Indicador económico

Cargar datos del indicador económico

library(readxl)
library(kableExtra)
IE <- read_excel("C:/Users/Carlos/Desktop/Documentos universidad/EDD 1 Documentos UES/Repaso R studios/Datos preliminares/IndicadorEconomico.xlsx")
head(IE, 5)
## # A tibble: 5 x 13
##    Años   PIB   FBK  Gg_S     X   IPC   IDH  PIBpp   Ins G_edusup Gemp_ID Invest
##   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl>    <dbl>   <dbl>  <dbl>
## 1  2000 5497. 1259.  674.  713.  80.4  80.4 30263.  63.5    1790.    104.  3361.
## 2  2001 5659. 1267.  731.  668.  82.6  82.6 30436.  63.7    1960.    111.  3512.
## 3  2002 5847. 1253.  800.  652.  84.2  84.2 31096.  68.7    2215.    106.  3638.
## 4  2003 6175. 1328.  872.  683.  86.3  86.3 33849.  70.2    2419.    110.  3686.
## 5  2004 6618. 1459.  939.  780.  88.2  88.2 36874.  70.9    2618.    115.  3904.
## # ... with 1 more variable: PT <dbl>

Definición de indicadores.

library(printr)
## Registered S3 method overwritten by 'printr':
##   method                from     
##   knit_print.data.frame rmarkdown
Num1<- c(1,2,3,4,5,6,7,8,9,10,11,12)
Indi1 <- c("PIB", "Formación bruta de capital/PIB", "Gasto público en salud/PIB", "Exportación de bienes y servicios", "Inflación", "IDH", "PIB per cápita", "Inscripción escolar nivel terciario", "Gasto en educación superior en I + D","Gasto empresarial en I+D", "Investigadores dedicados a investigación y desarrollo", "Productividad laboral")
Fuente1 <- c("Banco Mundial", "Banco Mundial", "Banco Mundial", "Banco Mundial", "Banco Mundial", "ONU", "Banco Mundial", "Banco Mundial", "OCDE", "Banco Mundial", "Banco Mundial", "OCDE")

dataf1 <- data.frame(Num1, Indi1, Fuente1)
dataf1
Num1 Indi1 Fuente1
1 PIB Banco Mundial
2 Formación bruta de capital/PIB Banco Mundial
3 Gasto público en salud/PIB Banco Mundial
4 Exportación de bienes y servicios Banco Mundial
5 Inflación Banco Mundial
6 IDH ONU
7 PIB per cápita Banco Mundial
8 Inscripción escolar nivel terciario Banco Mundial
9 Gasto en educación superior en I + D OCDE
10 Gasto empresarial en I+D Banco Mundial
11 Investigadores dedicados a investigación y desarrollo Banco Mundial
12 Productividad laboral OCDE

Resumen estadístico de variables: numérico.

IE1 <- IE[,-1]
summary(IE1[,1:12])
PIB FBK Gg_S X IPC IDH PIBpp Ins G_edusup Gemp_ID Invest PT
Min. : 5497 Min. :1253 Min. : 673.6 Min. : 651.7 Min. : 80.43 Min. : 80.43 Min. :30263 Min. :63.46 Min. :1790 Min. :103.6 Min. :3361 Min. :49.36
1st Qu.: 6982 1st Qu.:1501 1st Qu.: 988.7 1st Qu.: 846.7 1st Qu.: 90.09 1st Qu.: 90.09 1st Qu.:39361 1st Qu.:70.97 1st Qu.:2708 1st Qu.:118.2 1st Qu.:3934 1st Qu.:54.23
Median : 8217 Median :1746 Median :1280.7 Median :1172.3 Median : 99.17 Median : 99.17 Median :47723 Median :76.09 Median :3358 Median :150.7 Median :4268 Median :57.42
Mean : 8338 Mean :1749 Mean :1274.7 Mean :1129.5 Mean : 99.12 Mean : 99.12 Mean :45202 Mean :74.08 Mean :3231 Mean :156.2 Mean :4102 Mean :56.68
3rd Qu.: 9722 3rd Qu.:2013 3rd Qu.:1549.3 3rd Qu.:1389.8 3rd Qu.:108.18 3rd Qu.:108.18 3rd Qu.:52260 3rd Qu.:77.70 3rd Qu.:3728 3rd Qu.:179.8 3rd Qu.:4358 3rd Qu.:59.91
Max. :11585 Max. :2420 Max. :1865.0 Max. :1539.6 Max. :117.00 Max. :117.00 Max. :55746 Max. :79.21 Max. :4405 Max. :250.1 Max. :4404 Max. :62.25

Resumen estadístico de variables: gráfico.

library(ggplot2)
boxplot(IE1[,1], xlab= "1", ylab="Miles de millones de dólares estadounidenses", main = "Boxplot: PIB")

boxplot(IE1[,2], xlab= "2", ylab="Miles de millones de dólares estadounidenses", main = "Boxplot: FBK/PIB")

boxplot(IE1[,3], xlab= "3", ylab="Miles de millones de dólares estadounidenses", main = "Boxplot: Gasto público en salud/PIB")

boxplot(IE1[,4], xlab= "4", ylab="Miles de millones de dólares", main = "Boxplot: Exportaciónd e bienes y servicios")

boxplot(IE1[,5], xlab= "5", ylab="Tasas", main = "Boxplot: Inflación")

boxplot(IE1[,6], xlab= "6", ylab="Índice", main = "Boxplot: IDH")

boxplot(IE1[,7], xlab= "7", ylab="Dólares estadounidenses", main = "Boxplot: PIB per cápita")

boxplot(IE1[,8], xlab= "8", ylab="Porcentaje", main = "Boxplot: Inscripción escolar nivel terciario")

boxplot(IE1[,9], xlab= "9", ylab="Miles de millones de dólares estadounidenses", main = "Boxplot: Gasto en educación superior en I + D")

boxplot(IE1[,10], xlab= "10", ylab="Miles de millones de dólares estadounidenses", main = "Boxplot: Gasto empresarial en I+D")

boxplot(IE1[,11], xlab= "11", ylab="Por cada millón de personas", main = "Boxplot: Investigadores dedicados a investigación y desarrollo")

boxplot(IE1[,12], xlab= "12", ylab="Dólares estadounidenses", main = "Boxplot: Productividad laboral")

Estimacion del modelo

library(stargazer)
options(scipen = 9999)
model_eco <- lm(formula = Años~PIB+FBK+Gg_S+X+IPC+IDH+PIBpp+Ins+G_edusup+Gemp_ID+Invest+PT, data=IE)
stargazer(model_eco,title = "Modelo estimado",type = "text",digits = 8)
## 
## Modelo estimado
## ==================================================
##                          Dependent variable:      
##                     ------------------------------
##                                  Años             
## --------------------------------------------------
## PIB                          0.00284155*          
##                              (0.00129963)         
##                                                   
## FBK                         -0.00327286**         
##                              (0.00129350)         
##                                                   
## Gg_S                          0.00607449          
##                              (0.00362631)         
##                                                   
## X                            -0.00163979          
##                              (0.00207789)         
##                                                   
## IPC                          -21.07755000         
##                             (19.62064000)         
##                                                   
## IDH                          21.39666000          
##                             (19.61946000)         
##                                                   
## PIBpp                        -0.00007529          
##                              (0.00007034)         
##                                                   
## Ins                          -0.12894910*         
##                              (0.06064793)         
##                                                   
## G_edusup                      0.00079102          
##                              (0.00093556)         
##                                                   
## Gemp_ID                     -0.04855821**         
##                              (0.01603287)         
##                                                   
## Invest                       -0.00095493          
##                              (0.00061876)         
##                                                   
## PT                           -0.17953760          
##                              (0.23883360)         
##                                                   
## Constant                  1,986.08500000***       
##                             (12.58551000)         
##                                                   
## --------------------------------------------------
## Observations                      20              
## R2                            0.99987940          
## Adjusted R2                   0.99967250          
## Residual Std. Error      0.10705460 (df = 7)      
## F Statistic         4,834.79000000*** (df = 12; 7)
## ==================================================
## Note:                  *p<0.1; **p<0.05; ***p<0.01

Jarque Bera

library(normtest)
library(nortest)
library(fitdistrplus)
fit_norm_eco<- fitdist(data = model_eco$residuals, distr = "norm")
plot(fit_norm_eco)

jb.norm.test(model_eco$residuals)
## 
##  Jarque-Bera test for normality
## 
## data:  model_eco$residuals
## JB = 0.53199, p-value = 0.712
#Pasó la prueba

Prueba de Kolmogorov Smirnov

lillie.test(model_eco$residuals)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  model_eco$residuals
## D = 0.098664, p-value = 0.8772
#Pasó raspada la prueba

Prueba de Shairo-Wilk

shapiro.test(model_eco$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  model_eco$residuals
## W = 0.97735, p-value = 0.8955
#Pasó la prueba

Normalizacion de datos estimados

Eco.mat <- model.matrix(model_eco) 
Eco.nor<- scale(Eco.mat[,-1])
stargazer(head(Eco.nor, n=6), type="text")
## 
## ========================================================================================
##    PIB    FBK    Gg_S    X     IPC    IDH   PIBpp   Ins   G_edusup Gemp_ID Invest   PT  
## ----------------------------------------------------------------------------------------
## 1 -1.548 -1.392 -1.634 -1.318 -1.670 -1.670 -1.748 -2.205  -1.902  -1.267  -2.275 -1.897
## 2 -1.460 -1.370 -1.477 -1.461 -1.478 -1.478 -1.727 -2.152  -1.678  -1.100  -1.810 -1.648
## 3 -1.358 -1.409 -1.291 -1.511 -1.336 -1.336 -1.650 -1.111  -1.341  -1.207  -1.424 -1.351
## 4 -1.179 -1.196 -1.094 -1.412 -1.147 -1.147 -1.328 -0.815  -1.072  -1.103  -1.277 -1.107
## 5 -0.937 -0.825 -0.913 -1.104 -0.972 -0.972 -0.974 -0.651  -0.810  -0.992  -0.606 -0.861
## 6 -0.673 -0.357 -0.732 -0.825 -0.752 -0.752 -0.586 -0.645  -0.650  -0.892  -0.485 -0.562
## ----------------------------------------------------------------------------------------

Construyendo la matriz de correlación

library(Hmisc)
Eco_Mat_R<-rcorr(as.matrix(Eco.nor))
stargazer(Eco_Mat_R$r,type = "text")
## 
## ======================================================================================
##           PIB   FBK  Gg_S    X    IPC   IDH  PIBpp  Ins  G_edusup Gemp_ID Invest  PT  
## --------------------------------------------------------------------------------------
## PIB        1   0.971 0.996 0.963 0.995 0.995 0.945 0.888  0.981    0.977  0.886  0.982
## FBK      0.971   1   0.950 0.915 0.944 0.944 0.893 0.792  0.919    0.964  0.799  0.922
## Gg_S     0.996 0.950   1   0.956 0.997 0.997 0.939 0.906  0.985    0.967  0.900  0.989
## X        0.963 0.915 0.956   1   0.973 0.973 0.978 0.905  0.961    0.910  0.901  0.960
## IPC      0.995 0.944 0.997 0.973   1   1.000 0.959 0.920  0.992    0.959  0.917  0.992
## IDH      0.995 0.944 0.997 0.973 1.000   1   0.959 0.920  0.992    0.959  0.917  0.992
## PIBpp    0.945 0.893 0.939 0.978 0.959 0.959   1   0.948  0.970    0.874  0.950  0.964
## Ins      0.888 0.792 0.906 0.905 0.920 0.920 0.948   1    0.955    0.796  0.969  0.947
## G_edusup 0.981 0.919 0.985 0.961 0.992 0.992 0.970 0.955    1      0.933  0.945  0.995
## Gemp_ID  0.977 0.964 0.967 0.910 0.959 0.959 0.874 0.796  0.933      1    0.792  0.928
## Invest   0.886 0.799 0.900 0.901 0.917 0.917 0.950 0.969  0.945    0.792    1    0.944
## PT       0.982 0.922 0.989 0.960 0.992 0.992 0.964 0.947  0.995    0.928  0.944    1  
## --------------------------------------------------------------------------------------
library(corrplot)
corrplot(Eco_Mat_R$r, type = "upper", order = "hclust", 
         tl.col = "black", tl.srt = 90, html_font = "sans-serif")

#https://cran.r-project.org/web/packages/corrplot/vignettes/corrplot-intro.html
p.mat1 <- cor.mtest(Eco.nor)$p
corrplot(Eco_Mat_R$r, type = "upper", order = "hclust", 
         p.mat = p.mat1, sig.level = 0.01, tl.col = "black", html_font = "sans-serif")

library(PerformanceAnalytics)
library(GGally)
chart.Correlation(as.matrix(IE[,-1]),histogram = TRUE,pch=19)

Prueba de Farrar-Glaubar, en busca de evidencias de multicolinealidad

library(mctest)

mctest(model_eco)
## 
## Call:
## omcdiag(mod = mod, Inter = TRUE, detr = detr, red = red, conf = conf, 
##     theil = theil, cn = cn)
## 
## 
## Overall Multicollinearity Diagnostics
## 
##                            MC Results detection
## Determinant |X'X|:             0.0000         1
## Farrar Chi-Square:           923.6977         1
## Red Indicator:                 0.9437         1
## Sum of Lambda Inverse: 159924361.2204         1
## Theil's Method:                0.9697         1
## Condition Number:         414984.2898         1
## 
## 1 --> COLLINEARITY is detected by the test 
## 0 --> COLLINEARITY is not detected by the test
# El modelo ha identificado un valor crítico de 85.9649 menor que el valor calculado del estadístico de la prueba chi-cuadrado de 687.4918. El cual resulta, muy significativo, lo que implica la presencia de multicolinealidad en el modelo.

KMO tets

library(psych)
KMO(Eco.nor)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = Eco.nor)
## Overall MSA =  0.76
## MSA for each item = 
##      PIB      FBK     Gg_S        X      IPC      IDH    PIBpp      Ins 
##     0.81     0.79     0.82     0.72     0.72     0.72     0.75     0.76 
## G_edusup  Gemp_ID   Invest       PT 
##     0.87     0.69     0.83     0.71
#Si el valor:
  # KMO > 0.75 ► la idea de realizar análisis factorial es buena
  # 0.5 < KMO < 0.75 ► la idea es aceptable
  # KMO < 0.5 ► es inaceptable realizar el análisis

Metodo de ponderacion Critic

library(psych)
modelo_2<-principal(r = Eco_Mat_R$r,nfactors = 2,covar = FALSE,rotate = "varimax")
numero_de_factores<-2
modelo_2
## Principal Components Analysis
## Call: principal(r = Eco_Mat_R$r, nfactors = 2, rotate = "varimax", 
##     covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##           RC1  RC2   h2      u2 com
## PIB      0.81 0.59 1.00 0.00052 1.8
## FBK      0.88 0.44 0.97 0.03191 1.5
## Gg_S     0.78 0.62 0.99 0.00946 1.9
## X        0.70 0.68 0.95 0.04755 2.0
## IPC      0.75 0.65 1.00 0.00351 2.0
## IDH      0.75 0.65 1.00 0.00351 2.0
## PIBpp    0.61 0.77 0.97 0.03172 1.9
## Ins      0.46 0.88 0.98 0.01828 1.5
## G_edusup 0.69 0.72 0.99 0.00626 2.0
## Gemp_ID  0.89 0.44 0.99 0.01473 1.5
## Invest   0.46 0.88 0.98 0.02314 1.5
## PT       0.69 0.72 0.99 0.00915 2.0
## 
##                        RC1  RC2
## SS loadings           6.20 5.60
## Proportion Var        0.52 0.47
## Cumulative Var        0.52 0.98
## Proportion Explained  0.53 0.47
## Cumulative Proportion 0.53 1.00
## 
## Mean item complexity =  1.8
## Test of the hypothesis that 2 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.01 
## 
## Fit based upon off diagonal values = 1

Al incorporar el factor 2 la varianza acumulada alcanza a explicar el 100% del modelo, pero los indicadores poseen una predominancia de explicación en el factor 1, por otra parte el 100% de los indicadores alcanza un nivel de comunalidad de explicación por encima del 95%.

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

# Normalizando los datos
norm_directa <- function(x){
  return((x-min(x)) / (max(x)-min(x)))
}
norm_inversa <- function(x){
  return((max(x)-x) / (max(x)-min(x)))
}
IE[,-1] %>% dplyr::select(FBK, PIB, Gg_S, X, IDH, PIBpp, Ins, G_edusup, Gemp_ID, Invest, PT, IPC)%>% dplyr::transmute(FBK=norm_directa(FBK),PIB=norm_directa(PIB), Gg_S=norm_directa(Gg_S), X=norm_directa(X), 
                     IDH=norm_directa(IDH), PIBpp=norm_directa(PIBpp), Ins=norm_directa(Ins), 
                     G_edusup=norm_directa(G_edusup), Gemp_ID=norm_directa(Gemp_ID), 
                     Invest=norm_directa(Invest), PT=norm_directa(PT), IPC=norm_directa(IPC) ) ->data_eco_f1
print(data_eco_f1)
## # A tibble: 20 x 12
##        FBK    PIB   Gg_S      X    IDH   PIBpp    Ins G_edusup Gemp_ID Invest
##      <dbl>  <dbl>  <dbl>  <dbl>  <dbl>   <dbl>  <dbl>    <dbl>   <dbl>  <dbl>
##  1 0.00541 0      0      0.0687 0      0       0        0       0       0    
##  2 0.0119  0.0266 0.0485 0.0179 0.0588 0.00679 0.0162   0.0650  0.0473  0.145
##  3 0       0.0575 0.106  0      0.102  0.0327  0.335    0.163   0.0171  0.266
##  4 0.0644  0.111  0.167  0.0354 0.160  0.141   0.425    0.241   0.0465  0.312
##  5 0.176   0.184  0.223  0.145  0.214  0.259   0.475    0.317   0.0778  0.521
##  6 0.317   0.264  0.278  0.244  0.281  0.390   0.477    0.363   0.106   0.559
##  7 0.419   0.340  0.339  0.358  0.346  0.513   0.520    0.406   0.221   0.609
##  8 0.458   0.404  0.398  0.484  0.409  0.628   0.647    0.470   0.300   0.675
##  9 0.426   0.433  0.441  0.601  0.490  0.676   0.694    0.530   0.335   0.794
## 10 0.225   0.396  0.483  0.378  0.489  0.537   0.755    0.582   0.307   0.925
## 11 0.270   0.461  0.536  0.571  0.535  0.694   0.869    0.618   0.297   0.873
## 12 0.359   0.520  0.575  0.760  0.618  0.813   0.967    0.697   0.357   0.868
## 13 0.477   0.577  0.622  0.813  0.669  0.859   0.960    0.737   0.381   1    
## 14 0.541   0.627  0.657  0.862  0.703  0.888   0.862    0.740   0.444   0.909
## 15 0.641   0.685  0.719  0.924  0.754  0.891   0.868    0.746   0.509   0.955
## 16 0.681   0.722  0.782  0.821  0.773  0.783   0.850    0.735   0.553   0.971
## 17 0.703   0.760  0.844  0.791  0.813  0.780   0.900    0.802   0.617   0.992
## 18 0.801   0.836  0.902  0.895  0.869  0.877   0.958    0.870   0.698   0.909
## 19 0.926   0.928  0.971  1      0.941  0.957   1        0.945   0.856   0.967
## 20 1       1      1      0.992  1      1       0.915    1       1       0.959
## # ... with 2 more variables: PT <dbl>, IPC <dbl>

Ponderadores

funcion_critic <- function(ecofun) {
  
  # Desviación Típica
  desviacion <- apply(ecofun,MARGIN = 2,FUN = sd)
  
  # Matriz de Correlación
  coeficiente_correlacion<-cor(ecofun)
  
  # Ponderadores Brutos    
  1-coeficiente_correlacion->sum_data 
  colSums(sum_data)->sum_vector 
  desviacion * sum_vector->vj
  
  # Ponderadores netos
  wj <- vj/sum(vj)
  
  # Ponderadores    
  ponderadores<-round(wj*100,2)
  
  # Resultados en lista
  list(Desviacion_Estandar=desviacion,Ponderadores_Brutos=vj,Ponderadores_Netos=wj,Ponderadores=ponderadores)
}

# Probando la Función
library(kableExtra)
salida_critic<-funcion_critic(data_eco_f1)
salida_critic %>% as.data.frame() %>% kable(caption = "Prueba Función Critic",align = "c",digits = 3) %>% kable_minimal(html_font = "helvetica") %>% kable_styling(bootstrap_options = c("striped","hover"))
Prueba Función Critic
Desviacion_Estandar Ponderadores_Brutos Ponderadores_Netos Ponderadores
FBK 0.302 0.298 0.127 12.71
PIB 0.301 0.127 0.054 5.43
Gg_S 0.309 0.130 0.055 5.53
X 0.356 0.215 0.092 9.16
IDH 0.306 0.108 0.046 4.61
PIBpp 0.335 0.208 0.089 8.88
Ins 0.306 0.323 0.138 13.79
G_edusup 0.290 0.108 0.046 4.61
Gemp_ID 0.283 0.266 0.114 11.35
Invest 0.312 0.337 0.144 14.39
PT 0.299 0.115 0.049 4.92
IPC 0.306 0.108 0.046 4.61

Indicador de pobreza

Carga de datos

IP <- read_excel("C:/Users/Carlos/Desktop/Documentos universidad/EDD 1 Documentos UES/Repaso R studios/Datos preliminares/IndicadorPobreza.xlsx")
head(IP, 5)
Año Coef_arg C_casa Mort W_prom S_IN Pob_A
2000 0.0265 17.13277 6.10 49409.66 1123.022 15.3542
2001 0.0234 17.13767 6.00 49550.32 1081.934 15.5186
2002 0.0232 17.01401 6.20 49583.81 1065.072 15.6886
2003 0.0229 17.18054 6.05 49932.54 1101.878 15.8284
2004 0.0220 17.11427 6.05 50933.33 1205.216 15.9782

Definición de indicadores.

Num2<- c(1,2,3,4,5,6)
Indi2 <- c("Ahorro interno bruto", "Salario promedio", "Tasa de mortalidad infantil", "Gasto de la vivienda", "Coeficiente trabajadores de la actividad agrícola", "Población anual")
Fuente2 <- c("OCDE", "OCDE", "OCDE", "Banco Mundial", "OCDE", "OCDE")

dataf2 <- data.frame(Num2, Indi2, Fuente2)
dataf2
Num2 Indi2 Fuente2
1 Ahorro interno bruto OCDE
2 Salario promedio OCDE
3 Tasa de mortalidad infantil OCDE
4 Gasto de la vivienda Banco Mundial
5 Coeficiente trabajadores de la actividad agrícola OCDE
6 Población anual OCDE

Resumen estadístico de variables: numérico.

IP2 <- IP[,-1]
summary(IP2[,1:6])
Coef_arg C_casa Mort W_prom S_IN Pob_A
Min. :0.01770 Min. :16.93 Min. :5.035 Min. :49410 Min. :1065 Min. :15.35
1st Qu.:0.01887 1st Qu.:17.15 1st Qu.:5.237 1st Qu.:51440 1st Qu.:1222 1st Qu.:16.09
Median :0.01975 Median :17.29 Median :5.600 Median :54954 Median :1405 Median :16.92
Mean :0.02047 Mean :17.31 Mean :5.641 Mean :54386 Mean :1490 Mean :16.95
3rd Qu.:0.02205 3rd Qu.:17.48 3rd Qu.:6.013 3rd Qu.:56995 3rd Qu.:1789 3rd Qu.:17.76
Max. :0.02650 Max. :17.69 Max. :6.200 Max. :59517 Max. :2130 Max. :18.80

Resumen estadístico de variables: gráfico.

boxplot(IP2[,1], xlab= "1", ylab="Miles de millones de dólares", main = "Boxplot: Ahorro interno bruto")

boxplot(IP2[,2], xlab= "2", ylab="Dólares estadounidenses", main = "Boxplot: Salario promedio")

boxplot(IP2[,3], xlab= "3", ylab="Porcentaje (%)", main = "Boxplot: Tasa de mortalidad infantil")

boxplot(IP2[,4], xlab= "4", ylab="Porcentaje (%)", main = "Boxplot: Gasto de la vivienda")

boxplot(IP2[,5], xlab= "5", ylab="Porcentaje (%)", main = "Boxplot: Coeficiente trabajadores de la actividad agrícola")

boxplot(IP2[,6], xlab= "6", ylab="Millones de personas", main = "Boxplot: Población anual")

Estimación del modelo

options(scipen = 9999)
model_po <- lm(formula = Año~Coef_arg+C_casa+Mort+W_prom+S_IN+Pob_A, data=IP)
stargazer(model_po,title = "Modelo estimado",type = "text",digits = 8)
## 
## Modelo estimado
## ==================================================
##                          Dependent variable:      
##                     ------------------------------
##                                  Año              
## --------------------------------------------------
## Coef_arg                    -182.00530000         
##                             (110.02090000)        
##                                                   
## C_casa                        0.06110182          
##                              (0.42966620)         
##                                                   
## Mort                         -0.35595460          
##                              (0.81012350)         
##                                                   
## W_prom                       0.00023354*          
##                              (0.00013003)         
##                                                   
## S_IN                         -0.00000992          
##                              (0.00077458)         
##                                                   
## Pob_A                       4.42153800***         
##                              (0.53944560)         
##                                                   
## Constant                  1,926.53100000***       
##                             (14.64667000)         
##                                                   
## --------------------------------------------------
## Observations                      20              
## R2                            0.99852620          
## Adjusted R2                   0.99784600          
## Residual Std. Error      0.27457190 (df = 13)     
## F Statistic         1,467.97200000*** (df = 6; 13)
## ==================================================
## Note:                  *p<0.1; **p<0.05; ***p<0.01

Jarque Bera

fit_norm_po<- fitdist(data = model_po$residuals, distr = "norm")
plot(fit_norm_po)

jb.norm.test(model_po$residuals)
## 
##  Jarque-Bera test for normality
## 
## data:  model_po$residuals
## JB = 3.1523, p-value = 0.0595
#Pasó la prueba

Prueba de Kolmogorov Smirnov

lillie.test(model_po$residuals)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  model_po$residuals
## D = 0.15525, p-value = 0.2343
#Pasó raspada la prueba

Prueba de Shairo-Wilk

shapiro.test(model_po$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  model_po$residuals
## W = 0.94639, p-value = 0.3156
#Pasó raspada la prueba

Normalizacion de datos estimados

po.mat <- model.matrix(model_po) 
po.nor<- scale(po.mat[,-1])
stargazer(head(po.nor, n=6), type="text")
## 
## ============================================
##   Coef_arg C_casa Mort  W_prom  S_IN  Pob_A 
## --------------------------------------------
## 1  2.640   -0.831 1.176 -1.516 -1.113 -1.527
## 2  1.283   -0.807 0.920 -1.473 -1.238 -1.370
## 3  1.195   -1.399 1.432 -1.463 -1.289 -1.208
## 4  1.064   -0.602 1.048 -1.357 -1.177 -1.074
## 5  0.670   -0.919 1.048 -1.052 -0.864 -0.931
## 6  0.757   0.801  1.304 -0.846 -0.522 -0.788
## --------------------------------------------

Construyendo la matriz de correlación

po_Mat_R<-rcorr(as.matrix(po.nor))
stargazer(po_Mat_R$r,type = "text")
## 
## ====================================================
##          Coef_arg C_casa  Mort  W_prom  S_IN  Pob_A 
## ----------------------------------------------------
## Coef_arg    1     -0.541 0.871  -0.945 -0.832 -0.924
## C_casa    -0.541    1    -0.543 0.611  0.646  0.631 
## Mort      0.871   -0.543   1    -0.956 -0.904 -0.967
## W_prom    -0.945  0.611  -0.956   1    0.928  0.982 
## S_IN      -0.832  0.646  -0.904 0.928    1    0.953 
## Pob_A     -0.924  0.631  -0.967 0.982  0.953    1   
## ----------------------------------------------------
library(corrplot)
corrplot(po_Mat_R$r, type = "upper", order = "hclust", 
         tl.col = "black", tl.srt = 90, html_font = "sans-serif")

#https://cran.r-project.org/web/packages/corrplot/vignettes/corrplot-intro.html
p.mat2 <- cor.mtest(po.nor)$p
corrplot(po_Mat_R$r, type = "upper", order = "hclust", 
         p.mat = p.mat2, sig.level = 0.01, tl.col = "black", html_font = "sans-serif")

library(PerformanceAnalytics)
chart.Correlation(as.matrix(IP[,-1]),histogram = TRUE,pch=19)

Prueba de Farrar-Glaubar, en busca de evidencias de multicolinealidad

library(mctest)

mctest(model_po)
## 
## Call:
## omcdiag(mod = mod, Inter = TRUE, detr = detr, red = red, conf = conf, 
##     theil = theil, cn = cn)
## 
## 
## Overall Multicollinearity Diagnostics
## 
##                        MC Results detection
## Determinant |X'X|:         0.0000         1
## Farrar Chi-Square:       192.7920         1
## Red Indicator:             0.8316         1
## Sum of Lambda Inverse:   185.9489         1
## Theil's Method:            0.3168         0
## Condition Number:        723.0641         1
## 
## 1 --> COLLINEARITY is detected by the test 
## 0 --> COLLINEARITY is not detected by the test
# El modelo ha identificado un valor crítico de 24.99579 menor que el valor calculado del estadístico de la prueba chi-cuadrado de 192.7920. El cual resulta, muy significativo, lo que implica la presencia de multicolinealidad en el modelo.

KMO tets

library(psych)
KMO(po.nor)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = po.nor)
## Overall MSA =  0.79
## MSA for each item = 
## Coef_arg   C_casa     Mort   W_prom     S_IN    Pob_A 
##     0.74     0.84     0.75     0.86     0.79     0.76
#Si el valor:
  # KMO > 0.75 ► la idea de realizar análisis factorial es buena
  # 0.5 < KMO < 0.75 ► la idea es aceptable
  # KMO < 0.5 ► es inaceptable realizar el análisis

Metodologia de ponderacion Critic

modelo_P2<-principal(r = po_Mat_R$r,nfactors = 2,covar = FALSE,rotate = "varimax")
modelo_P2
## Principal Components Analysis
## Call: principal(r = po_Mat_R$r, nfactors = 2, rotate = "varimax", covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##            RC1   RC2   h2     u2 com
## Coef_arg -0.91 -0.26 0.90 0.1047 1.2
## C_casa    0.31  0.95 1.00 0.0035 1.2
## Mort     -0.93 -0.27 0.94 0.0562 1.2
## W_prom    0.93  0.34 0.98 0.0154 1.3
## S_IN      0.86  0.42 0.91 0.0873 1.5
## Pob_A     0.92  0.37 0.99 0.0097 1.3
## 
##                        RC1  RC2
## SS loadings           4.25 1.47
## Proportion Var        0.71 0.25
## Cumulative Var        0.71 0.95
## Proportion Explained  0.74 0.26
## Cumulative Proportion 0.74 1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 2 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.02 
## 
## Fit based upon off diagonal values = 1

Al incorporar el factor 2 la varianza acumulada alcanza a explicar el 100% del modelo, pero los indicadores poseen una predominancia de explicación en el factor 1, por otra parte el 100% de los indicadores alcanza un nivel de comunalidad de explicación por encima del 89%.

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

norm_directa <- function(x){
  return((x-min(x)) / (max(x)-min(x)))
}
norm_inversa <- function(x){
  return((max(x)-x) / (max(x)-min(x)))
}
IP[,-1] %>% dplyr::select(Coef_arg, C_casa, Mort, W_prom, S_IN, Pob_A)%>% dplyr::transmute(Coef_arg=norm_directa(Coef_arg),C_casa=norm_inversa(C_casa), Mort=norm_directa(Mort), S_IN=norm_inversa(S_IN),W_prom=norm_inversa(W_prom), Pob_A=norm_inversa(Pob_A)) ->data_po_f1
print(data_po_f1)
## # A tibble: 20 x 6
##    Coef_arg  C_casa   Mort   S_IN W_prom  Pob_A
##       <dbl>   <dbl>  <dbl>  <dbl>  <dbl>  <dbl>
##  1   1      0.730   0.914  0.946  1      1     
##  2   0.648  0.724   0.828  0.984  0.986  0.952 
##  3   0.625  0.887   1      1      0.983  0.903 
##  4   0.591  0.667   0.871  0.965  0.948  0.862 
##  5   0.489  0.755   0.871  0.868  0.849  0.819 
##  6   0.511  0.281   0.957  0.763  0.782  0.776 
##  7   0.443  0.565   0.700  0.674  0.667  0.728 
##  8   0.295  0.487   0.785  0.627  0.547  0.682 
##  9   0.261  0.429   0.700  0.694  0.514  0.629 
## 10   0.239  0.254   0.528  0.848  0.468  0.574 
## 11   0.216  0.564   0.442  0.760  0.435  0.520 
## 12   0.227  0.704   0.399  0.687  0.404  0.471 
## 13   0.159  1       0.313  0.548  0.347  0.418 
## 14   0.136  0.630   0.399  0.419  0.335  0.364 
## 15   0.125  0.473   0.185  0.323  0.260  0.312 
## 16   0.136  0.456   0.142  0.285  0.166  0.274 
## 17   0.114  0.00518 0.142  0.311  0.217  0.214 
## 18   0.0568 0.192   0.0987 0.221  0.152  0.152 
## 19   0.0227 0.228   0.123  0.0944 0.0893 0.0768
## 20   0      0       0      0      0      0

Ponderadores

funcion_critic2 <- function(pofun) {
  
  # Desviación Típica
  desviacion <- apply(pofun,MARGIN = 2,FUN = sd)
  
  # Matriz de Correlación
  coeficiente_correlacion<-cor(pofun)
  
  # Ponderadores Brutos    
  1-coeficiente_correlacion->sum_data 
  colSums(sum_data)->sum_vector 
  desviacion * sum_vector->vj
  
  # Ponderadores netos
  wj <- vj/sum(vj)
  
  # Ponderadores    
  ponderadores<-round(wj*100,2)
  
  # Resultados en lista
  list(Desviacion_Estandar=desviacion,Ponderadores_Brutos=vj,Ponderadores_Netos=wj,Ponderadores=ponderadores)
}

# Probando la Función
salida_critic2<-funcion_critic2(data_po_f1)
salida_critic2 %>% as.data.frame() %>% kable(caption = "Prueba Función Critic",align = "c",digits = 3) %>% kable_minimal(html_font = "helvetica") %>% kable_styling(bootstrap_options = c("striped","hover"))
Prueba Función Critic
Desviacion_Estandar Ponderadores_Brutos Ponderadores_Netos Ponderadores
Coef_arg 0.260 0.230 0.142 14.17
C_casa 0.276 0.559 0.344 34.41
Mort 0.335 0.255 0.157 15.66
S_IN 0.310 0.228 0.140 14.03
W_prom 0.325 0.188 0.116 11.57
Pob_A 0.304 0.165 0.102 10.16

Indicador de desigualdad

Carga de datos

ID <- read_excel("C:/Users/Carlos/Desktop/Documentos universidad/EDD 1 Documentos UES/Repaso R studios/Datos preliminares/IndicadorDesigualdad.xlsx")
head(ID, 5)
Año Gini Agua_serv Esp_vida T_empleo H_viv
2000 33.60 98.56452 77.88659 72.49728 33.60
2001 33.85 98.57089 78.08780 71.96364 33.85
2002 34.65 98.57426 78.21341 71.67298 34.65
2003 34.45 98.57765 78.38902 71.70333 34.45
2004 34.05 98.58103 78.69024 71.83624 34.05

Definición de indicadores.

Num3<- c(1,2,3,4,5)
Indi3 <- c("Índice de Gini", "Personas que utilizan servicios de agua potable", "Esperanza de vida al nacer", "Tasa de empleo", "Hacinamiento en las viviendas")
Fuente3 <- c("OCDE y WIID", "Banco Mundial", "Banco Mundial","OCDE", "OCDE")

dataf3 <- data.frame(Num3, Indi3, Fuente3)
dataf3
Num3 Indi3 Fuente3
1 Índice de Gini OCDE y WIID
2 Personas que utilizan servicios de agua potable Banco Mundial
3 Esperanza de vida al nacer Banco Mundial
4 Tasa de empleo OCDE
5 Hacinamiento en las viviendas OCDE

Resumen estadístico de variables: numérico.

ID3 <- ID[,-1]
summary(ID3[,1:5])
Gini Agua_serv Esp_vida T_empleo H_viv
Min. :33.60 Min. :98.56 Min. :77.89 Min. :68.99 Min. :33.60
1st Qu.:34.65 1st Qu.:98.60 1st Qu.:78.80 1st Qu.:70.06 1st Qu.:34.65
Median :34.85 Median :98.73 Median :79.79 Median :71.69 Median :34.85
Mean :34.86 Mean :98.74 Mean :79.47 Mean :71.18 Mean :34.86
3rd Qu.:35.31 3rd Qu.:98.86 3rd Qu.:80.24 3rd Qu.:72.12 3rd Qu.:35.31
Max. :35.80 Max. :98.96 Max. :80.32 Max. :72.75 Max. :35.80

Resumen estadístico de variables: gráfico.

boxplot(ID3[,1], xlab= "1", ylab="Índice", main = "Boxplot: Índice de Gini")

boxplot(ID3[,2], xlab= "2", ylab="% de la Población", main = "Boxplot: Personas que utilizan servicios de agua potable")

boxplot(ID3[,3], xlab= "3", ylab="Años", main = "Boxplot: Esperanza de vida al nacer")

boxplot(ID3[,4], xlab= "4", ylab="Porcentaje", main = "Boxplot: Tasa de empleo")

boxplot(ID3[,5], xlab= "5", ylab="Total", main = "Boxplot: Hacinamiento en las viviendas")

Estimación del modelo

options(scipen = 9999)
model_des <- lm(formula = Año~Gini+Agua_serv+Esp_vida+T_empleo+H_viv, data=ID)
stargazer(model_des,title = "Modelo estimado",type = "text",digits = 8)
## 
## Modelo estimado
## ================================================
##                         Dependent variable:     
##                     ----------------------------
##                                 Año             
## ------------------------------------------------
## Gini                         0.36005300         
##                             (0.38025100)        
##                                                 
## Agua_serv                  27.08406000***       
##                             (2.67517700)        
##                                                 
## Esp_vida                   2.61152900***        
##                             (0.56363950)        
##                                                 
## T_empleo                   0.49828710***        
##                             (0.13331580)        
##                                                 
## H_viv                                           
##                                                 
##                                                 
## Constant                  -920.34550000***      
##                            (221.49440000)       
##                                                 
## ------------------------------------------------
## Observations                     20             
## R2                           0.99477560         
## Adjusted R2                  0.99338250         
## Residual Std. Error     0.48126200 (df = 15)    
## F Statistic         714.04170000*** (df = 4; 15)
## ================================================
## Note:                *p<0.1; **p<0.05; ***p<0.01

Jarque Bera

fit_norm_des<- fitdist(data = model_des$residuals, distr = "norm")
plot(fit_norm_des)

jb.norm.test(model_des$residuals)
## 
##  Jarque-Bera test for normality
## 
## data:  model_des$residuals
## JB = 0.62573, p-value = 0.632
#Pasó la prueba

Prueba de Kolmogorov Smirnov

lillie.test(model_des$residuals)
## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  model_des$residuals
## D = 0.13912, p-value = 0.394
#Pasó raspada la prueba

Prueba de Shairo-Wilk

shapiro.test(model_des$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  model_des$residuals
## W = 0.96957, p-value = 0.7458
#Pasó raspada la prueba

Normalizacion de datos estimados

des.mat <- model.matrix(model_des) 
des.nor<- scale(des.mat[,-1])
stargazer(head(des.nor, n=6), type="text")
## 
## ===========================================
##    Gini  Agua_serv Esp_vida T_empleo H_viv 
## -------------------------------------------
## 1 -2.174  -1.253    -1.851   1.051   -2.174
## 2 -1.744  -1.208    -1.616   0.624   -1.744
## 3 -0.367  -1.184    -1.470   0.391   -0.367
## 4 -0.711  -1.160    -1.264   0.415   -0.711
## 5 -1.399  -1.135    -0.912   0.522   -1.399
## 6 -0.194  -0.940    -0.737   0.642   -0.194
## -------------------------------------------

Construyendo la matriz de correlación

des_Mat_R<-rcorr(as.matrix(des.nor))
stargazer(des_Mat_R$r,type = "text")
## 
## ===================================================
##            Gini  Agua_serv Esp_vida T_empleo H_viv 
## ---------------------------------------------------
## Gini        1      0.805    0.858    -0.346    1   
## Agua_serv 0.805      1      0.927    -0.273  0.805 
## Esp_vida  0.858    0.927      1      -0.509  0.858 
## T_empleo  -0.346  -0.273    -0.509     1     -0.346
## H_viv       1      0.805    0.858    -0.346    1   
## ---------------------------------------------------
corrplot(des_Mat_R$r, type = "upper", order = "hclust", 
         tl.col = "black", tl.srt = 90, html_font = "sans-serif")

#https://cran.r-project.org/web/packages/corrplot/vignettes/corrplot-intro.html
p.mat3 <- cor.mtest(des.nor)$p
corrplot(des_Mat_R$r, type = "upper", order = "hclust", 
         p.mat = p.mat3, sig.level = 0.01, tl.col = "black", html_font = "sans-serif")

library(PerformanceAnalytics)
chart.Correlation(as.matrix(ID[,-1]),histogram = TRUE,pch=19)

Prueba de Farrar-Glaubar, en busca de evidencias de multicolinealidad

library(mctest)

mctest(model_des)
## Warning in summary.lm(lm(x[, i] ~ x[, -i])): essentially perfect fit: summary
## may be unreliable

## Warning in summary.lm(lm(x[, i] ~ x[, -i])): essentially perfect fit: summary
## may be unreliable

## Warning in summary.lm(lm(x[, i] ~ x[, -i])): essentially perfect fit: summary
## may be unreliable

## Warning in summary.lm(lm(x[, i] ~ x[, -i])): essentially perfect fit: summary
## may be unreliable
## Warning in sqrt(max(ev)/ev): Se han producido NaNs
## Warning in sqrt(ordev): Se han producido NaNs
## 
## Call:
## omcdiag(mod = mod, Inter = TRUE, detr = detr, red = red, conf = conf, 
##     theil = theil, cn = cn)
## 
## 
## Overall Multicollinearity Diagnostics
## 
##                                   MC Results detection
## Determinant |X'X|:                    0.0000         1
## Farrar Chi-Square:                       Inf         1
## Red Indicator:                        0.7212         1
## Sum of Lambda Inverse: 3983880259828268.5000         1
## Theil's Method:                       0.4419         0
## Condition Number:                        NaN        NA
## 
## 1 --> COLLINEARITY is detected by the test 
## 0 --> COLLINEARITY is not detected by the test
# El modelo ha identificado un valor crítico de 18.30704 menor que el valor calculado del estadístico de la prueba chi-cuadrado infinito. El cual resulta, muy significativo, lo que implica la presencia de multicolinealidad en el modelo.

KMO tets

KMO(des.nor)
## Error in solve.default(r) : 
##   Lapack routine dgesv: system is exactly singular: U[5,5] = 0
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = des.nor)
## Overall MSA =  0.5
## MSA for each item = 
##      Gini Agua_serv  Esp_vida  T_empleo     H_viv 
##       0.5       0.5       0.5       0.5       0.5
#Si el valor:
  # KMO > 0.75 ► la idea de realizar análisis factorial es buena
  # 0.5 < KMO < 0.75 ► la idea es aceptable
  # KMO < 0.5 ► es inaceptable realizar el análisis

Metodologia de ponderacion Critic

modelo_D2<-principal(r = des_Mat_R$r,nfactors = 2,covar = FALSE,rotate = "varimax")
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
modelo_D2
## Principal Components Analysis
## Call: principal(r = des_Mat_R$r, nfactors = 2, rotate = "varimax", 
##     covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##             RC1   RC2   h2     u2 com
## Gini       0.95 -0.17 0.93 0.0702 1.1
## Agua_serv  0.92 -0.11 0.87 0.1335 1.0
## Esp_vida   0.90 -0.36 0.94 0.0621 1.3
## T_empleo  -0.19  0.98 1.00 0.0019 1.1
## H_viv      0.95 -0.17 0.93 0.0702 1.1
## 
##                        RC1  RC2
## SS loadings           3.51 1.16
## Proportion Var        0.70 0.23
## Cumulative Var        0.70 0.93
## Proportion Explained  0.75 0.25
## Cumulative Proportion 0.75 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 2 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.06 
## 
## Fit based upon off diagonal values = 0.99

Al incorporar el factor 2 la varianza acumulada alcanza a explicar el 100% del modelo, pero los indicadores poseen una predominancia de explicación en el factor 1, por otra parte el 100% de los indicadores alcanza un nivel de comunalidad de explicación por encima del 85%.

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

# Normalizando los datos
norm_directa <- function(x){
  return((x-min(x)) / (max(x)-min(x)))
}
norm_inversa <- function(x){
  return((max(x)-x) / (max(x)-min(x)))
}

ID[,-1] %>% dplyr::select(Gini, Agua_serv, Esp_vida, T_empleo, H_viv)%>%dplyr::transmute(Gini=norm_directa(Gini),Agua_serv=norm_inversa(Agua_serv), Esp_vida=norm_inversa(Esp_vida), T_empleo=norm_inversa(T_empleo),H_viv=norm_inversa(H_viv)) ->data_des_f1
print(data_des_f1)
## # A tibble: 20 x 5
##     Gini Agua_serv Esp_vida T_empleo  H_viv
##    <dbl>     <dbl>    <dbl>    <dbl>  <dbl>
##  1 0        1        1        0.0683 1     
##  2 0.114    0.984    0.917    0.210  0.886 
##  3 0.477    0.976    0.866    0.287  0.523 
##  4 0.386    0.967    0.794    0.279  0.614 
##  5 0.205    0.959    0.670    0.244  0.795 
##  6 0.523    0.890    0.608    0.204  0.477 
##  7 0.636    0.822    0.536    0.107  0.364 
##  8 0.477    0.752    0.433    0.0534 0.523 
##  9 0.477    0.682    0.392    0.169  0.523 
## 10 0.523    0.613    0.258    0.879  0.477 
## 11 0.545    0.544    0.175    1      0.455 
## 12 0.682    0.475    0.113    0.949  0.318 
## 13 0.773    0.409    0.0516   0.856  0.227 
## 14 1        0.344    0.0311   0.778  0     
## 15 0.795    0.278    0        0.694  0.205 
## 16 0.818    0.212    0.0105   0.590  0.182 
## 17 0.591    0.146    0.0416   0.508  0.409 
## 18 0.636    0.0795   0.0316   0.298  0.364 
## 19 0.892    0.0589   0.0316   0.166  0.108 
## 20 0.930    0        0.0230   0      0.0701

Ponderadores

funcion_critic3 <- function(desfun) {
  
  # Desviación Típica
  desviacion <- apply(desfun,MARGIN = 2,FUN = sd)
  
  # Matriz de Correlación
  coeficiente_correlacion<-cor(desfun)
  
  # Ponderadores Brutos    
  1-coeficiente_correlacion->sum_data 
  colSums(sum_data)->sum_vector 
  desviacion * sum_vector->vj
  
  # Ponderadores netos
  wj <- vj/sum(vj)
  
  # Ponderadores    
  ponderadores<-round(wj*100,2)
  
  # Resultados en lista
  list(Desviacion_Estandar=desviacion,Ponderadores_Brutos=vj,Ponderadores_Netos=wj,Ponderadores=ponderadores)
}

# Probando la Función
salida_critic3<-funcion_critic3(data_des_f1)
salida_critic3 %>% as.data.frame() %>% kable(caption = "Prueba Función Critic",align = "c",digits = 3) %>% kable_minimal(html_font = "helvetica") %>% kable_styling(bootstrap_options = c("striped","hover"))
Prueba Función Critic
Desviacion_Estandar Ponderadores_Brutos Ponderadores_Netos Ponderadores
Gini 0.264 1.668 0.250 25.04
Agua_serv 0.352 1.176 0.177 17.66
Esp_vida 0.352 1.259 0.189 18.90
T_empleo 0.332 1.587 0.238 23.82
H_viv 0.264 0.972 0.146 14.60