library(readxl)
datos <- read_excel("C:/Users/Yohana Argueta/Desktop/datos_parcial_2.xlsx")
datos1<-datos[,-2]
head(datos1)

## # A tibble: 6 x 9
##      ID    X1    X2    X3    X4    X5    X6    X7    X8
##   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1     1     9     2  20    20     0    0        2  56.4
## 2     2    10     6  62.5  50    37.5  3.95    11 147. 
## 3     3    10    20  50    50    50    2.56    16 135  
## 4     4     8     3  42.9  42.9  14.3  1.35    35 121. 
## 5     5     7     7  75    75    75    9.09     8 202. 
## 6     6     6    13  30    30    30    8.11    25  81

datos2<-datos1[,-1]
head(datos2)

## # A tibble: 6 x 8
##      X1    X2    X3    X4    X5    X6    X7    X8
##   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1     9     2  20    20     0    0        2  56.4
## 2    10     6  62.5  50    37.5  3.95    11 147. 
## 3    10    20  50    50    50    2.56    16 135  
## 4     8     3  42.9  42.9  14.3  1.35    35 121. 
## 5     7     7  75    75    75    9.09     8 202. 
## 6     6    13  30    30    30    8.11    25  81

MATRIZ DE CARGAS

library(Hmisc)
library(readr)
library(stargazer)
Mat_R<-rcorr(as.matrix(datos2))
descomposicion<-eigen(Mat_R$r)
stargazer(descomposicion$values,type = "text")

## 
## ===============================================
## 3.897 1.964 0.841 0.500 0.454 0.276 0.066 0.002
## -----------------------------------------------

stargazer(descomposicion$vectors,type = "text")

## 
## ======================================================
## 0.160  0.537 -0.059 0.734  0.358  -0.128 0.005  -0.003
## 0.063  0.593 0.077  -0.076 -0.788 -0.107 -0.001 0.009 
## -0.473 0.074 0.283  0.083  0.023  0.105  -0.806 -0.151
## -0.474 0.106 0.314  0.024  0.057  0.035  0.523  -0.622
## -0.396 0.080 -0.490 -0.189 0.099  -0.741 -0.044 -0.009
## -0.347 0.087 -0.691 0.120  -0.123 0.601  0.056  0.004 
## 0.127  0.565 0.001  -0.630 0.467  0.218  -0.044 -0.006
## -0.479 0.100 0.307  0.031  0.067  0.040  0.264  0.768 
## ------------------------------------------------------

SOLUCION CON 3 FACTORES

library(psych)
modelo<-principal(r = datos2,nfactors = 3,covar = FALSE,rotate = "none")
modelo

## Principal Components Analysis
## Call: principal(r = datos2, nfactors = 3, rotate = "none", covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##      PC1  PC2   PC3   h2     u2 com
## X1 -0.32 0.75  0.05 0.67 0.3316 1.4
## X2 -0.12 0.83 -0.07 0.71 0.2879 1.1
## X3  0.93 0.10 -0.26 0.95 0.0493 1.2
## X4  0.94 0.15 -0.29 0.98 0.0208 1.2
## X5  0.78 0.11  0.45 0.83 0.1742 1.6
## X6  0.68 0.12  0.63 0.89 0.1142 2.1
## X7 -0.25 0.79  0.00 0.69 0.3107 1.2
## X8  0.94 0.14 -0.28 0.99 0.0087 1.2
## 
##                        PC1  PC2  PC3
## SS loadings           3.90 1.96 0.84
## Proportion Var        0.49 0.25 0.11
## Cumulative Var        0.49 0.73 0.84
## Proportion Explained  0.58 0.29 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  0.06 
##  with the empirical chi square  21.68  with prob <  0.0029 
## 
## Fit based upon off diagonal values = 0.98

SOLUCION ROTADA

library(psych)
modelo_5<-principal(r = datos2,nfactors = 3,covar = FALSE,rotate = "varimax")
modelo_5$loadings

## 
## Loadings:
##    RC1    RC2    RC3   
## X1 -0.162  0.801       
## X2         0.840       
## X3  0.930         0.278
## X4  0.954         0.260
## X5  0.428         0.800
## X6  0.250         0.907
## X7         0.826       
## X8  0.957         0.270
## 
##                  RC1   RC2   RC3
## SS loadings    2.974 2.046 1.682
## Proportion Var 0.372 0.256 0.210
## Cumulative Var 0.372 0.628 0.838

EN LA SOLUCION QUEDAN INCLUIDAS PARA EL FACTOR 1: X3, X4 Y X8

EN LA SOLUCION QUEDAN INCLUIDAS PARA EL FACTOR 2: X1, X2 Y X7

EN LA SOLUCION QUEDAN INCLUIDAS PARA EL FACTOR 3: X5 Y X6

FUNCIONES PARA NORMALIZAR LOS DATOS

norm_directa <- function(x){
return((x-min(x)) / (max(x)-min(x)))
}
norm_inverza <- function(x){
return((max(x)-x) / (max(x)-min(x)))
}

PONDERADORES NORMALIZADOS PARA CADA FACTOR

PONDERADORES NORMALIZADOS PARA EL FACTOR 1

library(dplyr)
datos2 %>% dplyr::select(X3,X4,X8) %>% dplyr::transmute(X3=norm_inverza(X3), X4=norm_inverza(X4), X8=norm_inverza(X8) ) ->data_factor_1
print(data_factor_1)

## # A tibble: 108 x 3
##       X3    X4    X8
##    <dbl> <dbl> <dbl>
##  1 0.96  0.8   0.842
##  2 0.45  0.5   0.483
##  3 0.6   0.5   0.532
##  4 0.686 0.571 0.587
##  5 0.3   0.25  0.266
##  6 0.84  0.7   0.745
##  7 0.327 0.273 0.286
##  8 0.45  0.5   0.554
##  9 0.6   0.563 0.567
## 10 0.320 0.467 0.448
## # ... with 98 more rows

PONDERADORES NORMALIZADOS PARA EL FACTOR 2

library(dplyr)
datos2 %>% dplyr::select(X1,X2,X7) %>% dplyr::transmute(X1=norm_inverza(X1), X2=norm_inverza(X2), X7=norm_inverza(X7) ) ->data_factor_2
print(data_factor_2)

## # A tibble: 108 x 3
##       X1    X2    X7
##    <dbl> <dbl> <dbl>
##  1 0.806 1     1    
##  2 0.774 0.983 0.901
##  3 0.774 0.923 0.846
##  4 0.839 0.996 0.637
##  5 0.871 0.979 0.934
##  6 0.903 0.953 0.747
##  7 0.742 0.970 0.923
##  8 0.806 0.996 0.956
##  9 0.774 0.991 0.967
## 10 0.710 0.983 0.956
## # ... with 98 more rows

PONDERADORES NORMALIZADOS PARA EL FACTOR 3

library(dplyr)
datos2 %>% dplyr::select(X5,X6) %>% dplyr::transmute(X5=norm_inverza(X5), X6=norm_inverza(X6) ) ->data_factor_3
print(data_factor_3)

## # A tibble: 108 x 2
##       X5    X6
##    <dbl> <dbl>
##  1 1     1    
##  2 0.571 0.784
##  3 0.429 0.860
##  4 0.837 0.926
##  5 0.143 0.503
##  6 0.657 0.557
##  7 0.273 0.497
##  8 0.714 0.852
##  9 0.857 0.752
## 10 0.543 0.538
## # ... with 98 more rows

METODO CRITIC FACTOR 1

CALCULO DE LAS DESVIACIONES ESTANDAR PARA CADA VARIABLE

data_factor_1 %>% dplyr::summarise(S=sd(X3),Y=sd(X4),Z=sd(X4))-> sd_vector
print(sd_vector)

## # A tibble: 1 x 3
##       S     Y     Z
##   <dbl> <dbl> <dbl>
## 1 0.246 0.201 0.201

CALCULO DE LA MATRIZ DE CORRELACION

cor(data_factor_1)->mat_R_F1
print(mat_R_F1)

##           X3        X4        X8
## X3 1.0000000 0.9387159 0.9590445
## X4 0.9387159 1.0000000 0.9958479
## X8 0.9590445 0.9958479 1.0000000

CALCULO DE LOS PONDERADORES BRUTOS

1-mat_R_F1->sum_data
colSums(sum_data)->sum_vector
sd_vector*sum_vector->vj
print(vj)

##            S          Y           Z
## 1 0.02517949 0.01316004 0.009071691

CALCULO DE LOS PONDERADORES NETOS

vj/sum(vj)->wj
print(wj)

##           S         Y         Z
## 1 0.5310871 0.2775722 0.1913406

PONDERADORES

print(round(wj*100,2))

##       S     Y     Z
## 1 53.11 27.76 19.13

METODO ENTROPIA FACTOR 2

NORMALIZACION DE LOS DATOS

datos2 %>% dplyr::select(X1,X2,X7)->data_norm
apply(data_norm,2,prop.table)->data_norm
head(data_norm,n=10)

##                X1           X2          X7
##  [1,] 0.007812500 0.0007073386 0.001398601
##  [2,] 0.008680556 0.0021220159 0.007692308
##  [3,] 0.008680556 0.0070733864 0.011188811
##  [4,] 0.006944444 0.0010610080 0.024475524
##  [5,] 0.006076389 0.0024756852 0.005594406
##  [6,] 0.005208333 0.0045977011 0.017482517
##  [7,] 0.009548611 0.0031830239 0.006293706
##  [8,] 0.007812500 0.0010610080 0.004195804
##  [9,] 0.008680556 0.0014146773 0.003496503
## [10,] 0.010416667 0.0021220159 0.004195804

FORMULA DE ENTROPIA

entropy<-function(x){
  return(x*log(x))
}
apply(data_norm,2,entropy)->data_norm_2
head(data_norm_2,n=10)

##                X1           X2           X7
##  [1,] -0.03790649 -0.005131035 -0.009192004
##  [2,] -0.04120373 -0.013061833 -0.037442573
##  [3,] -0.04120373 -0.035023278 -0.050269550
##  [4,] -0.03451259 -0.007266351 -0.090806195
##  [5,] -0.03100991 -0.014857176 -0.029012521
##  [6,] -0.02738279 -0.024745742 -0.070743949
##  [7,] -0.04441402 -0.018302144 -0.031897795
##  [8,] -0.03790649 -0.007266351 -0.022966449
##  [9,] -0.04120373 -0.009281491 -0.019776195
## [10,] -0.04754529 -0.013061833 -0.022966449

NUMERO DE VARIABLES EN EL FACTOR

ncol(data_norm)->m
m

## [1] 3

CONSTANTE DE ENTROPIA

-1/log(m)->K
print(K)

## [1] -0.9102392

CALCULO DE LAS ENTROPIAS

K*colSums(data_norm_2)->Ej
print(Ej)

##       X1       X2       X7 
## 4.180549 3.202899 3.701923

CALCULO DE LAS ESPECIFICIDADES

1-Ej->vj
print(vj)

##        X1        X2        X7 
## -3.180549 -2.202899 -2.701923

CALCULO DE LOS PONDERADORES

prop.table(vj)->wj #es igual a usar vj/sum(vj)
print(wj)

##        X1        X2        X7 
## 0.3933708 0.2724549 0.3341743

METODO DE RANKING PARA FACTOR 3

library(readxl)
datos100 <- read_excel("C:/Users/Yohana Argueta/Desktop/subjetivo.xlsx")
datos100

## # A tibble: 4 x 8
##   ..1     ..2 `Rank Sum` ..4   `Ran reciprocal` ..6   `Rank exponent` ..8  
##   <chr> <dbl> <chr>      <chr> <chr>            <chr> <chr>           <chr>
## 1 <NA>     NA Weigth     Norm~ Weight           Norm~ Weight          Norm~
## 2 X5        5 -2         0.4   0.2              0.54~ 4               0.30~
## 3 X6        6 -3         0.6   0.1666666666666~ 0.45~ 9               0.69~
## 4 Total    NA -5         1     0.3666666666666~ 0.99~ 13              1

PARCIAL 2

DENIS FERNANDO FLAMENCO NOLASCO

23 de octubre de 2019

MATRIZ DE CARGAS

SOLUCION CON 3 FACTORES

SOLUCION ROTADA

FUNCIONES PARA NORMALIZAR LOS DATOS

PONDERADORES NORMALIZADOS PARA CADA FACTOR

PONDERADORES NORMALIZADOS PARA EL FACTOR 1

PONDERADORES NORMALIZADOS PARA EL FACTOR 2

PONDERADORES NORMALIZADOS PARA EL FACTOR 3

METODO CRITIC FACTOR 1

CALCULO DE LAS DESVIACIONES ESTANDAR PARA CADA VARIABLE

CALCULO DE LA MATRIZ DE CORRELACION

CALCULO DE LOS PONDERADORES BRUTOS

CALCULO DE LOS PONDERADORES NETOS

PONDERADORES

METODO ENTROPIA FACTOR 2

NORMALIZACION DE LOS DATOS

FORMULA DE ENTROPIA

NUMERO DE VARIABLES EN EL FACTOR

CONSTANTE DE ENTROPIA

CALCULO DE LAS ENTROPIAS

CALCULO DE LAS ESPECIFICIDADES

CALCULO DE LOS PONDERADORES

METODO DE RANKING PARA FACTOR 3