00 0.01 0.00 0.00 0.00 0.00 0.00
## Medical_History_19 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00
## Medical_History_20 0.01 0.00 0.01 0.05 0.01 0.00 0.01 0.01
## Medical_History_21 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_22 0.00 0.01 0.00 0.00 0.01 0.00 0.00 0.00
## Medical_History_23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_25 0.03 0.04 0.00 0.08 0.01 0.03 0.01 0.04
## Medical_History_26 0.05 0.20 0.03 0.18 0.00 0.02 0.06 0.04
## Medical_History_27 0.05 0.00 0.00 0.03 0.00 0.01 0.01 0.03
## Medical_History_28 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_29 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.00
## Medical_History_30 0.01 0.00 0.01 0.01 0.00 0.00 0.00 0.00
## Medical_History_31 0.10 0.05 0.05 0.01 0.03 0.06 0.14 0.03
## Medical_History_33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_34 0.00 0.02 0.00 0.00 0.00 0.01 0.00 0.02
## Medical_History_35 0.13 0.00 0.21 0.04 0.30 0.02 0.08 0.02
## Medical_History_36 0.01 0.03 0.04 0.01 0.11 0.00 0.00 0.02
## Medical_History_37 0.12 0.15 0.05 0.03 0.19 0.08 0.04 0.10
## Medical_History_38 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00
## Medical_History_39 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_History_41 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## Medical_Keyword_3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## dim 27 dim 28 dim 29 dim 30
## Medical_History_1 0.03 0.00 0.00 0.00
## Medical_History_2 0.13 0.14 0.04 0.02
## Medical_History_3 0.09 0.05 0.00 0.04
## Medical_History_4 0.00 0.00 0.00 0.00
## Medical_History_5 0.09 0.00 0.03 0.09
## Medical_History_6 0.02 0.20 0.00 0.11
## Medical_History_7 0.10 0.00 0.02 0.12
## Medical_History_8 0.03 0.00 0.00 0.00
## Medical_History_9 0.01 0.00 0.00 0.01
## Medical_History_11 0.00 0.01 0.17 0.01
## Medical_History_12 0.03 0.01 0.00 0.03
## Medical_History_13 0.00 0.00 0.00 0.00
## Medical_History_14 0.01 0.15 0.01 0.04
## Medical_History_16 0.11 0.02 0.01 0.01
## Medical_History_17 0.01 0.01 0.06 0.03
## Medical_History_18 0.03 0.00 0.00 0.07
## Medical_History_19 0.00 0.03 0.00 0.00
## Medical_History_20 0.01 0.00 0.11 0.00
## Medical_History_21 0.01 0.02 0.00 0.00
## Medical_History_22 0.01 0.00 0.02 0.00
## Medical_History_23 0.00 0.00 0.00 0.01
## Medical_History_25 0.00 0.01 0.32 0.00
## Medical_History_26 0.00 0.01 0.01 0.03
## Medical_History_27 0.05 0.02 0.05 0.00
## Medical_History_28 0.02 0.02 0.00 0.01
## Medical_History_29 0.01 0.02 0.00 0.00
## Medical_History_30 0.00 0.00 0.00 0.00
## Medical_History_31 0.09 0.12 0.01 0.21
## Medical_History_33 0.00 0.00 0.00 0.00
## Medical_History_34 0.00 0.07 0.01 0.00
## Medical_History_35 0.01 0.00 0.02 0.05
## Medical_History_36 0.03 0.02 0.01 0.01
## Medical_History_37 0.03 0.02 0.06 0.05
## Medical_History_38 0.01 0.00 0.00 0.00
## Medical_History_39 0.00 0.00 0.00 0.00
## Medical_History_40 0.00 0.00 0.00 0.00
## Medical_History_41 0.00 0.02 0.00 0.00
## Medical_Keyword_3 0.00 0.00 0.00 0.00Gráficos
#---- quantitative variables
plot(res.mfamix,choice="cor",cex=0.6,coloring.var="groups")
#----partial axes
plot(res.mfamix,choice="axes",cex=0.6,coloring.var="groups")
#----groups
plot(res.mfamix,choice="groups",cex=0.6,coloring.var="groups") 
#----squared loadings
plot(res.mfamix,choice="sqload",cex=0.8,coloring.var="groups",
posleg="topright") 
En el Círculo de correlación , se puede observar que hay una correlacioín cercana a 1 entre las variables Ht,Employment_Info_1, Product_Info_3.
Groups contributions es la gráfica de los grupos de acuerdo con sus contribuciones a los dos primeros componentes principales. Este mapa confirma las interpretaciones anteriores de los componentes principales de MFAmix y el impacto de las variables Insuredinfo y Product_Info en la primera dimensión, así como el impacto de las variables Medical_History y Insurance_History en la segunda dimensión.
INDICE
Se ha realizado el índice con respecto del primer grupo y se ha obtenido lo siguiente:
ind<-res.mfamix$separate.analyses$Product_Info$scores
d<-data.frame(ind[,c(1:6)])
datatable(round(d,4), options = list(pageLength = 5,
initComplete = JS(
"function(settings, json) {",
"$(this.api().table().header()).css({'background-color': '#fca56f', 'color': '#fff'});",
"}")))Se suman las componentes que han sido previmente multiplicadas por su variabilidad explicada.
i<-vector()
for(j in 1:1700){
i[j]<-d[j,1]+d[j,2]+d[j,3]+d[j,4]+d[j,5]+d[j,6]
}
show(i)## [1] -2.5743440191 -0.1044255642 -0.4523137827 -2.5376753899 -0.3270244324
## [6] 17.6895970017 -2.4848359765 -0.3943324130 -0.3463515557 -1.1661189946
## [11] -0.3912235429 -0.3656786789 -0.1125346905 3.1014266006 -0.2534987117
## [16] -0.2540422940 3.0434452308 -0.2790435751 -0.4136595362 -0.2534987117
## [21] -0.2372804585 0.4229145140 -0.3656786789 -0.0788807007 -0.0720251465
## [26] -0.1337531999 0.2994223186 -0.3463515557 -0.2534987117 -0.0098116534
## [31] -0.1106793930 -0.3076973092 -0.4329866595 -0.2621514203 -0.1955173419
## [36] -2.6785090912 -0.1430798107 -0.3463515557 -0.2172794336 -0.3943324130
## [41] 0.1523347884 -0.3750052897 -2.5463280985 10.3788281285 -0.3943324130
## [46] -0.0602274791 -0.1955173419 -0.3270244324 -0.3656786789 -2.5463280985
## [51] -0.2397154269 -2.4565841246 -0.4136595362 0.3674536563 0.0339507142
## [56] -0.4136595362 -0.1237526874 -0.3014795689 0.0288425931 -0.1555513798
## [61] -0.1955173419 -0.3045884391 -0.1955173419 -2.6498553572 0.0943534187
## [66] -0.3943324130 -2.5238921052 -0.1300065163 -0.1499714530 -0.1026644974
## [71] -0.1144260767 1.6454338499 -2.5014561118 -0.1817340572 -0.3718964196
## [76] 0.0632647162 0.0943534187 3.1731912551 0.0183927295 17.7293745011
## [81] -0.0489152510 -0.2534987117 -0.4136595362 -0.3656786789 -0.3750052897
## [86] -0.1780816048 -0.3432426856 -0.1386592249 -0.3943324130 -0.4298777894
## [91] -0.2565133506 -0.4329866595 -0.2883701859 -0.2534987117 -0.3432426856
## [96] 10.4462303402 0.0095154698 -0.2148444652 -0.0178265486 -2.7171633377
## [101] -0.1386592249 -0.2010611804 -0.1182088489 -0.0098116534 -0.1337531999
## [106] -0.2341715884 -1.9647038792 -0.3463515557 -0.3606784227 3.2566814001
## [111] 0.0028483781 -0.3270244324 -0.1106793930 -2.4079293657 -0.3463515557
## [116] -2.3037642935 -0.2035322371 -0.3656786789 -0.3750052897 -0.3301333030
## [121] -0.2228593603 -0.2534987117 -0.3912235429 -0.0757718302 -0.3432426856
## [126] -0.1337531999 -0.2360934992 -0.2341715884 -0.2509334239 -0.1156435611
## [131] -0.2983706984 -1.9847543596 -0.3943324130 -0.3853580158 -0.0595535774
## [136] -2.4952383711 -0.2148444652 -0.3943324130 -2.4659107354 -0.1305500986
## [141] -0.4105506661 -0.2515130943 -0.2515130943 0.0095154698 -0.3076973092
## [146] -0.3208066922 -0.2341715884 -0.1761902187 -0.0291387767 -0.1337531999
## [151] -0.1499714530 -0.4523137827 -0.2852613158 -0.3750052897 -0.0757718302
## [156] -0.2983706984 0.0071747326 -0.1555513798 0.2105421305 -0.1162232316
## [161] -2.6978362144 -0.4136595362 -0.2341715884 -0.3463515557 -0.2228593603
## [166] -0.2397154269 -0.3076973092 -0.0866086176 -0.3912235429 0.2558756808
## [171] 0.0674968396 0.0288425931 -0.1237526874 -0.2534987117 0.0095154698
## [176] -0.4523137827 -0.2110616929 -0.0602274791 -0.1935317246 -0.3556781665
## [181] 0.1641324558 0.2414409489 -0.3850058022 -1.5806324708 -0.3750052897
## [186] -0.4136595362 -0.3045884391 0.4035873907 -2.7140544676 -0.2172794336
## [191] -0.2066411076 -0.3943324130 -0.1050994659 -2.4565841246 -0.3432426856
## [196] -0.4523137827 -0.0098116534 -0.3750052897 -2.6498553572 -0.4136595362
## [201] 0.0221755013 -0.1162232316 -0.1219916207 -0.0788807007 -0.0538416832
## [206] 2.9505923868 -0.4329866595 -0.1044255642 -0.1162232316 10.6031880635
## [211] 0.3494024265 0.0519524886 -0.2148444652 -0.2515130943 0.2994223186
## [216] 0.0119889728 0.2982766109 -0.0291387767 -0.1617691204 -0.1044255642
## [221] -0.3463515557 -0.3656786789 -0.0988817256 -0.3629220220 -0.1842051138
## [226] -0.3239155623 -2.4565841246 -0.0178265486 -0.0291387767 -0.3656786789
## [231] -0.2341715884 -0.2341715884 -2.3212942619 -0.3270244324 -0.1724074464
## [236] 0.0288425931 -0.0802285041 -0.3750052897 -0.0340087135 -0.1026644974
## [241] 0.3262788977 3.4830405861 -0.2043213010 -0.4136595362 -0.3800055460
## [246] 0.1136805419 -0.3117679568 -0.1861907311 -0.3687875495 -0.0178265486
## [251] -2.3830584039 -2.4410397736 0.1941115388 -0.2646224774 -0.1013166941
## [256] -2.3444041574 0.1523347884 -0.2179533353 -2.4003999098 -0.4230630808
## [261] -0.0091377517 -0.3850058022 -0.3718964196 -2.2171291897 -0.1955173419
## [266] -0.3463515557 -0.1219916207 -0.3432426856 -0.2728258349 -0.3270244324
## [271] -0.3750052897 -0.3208066922 -0.2515130943 -0.0484658999 -0.2228593603
## [276] -0.3463515557 -2.2284414178 -0.1044255642 -2.5918739874 -0.4101727050
## [281] 0.1885677002 -2.4790201184 -2.5183482666 -0.4136595362 -0.4523137827
## [286] -0.3912235429 -2.3106559359 -0.3943324130 -0.1413187440 -0.3750052897
## [291] -0.2852613158 -0.2148444652 -0.3239155623 -0.2148444652 -0.2901673408
## [296] -0.2621514203 0.1754446839 -0.4136595362 -2.4003999098 0.4086955119
## [301] -0.4298777894 0.0626044482 -0.2534987117 -0.2148444652 0.2800951954
## [306] -2.6978362144 -0.2341715884 0.1136805419 -0.3463515557 -0.0153554920
## [311] -0.0988817256 -2.5183482666 -0.1337531999 -0.3687875495 -2.0033581257
## [316] -0.3239155623 -0.4410957858 -0.2228593603 0.1136805419 -0.2540422940
## [321] -0.2708402176 -2.4061682989 3.1862645495 -0.2341715884 -2.7171633377
## [326] -0.3139150498 -0.3463515557 1.1230219848 -2.4796940201 -0.3270244324
## [331] 0.1012586947 -2.9833582992 -2.7171633377 0.0108632736 0.1742408332
## [336] -0.1337531999 -0.2341715884 -0.3750052897 -0.1948434402 -0.3750052897
## [341] -0.4298777894 -0.0602274791 1.6454338499 -2.5376753899 -1.0888105017
## [346] -0.4136595362 -0.3076973092 0.0943534187 -0.1237526874 -0.0215732326
## [351] -0.2783696735 -0.4136595362 -0.2540422940 0.2982766109 -0.1748785030
## [356] -0.2534987117 -0.3656786789 -0.1430798107 -0.2983706984 -2.5936711423
## [361] -0.1182088489 -2.3523219146 -0.2790435751 -0.4105506661 -0.2421864836
## [366] 1.3163291723 -0.0098116534 -0.0291387767 -0.2534987117 2.9505923868
## [371] -0.1162232316 -0.3301333030 -0.0988817256 3.2055916727 -0.3076973092
## [376] -0.3270244324 -2.6650474950 -2.2939883317 -0.2172794336 -0.0564447069
## [381] -0.2341715884 -0.1413187440 -0.1413187440 0.1823363259 -0.3463515557
## [386] -0.2540422940 -0.1955173419 -0.2540422940 -0.2397154269 -2.6112011107
## [391] -0.2540422940 -0.2056876530 -0.2615136068 0.0257974291 -0.1337531999
## [396] 0.0208276979 0.4571257202 -0.2597164519 -0.2397154269 -0.1044255642
## [401] -0.4136595362 -0.0707715739 -0.4136595362 -0.3463515557 2.9505923868
## [406] 0.0339507142 -0.3850058022 -0.3656786789 -0.2197504902 -0.2341715884
## [411] 0.0632647162 -0.3750052897 -0.0098116534 -3.2569661641 -0.2534987117
## [416] -0.1219916207 0.0183927295 -0.3750052897 -0.1786251871 -0.3170239200
## [421] -0.1237526874 -0.1219916207 -0.4105506661 -0.2728258349 -2.6978362144
## [426] 0.0750623836 -0.2341715884 -0.3656786789 -0.3463515557 -0.2534987117
## [431] 0.0943534187 1.5332538826 -0.0291387767 -0.2148444652 0.0557352604
## [436] -0.3463515557 -0.3750052897 -0.3943324130 -0.3656786789 -0.4136595362
## [441] -2.4728023778 3.0547574589 -0.3463515557 -0.2852613158 -0.3076973092
## [446] 0.1136805419 -0.3176978216 -0.4329866595 -0.1044255642 -0.4410957858
## [451] -2.6691824804 -0.4329866595 -0.2540422940 -0.0215732326 -2.4179298781
## [456] -0.3239155623 -0.0022461094 -0.3718964196 -0.2509334239 -1.9965520270
## [461] -0.0489152510 0.1212460860 -0.3656786789 -0.0471180961 -0.1948434402
## [466] -0.2983706984 -0.2534987117 -0.1044255642 -2.4565841246 -0.2597164519
## [471] -0.3525692963 -0.3463515557 -0.3943324130 -0.2341715884 0.0288425931
## [476] 10.3788281285 -0.3014795689 -0.3170239200 0.1941115388 -0.3656786789
## [481] -0.3912235429 -0.3943324130 -0.3943324130 0.0753254091 -0.0291387767
## [486] -0.3656786789 -0.3270244324 -0.2621514203 -0.1724074464 -0.0291387767
## [491] -0.3912235429 -0.3656786789 -2.4141831945 -0.2035322371 1.1735681299
## [496] -0.3463515557 0.5419636691 -0.2534987117 -0.2790435751 -0.2534987117
## [501] -0.1530803232 -0.2341715884 -0.0595535774 -0.2540422940 -0.2983706984
## [506] -0.2621514203 -0.1275354597 -0.3076973092 -0.3656786789 -0.1393331271
## [511] -0.1162232316 0.0095154698 0.0288425931 -0.3270244324 -0.2883701859
## [516] 0.1183060417 0.1254782093 -2.6112011107 10.6031880635 -0.3270244324
## [521] -0.1724074464 -0.1044255642 -0.4136595362 3.0996294457 3.1601749083
## [526] -0.2341715884 0.1523347884 -0.0098116534 -0.0713512448 -0.4217686626
## [531] -0.4145019540 -2.3057499109 -0.0291387767 -0.3912235429 -0.2428242971
## [536] 0.4184714737 -0.2534987117 -0.0291387767 -2.6785090912 -0.3656786789
## [541] -2.6080922405 10.2186673039 -0.3432426856 -0.4136595362 3.3079014473
## [546] -0.3656786789 -0.3432426856 0.4764528435 -0.1237526874 -0.0757718302
## [551] -0.1430798107 -0.1842051138 -0.0602274791 -0.0384653875 -0.2341715884
## [556] -0.2341715884 -0.0215732326 -0.2172794336 -0.0484658999 -0.3943324130
## [561] -0.1413187440 -0.2148444652 -0.1050994659 0.0532778375 -0.4136595362
## [566] -0.0720251465 -0.1044255642 0.1212460860 -0.1842051138 -0.3076973092
## [571] -0.1568630954 -2.4254954222 -0.3525692963 -0.1188827506 -0.4329866595
## [576] -0.4523137827 -0.3094944641 -0.0371175836 -0.2901673408 -0.2534987117
## [581] -0.2534987117 -0.1444276145 2.9730283802 -0.2397154269 0.3262788977
## [586] -0.2534987117 -0.3750052897 -0.3912235429 0.0750623836 -0.1444276145
## [591] -0.2341715884 -0.4136595362 -0.1237526874 -0.1724074464 -0.2534987117
## [596] -0.1611894499 -0.2534987117 -0.2790435751 3.2480286914 -0.0215732326
## [601] -0.4298777894 -0.3718964196 -0.2397154269 -0.2341715884 -2.6978362144
## [606] -0.3943324130 -0.3943324130 -2.4254954222 -0.3750052897 -0.0291387767
## [611] 17.6334127870 -0.3002562196 -0.2403893286 -2.6498553572 -0.3463515557
## [616] -0.0988817256 -0.0757718302 -1.3096033942 -0.0664452194 -0.3750052897
## [621] -0.2303888162 -0.0098116534 -0.0098116534 3.0965205755 -0.1026644974
## [626] -0.3076973092 -0.2540422940 -0.4136595362 -0.4523137827 0.0288425931
## [631] -0.2534987117 -0.1300065163 -0.3076973092 -0.2983706984 -0.4136595362
## [636] -0.2534987117 -0.1182088489 -0.4136595362 -2.7364904609 0.1136805419
## [641] -0.3656786789 -0.3463515557 -0.2397154269 -0.3045884391 -2.7364904609
## [646] 0.2134386620 -0.0595535774 -0.2466070693 -2.3562018248 -0.3076973092
## [651] -0.2534987117 -0.0720251465 -0.1136564904 -0.1624069339 -0.2534987117
## [656] -0.2310627183 13.7793935608 -0.3656786789 -0.3463515557 -0.3094944641
## [661] -0.2534987117 -0.3463515557 -0.1630808356 -2.5463280985 -0.1237526874
## [666] -2.5825473766 -0.4024415393 -0.3750052897 -0.0988817256 -0.0291387767
## [671] -0.2010611804 -0.4136595362 -0.0022461094 -0.3270244324 -0.2172794336
## [676] -0.3656786789 -0.3256461040 -0.1300065163 -0.0291387767 -0.1699724780
## [681] -0.1044255642 -0.2728258349 3.1862645495 -0.2708402176 -2.6978362144
## [686] -0.3656786789 -0.0098116534 -0.0098116534 -0.2534987117 -0.0664452194
## [691] -0.2341715884 -0.0691787894 -2.4228359032 -0.0215732326 -0.0178265486
## [696] -0.2534987117 -0.0988817256 -0.0471180961 0.1523347884 -0.3076973092
## [701] -0.2148444652 -0.2421864836 -0.2708402176 -0.2066411076 -0.3967903613
## [706] -0.1430798107 -0.2228593603 -0.2852613158 10.4019380240 -0.2628253224
## [711] -0.3363510432 -0.3432426856 -0.0371175836 -0.1817340572 -0.2397154269
## [716] -0.2397154269 0.0532778375 -0.2534987117 0.4597629180 -0.2534987117
## [721] 0.7545620249 -0.2540422940 -0.3943324130 -2.2284414178 -0.1237526874
## [726] -0.3463515557 -0.1413187440 -0.0215732326 -0.2397154269 0.1641324558
## [731] -0.1761902187 -2.7252724640 -0.0371175836 -0.4136595362 -0.2870584707
## [736] -0.2534987117 -0.3637872928 -0.0514805388 -0.0291387767 -0.0757718302
## [741] -0.1337531999 10.2666481612 -2.6785090912 -0.3463515557 -0.3239155623
## [746] -0.3494604262 -0.1724074464 -0.0988817256 -0.1106793930 0.0085208922
## [751] 10.1606859342 -0.4523137827 -1.6747970305 -0.3656786789 0.0750623836
## [756] -0.4136595362 -0.4136595362 -0.2677313475 -0.3076973092 -0.2783696735
## [761] -0.2621514203 -0.3656786789 10.3084112779 -0.4246201386 -2.5376753899
## [766] -0.3850058022 -0.0002604921 -0.3912235429 -0.1413187440 -0.2852613158
## [771] -0.2534987117 -0.0098116534 -0.3750052897 -0.3656786789 -0.2397154269
## [776] -0.2540422940 -0.3750052897 -0.3076973092 -0.2397154269 -2.6112011107
## [781] -0.2341715884 -0.3463515557 -0.0240306556 -0.3270244324 -0.1206438173
## [786] -0.2615136068 -0.1392021760 -0.0788807007 -0.3943324130 0.0090661187
## [791] -2.4990211434 10.1800130574 -0.2473114961 10.2666481612 -0.2148444652
## [796] -1.8131957633 -0.2341715884 -0.1413187440 -0.1637547378 0.0656996847
## [801] -0.0564447069 -0.3463515557 10.9424011184 17.5181239492 -0.1886256995
## [806] -0.3432426856 -0.1815671650 -0.3432426856 -0.2534987117 -0.3687875495
## [811] -0.0098116534 -0.3750052897 -0.0291387767 -0.0098116534 -0.1026644974
## [816] -0.4329866595 -0.3239155623 -0.1444276145 -0.3943324130 10.1993401807
## [821] -0.0995556273 -0.2421864836 -0.3656786789 -0.4461730515 -0.3750052897
## [826] -0.2621514203 -0.0215732326 -0.2315222511 -0.2983706984 -0.3687875495
## [831] 10.2635392907 -0.3943324130 -0.1955173419 -0.1044255642 0.0532778375
## [836] 4.6251289252 -0.0215732326 -0.3656786789 -0.1955173419 13.9001320060
## [841] -2.6785090912 0.1136805419 -0.1955173419 -0.2484042242 0.1523347884
## [846] -0.0982078240 -0.0833373742 0.0750623836 -0.2110616929 -0.2172794336
## [851] -0.1237526874 -0.2148444652 3.3257865356 -0.3850058022 -2.4141831945
## [856] -0.1724074464 -0.1219916207 -0.3463515557 -0.3850058022 -0.4136595362
## [861] -0.2534987117 -2.6498553572 0.1136805419 -0.2534987117 -0.2421864836
## [866] -0.2484042242 0.2027867023 -0.3463515557 -0.1168971333 0.0681707413
## [871] -0.1430798107 -0.2341715884 -0.1156435611 -0.3912235429 -2.6305282339
## [876] 0.0463725614 -0.3912235429 -0.0651335042 -0.1219916207 -0.4136595362
## [881] -0.3270244324 -0.0833373742 0.2053654906 0.1136805419 -2.3854933723
## [886] -0.0564447069 -0.3943324130 -0.1044255642 -0.3270244324 -0.3750052897
## [891] -2.3133154549 -2.1511690130 3.1556251985 -0.1337531999 -0.2341715884
## [896] -0.3850058022 10.2859752845 -0.3656786789 -2.6591819679 -0.0291387767
## [901] -0.2397154269 -0.0215732326 -0.4024415393 0.0288425931 -2.4952383711
## [906] 3.2211721123 -0.4136595362 -0.2172794336 -0.1810962437 -0.1237526874
## [911] -0.1106793930 -0.2172794336 -0.2341715884 -0.3750052897 -0.3750052897
## [916] 0.0670474885 -0.2172794336 -0.2540422940 -0.3750052897 -0.1044255642
## [921] -0.3094944641 -0.0291387767 -0.3463515557 -0.4136595362 -0.0932075673
## [926] -0.2284974300 -0.4252721284 -0.0291387767 -0.2341715884 -0.1724074464
## [931] -2.6947273443 -0.4136595362 0.0121749888 -0.2534987117 -0.2110616929
## [936] -0.1219916207 -0.2534987117 3.2871322891 -0.3656786789 -0.2553165193
## [941] -0.3750052897 -0.2341715884 -0.2534987117 -0.2621514203 -0.1237526874
## [946] 0.0095154698 10.4829932006 -0.2148444652 0.2272219467 -0.3239155623
## [951] -2.5376753899 -0.0988817256 -0.0446831277 -0.3270244324 0.0015005747
## [956] -0.4136595362 -0.1044255642 -0.2783696735 -2.6129982656 -0.2901673408
## [961] -0.3463515557 0.0015005747 -0.1954231107 -0.2341715884 -2.2844371703
## [966] -0.0888812132 -0.3432426856 -0.3076973092 0.1088106051 17.6396305272
## [971] -0.3625698088 -0.1300065163 -0.1300065163 3.1731912551 -0.1237526874
## [976] -0.1886256995 -0.1219916207 -0.3912235429 -0.3076973092 -2.6305282339
## [981] 0.0657133183 -0.2341715884 -0.4136595362 -0.2821524457 -0.1219916207
## [986] -0.4329866595 -2.6947273443 -0.2341715884 -0.0098116534 -2.6391559415
## [991] -0.4136595362 -0.1386592249 -0.3432426856 -0.2883701859 -0.3943324130
## [996] -0.2690430627 0.0626044482 -0.1842051138 10.2921930247 -0.3943324130
## [1001] -0.0995556273 -0.2148444652 -0.3463515557 -0.2515130943 -0.3356466164
## [1006] -0.4523137827 0.4516537916 -0.3943324130 -0.0602274791 0.1012586947
## [1011] -0.3718964196 -0.4010455719 -0.3270244324 -0.2534987117 -2.5356897726
## [1016] -0.4136595362 0.0632647162 -0.0913522698 -0.0215732326 0.2858411300
## [1021] -2.7477084578 -0.4329866595 0.1136805419 -0.0215732326 0.0863746117
## [1026] -2.5222726754 -0.3750052897 -2.5725468641 0.3001456757 -0.3076973092
## [1031] -0.2534987117 -0.2852613158 -0.3270244324 -0.2403893286 -0.1413187440
## [1036] -2.2202380603 -2.6080922405 -0.0720251465 3.4492787309 -2.6274193638
## [1041] -2.6978362144 -0.3943324130 -2.5356897726 0.0064065997 -0.3463515557
## [1046] -0.3656786789 -0.4136595362 -0.3750052897 -0.2495550954 -0.3850058022
## [1051] -2.6498553572 -0.2901673408 0.1136805419 -0.2341715884 -0.3687875495
## [1056] 2.9312652636 -0.2397154269 10.2514560234 10.3732842900 -0.3943324130
## [1061] 0.0806062222 -0.0215732326 -0.2397154269 -0.3270244324 -0.3750052897
## [1066] -0.0291387767 -0.2148444652 0.1136805419 -0.2341715884 -0.2534987117
## [1071] 0.0943534187 -0.1106793930 -2.5463280985 -0.3943324130 -0.0950989534
## [1076] -2.5438931301 -0.3239155623 -0.3525692963 -0.2540422940 -2.5376753899
## [1081] -0.0964467572 -0.3850058022 -0.1275354597 -0.1842051138 -0.1337531999
## [1086] -0.3239155623 10.6031880635 -0.2403071812 -0.3270244324 -0.1413187440
## [1091] -0.3432426856 -1.7907597700 -0.4523137827 -0.1385926121 0.0639386179
## [1096] -0.2397154269 -0.4105506661 -0.3996006940 -0.2902615720 -0.3432426856
## [1101] -0.3625698088 -0.3239155623 -0.1668636079 -0.1337531999 0.0288425931
## [1106] -0.2391540784 -0.3463515557 2.9892466333 0.1136805419 -0.3750052897
## [1111] -0.3943324130 -0.0146815903 -0.0720251465 -0.3656786789 0.0632647162
## [1116] -0.2534987117 -0.2534987117 -2.3444041574 -0.4329866595 -0.4136595362
## [1121] 0.0863746117 -0.3656786789 -2.6498553572 -0.3750052897 -0.2728258349
## [1126] 0.0146235909 -0.2290771010 -0.0757718302 -0.2650689217 -0.1113172065
## [1131] -0.0098116534 0.1254782093 -2.6305282339 -0.1955173419 -0.3463515557
## [1136] 3.1862645495 -0.4136595362 -0.2172794336 -0.2515130943 -0.0098116534
## [1141] -0.3463515557 -0.4523137827 3.2678051658 -0.1337531999 2.9792461208
## [1146] -0.0720251465 -0.3463515557 0.0121749888 -0.2060614367 -0.3750052897
## [1151] -0.3850058022 -2.6305282339 -0.2397154269 -0.2148444652 -0.3656786789
## [1156] -0.2228593603 -0.4329866595 -0.0098116534 -2.5376753899 -0.0308998434
## [1161] -0.3656786789 -0.3463515557 -0.1761902187 0.7592685526 -0.3463515557
## [1166] -0.0215732326 -0.4329866595 -0.0291387767 -0.2728258349 -0.0098116534
## [1171] -0.1842051138 -0.2534987117 0.0674968396 -0.3463515557 -0.2621514203
## [1176] -0.1724074464 -0.2341715884 -0.2228593603 -0.0913522698 -0.2534987117
## [1181] 10.5838609402 -0.3239155623 -0.2341715884 -0.1026644974 -0.2397154269
## [1186] 3.2678051658 -2.4952383711 -2.4565841246 -0.4136595362 -0.2373372118
## [1191] 17.9026447087 0.0626044482 -0.1237526874 2.9730283802 -0.1300065163
## [1196] -0.0098116534 -0.1955173419 -0.3006142981 -0.2421864836 -0.1842051138
## [1201] -0.4298777894 -0.1193321017 -0.3076973092 -0.3463515557 -0.1337531999
## [1206] -0.0833373742 -0.4136595362 9.0210550180 -0.4136595362 -0.3750052897
## [1211] -0.2148444652 -0.3656786789 -0.2334948236 0.5413977655 -0.3463515557
## [1216] -0.2341715884 -0.4105506661 -0.3463515557 -0.2790435751 -0.3239155623
## [1221] -0.1661897062 -0.2540422940 -0.3656786789 -0.2341715884 -0.3750052897
## [1226] -0.4105707193 -0.3014795689 -0.1044255642 -0.2885310304 -2.5463280985
## [1231] 0.0095154698 -0.0098116534 -0.0720251465 -0.4136595362 -0.1499714530
## [1236] 10.2379944272 -0.1855168294 -0.2540422940 -0.2397154269 -0.3463515557
## [1241] -0.3912235429 -0.1300065163 -0.3076973092 -0.2945879266 -0.2341715884
## [1246] -0.3463515557 -0.0884922800 -0.3463515557 -0.2484042242 -0.2421864836
## [1251] -0.1044255642 0.0146235909 -0.2010611804 -0.3463515557 -0.1219916207
## [1256] 3.0347925222 -0.2983706984 -0.4105506661 -2.7364904609 -0.1044255642
## [1261] 3.0067766016 3.3912973612 -2.6080922405 -0.2534987117 -0.2397154269
## [1266] -0.0098116534 -0.3288215874 -0.1477278538 -0.3378258784 -0.2452953541
## [1271] -0.0291387767 -0.2540422940 -0.3850058022 0.0090661187 10.2859752845
## [1276] -0.1724074464 -0.3342682880 -0.3014795689 -2.2746612084 0.0095154698
## [1281] -0.4329866595 14.0622784479 -0.2397154269 -0.1237526874 -0.0291387767
## [1286] 3.1669374262 -0.2341715884 -0.2534987117 -0.2397154269 -0.0371175836
## [1291] -0.4329866595 -0.1892996012 -0.1188827506 -1.9167230220 3.1127388287
## [1296] -2.4397280580 -0.1955173419 -0.0215732326 -0.4329866595 -0.3943324130
## [1301] -0.1430798107 -0.3432426856 -2.6498553572 -0.2172794336 -0.2621514203
## [1306] -0.2341715884 -0.3076973092 -0.4329866595 -0.3174943810 -0.2983706984
## [1311] -0.3912235429 -0.3850058022 -0.2228593603 -2.6978362144 -2.4272564889
## [1316] -0.3656786789 10.2666481612 -2.2732191734 -2.4565841246 0.0532778375
## [1321] -0.3718964196 0.1212460860 -0.1050994659 -0.0098116534 -2.5183482666
## [1326] 0.1523347884 10.2921930247 -0.3943324130 -0.0489152510 -0.2397154269
## [1331] -0.4523137827 -0.0291387767 3.0434452308 0.4061079028 -2.5270009753
## [1336] -2.4079293657 -2.4079293657 -0.4096111857 0.0288425931 -0.2598379162
## [1341] -0.0098116534 -0.2341715884 -2.6978362144 -0.0098116534 -0.3463515557
## [1346] -2.6403679023 0.0721240719 -0.0775689851 -2.6591819679 -0.1044255642
## [1351] -0.2621514203 -0.3463515557 -0.2341715884 -0.2852613158 -0.2397154269
## [1356] -2.5183482666 -0.3656786789 0.0095154698 -0.2389642699 -0.3076973092
## [1361] -0.4136595362 -2.4179298781 -0.2534987117 -0.1300065163 -0.1106793930
## [1366] -0.2148444652 -0.4136595362 -0.1748785030 -0.3750052897 -0.0937872382
## [1371] -0.1300065163 -0.0713512448 -2.5376753899 -0.3463515557 -0.2901673408
## [1376] -0.3463515557 -0.0098116534 -2.6112011107 -0.1948434402 -2.5183482666
## [1381] -0.1724074464 -0.3881146727 -0.0399582901 -0.2534987117 -2.5376753899
## [1386] -0.3750052897 -0.2534987117 -0.3525692963 0.2027867023 -0.2284974300
## [1391] -0.4329866595 -0.0098116534 -0.1386592249 -0.0291387767 -0.3432426856
## [1396] -0.2852613158 -0.3943324130 -0.3076973092 -0.0988817256 -0.2852613158
## [1401] -0.0720251465 -0.2534987117 -0.2341715884 -0.0937872382 -0.2628253224
## [1406] -2.4079293657 -0.2341715884 -0.1413187440 -0.3463515557 0.0288425931
## [1411] -0.4136595362 -0.2864787998 -0.0819895708 -0.2621514203 -0.3750052897
## [1416] -0.3687875495 -2.5625463517 -0.2790435751 -0.0819895708 -0.2621514203
## [1421] -0.4136595362 -0.3625698088 -0.1724074464 -0.3239155623 -0.1106793930
## [1426] -0.0098116534 -0.1724074464 -0.0102610045 -0.3463515557 -0.3463515557
## [1431] 0.1205858180 -0.1237526874 10.5304304756 -0.2534987117 -0.3045884391
## [1436] -0.2728258349 -2.3886022424 -0.3850058022 -0.1013166941 -0.1219916207
## [1441] -0.3463515557 -0.0098116534 -0.0658074059 -0.2341715884 -0.1842051138
## [1446] -0.1337531999 -0.2086267245 -0.0098116534 -0.1886256995 -0.4298777894
## [1451] -0.0098116534 -0.4136595362 0.0288425931 -0.1237526874 -0.3656786789
## [1456] -0.0757718302 -0.1044255642 -2.3730578914 -0.2852613158 -0.1219916207
## [1461] -0.2534987117 -0.2534987117 -0.2821524457 0.0988903063 -0.3045884391
## [1466] -1.9734421315 -0.2148444652 -0.2515130943 -0.2341715884 -2.2944376828
## [1471] 0.0288425931 -0.2397154269 -0.4136595362 -0.2403893286 -0.2708402176
## [1476] -0.3463515557 -0.4329866595 -0.2531448542 0.0146235909 -0.2397154269
## [1481] -0.0869898271 -0.4136595362 -0.0215732326 10.7560215283 -0.3750052897
## [1486] 3.3912973612 -0.3463515557 0.0103157716 -0.4136595362 -0.1413187440
## [1491] -0.2421864836 -0.2039048889 -0.3234025047 3.2791173939 -0.0098116534
## [1496] -0.3045884391 0.0481697163 -0.3270244324 -0.3687875495 -0.2372804585
## [1501] 0.0819315715 -2.5625463517 -0.4136595362 -0.2534987117 -0.0291387767
## [1506] -0.1555513798 -0.3270244324 -0.2352282284 -2.6274193638 -2.6591819679
## [1511] -0.1337531999 -0.0264792577 0.0863746117 -0.1144260767 -0.0098116534
## [1516] -0.4136595362 -0.3076973092 -0.3270244324 -0.2540422940 0.0519524886
## [1521] -0.4136595362 -0.2790435751 -0.2341715884 -0.3943324130 -0.3750052897
## [1526] -0.0215732326 -0.0291387767 -0.2566075818 -0.0471180961 -0.3045884391
## [1531] -0.3463515557 0.0095154698 -0.0215732326 -0.3943324130 -0.3463515557
## [1536] -0.3045884391 0.1661180732 3.3064594123 -1.9840310025 -2.4079293657
## [1541] -2.6978362144 -0.3656786789 -0.3750052897 -2.0033581257 -2.5183482666
## [1546] 4.4654826112 -0.2870584707 -0.1474422534 -0.1851646158 -0.2397154269
## [1551] -0.2341715884 -2.4179298781 -0.3270244324 -0.2534987117 -0.0146815903
## [1556] 0.2140989304 -0.1106793930 -0.0102610045 -0.2397154269 -0.2901673408
## [1561] -0.0098116534 -0.2168893135 -0.0291387767 0.0415026246 -0.1955173419
## [1566] -0.3831144161 -0.3656786789 10.2604304206 -0.1337531999 -0.1013166941
## [1571] -0.3556781665 -0.4329866595 -0.1044255642 -0.3881146727 -0.0098116534
## [1576] 0.0288425931 -0.1399709406 -0.0291387767 -0.3750052897 -0.3463515557
## [1581] -0.1393331271 0.0674968396 -2.4684400683 10.2666481612 -0.0371175836
## [1586] 3.1525163280 -0.3687875495 -0.1337531999 -0.2197504902 10.3788281285
## [1591] -0.3270244324 -0.3881146727 -0.3270244324 0.0042267065 -0.2035322371
## [1596] -0.1094258204 -0.1106793930 -0.1162232316 0.0295164948 -0.2397154269
## [1601] -0.4298777894 -0.1044255642 -0.0291387767 -2.6978362144 -2.6305282339
## [1606] -0.2534987117 -0.2452953541 -0.2883701859 -0.3463515557 -0.3208066922
## [1611] -0.3656786789 -0.1106793930 -0.0371175836 -0.2534987117 -0.3239155623
## [1616] -1.9840310025 0.0632647162 -0.1955173419 -0.1296182145 -0.0098116534
## [1621] -0.1955173419 -0.1955173419 -1.6074890499 -0.4523137827 0.1136805419
## [1626] -0.2540422940 0.1254782093 -0.2228593603 -0.0291387767 -0.1144260767
## [1631] 0.1885677002 -0.0291387767 0.1019189627 -2.4928034027 -0.2341715884
## [1636] -0.2341715884 -0.1337531999 -0.2534987117 -0.1668636079 -2.4351476331
## [1641] 10.7266802589 -0.3656786789 -2.5376753899 -0.1337531999 -0.1341054135
## [1646] 0.1187303868 -0.3912235429 -0.4217686626 -0.2540422940 -0.3656786789
## [1651] -2.6978362144 -0.3288215874 -0.0098116534 -2.6947273443 0.1136805419
## [1656] -0.1300065163 -0.2540422940 0.4067098945 -0.2397154269 -0.0002604921
## [1661] -0.6817818388 -0.2086267245 17.6589576505 -0.1337531999 -0.3270244324
## [1666] -0.4105506661 -0.3326464758 -2.4179298781 -0.3041604994 -0.2515130943
## [1671] -0.3750052897 3.2822623522 -0.1506453547 -0.3176978216 -0.2341715884
## [1676] -0.3270244324 -2.5887651173 -0.1337531999 -0.2231127917 -0.2428242971
## [1681] 0.0626044482 -0.1724074464 -0.2148444652 -2.4565841246 -0.2621514203
## [1686] 0.1136805419 -0.3943324130 -0.2276462085 -0.2534987117 -0.1437537124
## [1691] -0.0098116534 -0.3850058022 -0.4298777894 -0.1362242565 -0.4136595362
## [1696] -0.2587569499 2.9119381403 -0.1337531999 -0.3943324130 -0.2148444652Conclusiones
De manera general se puede observar claramente que dividir las variables en grupos resulta mejor para la vizualización y comprensión de resultados.
El Análisis de Componentes Principales ayuda a reducir la dimensión de la data, siempre y cuando las variables no estén incorrelacionadas pues las componentes que genera son de la misma dimensión si solo se trabaja con variables numéricas y de mayor dimensión que las variables originales si trabajamos con variables categóricas.