#1. A través del analisis de componentes principales, identifique para un modelo de 3 factores
library(psych)
modelo_4<-principal(r = datos_ejer,nfactors = 3,covar = FALSE,rotate = "varimax")
modelo_4$loadings##
## Loadings:
## RC1 RC2 RC3
## X1 0.490 -0.545
## X2 0.815
## X3 0.876 -0.104
## X4 0.922 -0.113
## X5 0.178
## X6 0.125 0.777
## X7 -0.613 0.580
## X8 -0.241 0.715 0.252
## X9 0.815 0.310
## X10 0.620 -0.562
## X11 0.794 -0.137
##
## RC1 RC2 RC3
## SS loadings 2.967 2.601 1.408
## Proportion Var 0.270 0.236 0.128
## Cumulative Var 0.270 0.506 0.634En el factor 1: x2, x3, x4, x7 En el factor 2: x5, x8, x9, x10, x11 En el factor 3: x1, x6
#2. Entropía factor 1
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union#Normalización de los datos
datos_ejer %>% dplyr::select(X2,X3,X4,X7)->data_norm
apply(data_norm,2,prop.table)->data_norm
1+data_norm->data_NormPos
print(data_NormPos)## X2 X3 X4 X7
## [1,] 1.006302 1.006895 1.004056 1.016739
## [2,] 1.000000 1.003134 1.001690 1.023913
## [3,] 1.000000 1.000000 1.000000 1.022822
## [4,] 1.006302 1.004388 1.003380 1.016261
## [5,] 1.000000 1.010324 1.001591 1.012378
## [6,] 1.009695 1.007714 1.003120 1.013980
## [7,] 1.004201 1.001880 1.001352 1.019130
## [8,] 1.008813 1.011484 1.015978 1.008294
## [9,] 1.000000 1.000000 1.000000 1.017217
## [10,] 1.000000 1.000000 1.000000 1.018853
## [11,] 1.007638 1.007408 1.004916 1.020869
## [12,] 1.006302 1.019431 1.009464 1.007652
## [13,] 1.023106 1.015043 1.020280 1.007652
## [14,] 1.000000 1.003134 1.000000 1.019130
## [15,] 1.018905 1.008148 1.006760 1.002870
## [16,] 1.004201 1.001254 1.002028 1.009565
## [17,] 1.002101 1.003761 1.002028 1.007652
## [18,] 1.004201 1.006895 1.007436 1.009087
## [19,] 1.006302 1.006895 1.010140 1.013869
## [20,] 1.003501 1.001045 1.000000 1.015942
## [21,] 1.002101 1.003761 1.006760 1.017696
## [22,] 1.012603 1.014416 1.018252 1.007174
## [23,] 1.014704 1.002507 1.006084 1.010522
## [24,] 1.003112 1.002786 1.002003 1.022673
## [25,] 1.014704 1.008775 1.012168 1.007174
## [26,] 1.006302 1.012536 1.012168 1.008609
## [27,] 1.008402 1.003134 1.001352 1.016261
## [28,] 1.008264 1.004932 1.004433 1.008154
## [29,] 1.014704 1.010029 1.010140 1.007652
## [30,] 1.000000 1.007163 1.000000 1.008199
## [31,] 1.019770 1.028021 1.033402 1.002251
## [32,] 1.004201 1.013163 1.005408 1.010043
## [33,] 1.003055 1.003647 1.007866 1.018087
## [34,] 1.011457 1.005698 1.014749 1.007826
## [35,] 1.002435 1.000727 1.001567 1.013863
## [36,] 1.000000 1.000627 1.000676 1.010043
## [37,] 1.018972 1.022645 1.023550 1.008022
## [38,] 1.002101 1.003134 1.002704 1.015783
## [39,] 1.008402 1.006268 1.013520 1.005261
## [40,] 1.004201 1.008148 1.007436 1.007174
## [41,] 1.016597 1.009905 1.010682 1.010392
## [42,] 1.006302 1.014416 1.005408 1.007652
## [43,] 1.006302 1.001880 1.002028 1.011956
## [44,] 1.014522 1.012381 1.004006 1.005196
## [45,] 1.000000 1.006268 1.004507 1.019130
## [46,] 1.008402 1.005641 1.003380 1.011956
## [47,] 1.002897 1.002594 1.002797 1.015172
## [48,] 1.004201 1.003134 1.005408 1.010043
## [49,] 1.018905 1.021938 1.026363 1.007652
## [50,] 1.002101 1.008775 1.010140 1.006696
## [51,] 1.000000 1.016411 1.009832 1.007652
## [52,] 1.007469 1.007800 1.009614 1.004251
## [53,] 1.002101 1.005641 1.002028 1.006696
## [54,] 1.025206 1.008148 1.009464 1.005739
## [55,] 1.018905 1.011282 1.012844 1.007652
## [56,] 1.002101 1.002507 1.004732 1.011000
## [57,] 1.008402 1.002507 1.006760 1.009087
## [58,] 1.014522 1.011143 1.007344 1.008502
## [59,] 1.017275 1.015152 1.018700 1.007032
## [60,] 1.029407 1.016297 1.018928 1.008130
## [61,] 1.002101 1.007522 1.008112 1.005739
## [62,] 1.006302 1.001254 1.005408 1.011956
## [63,] 1.014704 1.010655 1.011492 1.004783
## [64,] 1.007638 1.003419 1.003687 1.008696
## [65,] 1.025206 1.014416 1.021631 1.005261
## [66,] 1.020165 1.007354 1.005768 1.009693
## [67,] 1.000000 1.001880 1.002704 1.013869
## [68,] 1.006191 1.007126 1.005408 1.013693
## [69,] 1.033608 1.025072 1.023659 1.006217
## [70,] 1.011203 1.017829 1.016824 1.007652
## [71,] 1.012603 1.008775 1.014196 1.003826
## [72,] 1.006302 1.023191 1.014872 1.010522
## [73,] 1.008402 1.010655 1.004732 1.002391
## [74,] 1.008402 1.003134 1.007436 1.012435
## [75,] 1.006302 1.006268 1.010140 1.005261
## [76,] 1.002101 1.014416 1.012844 1.009565
## [77,] 1.012603 1.011909 1.010816 1.006217
## [78,] 1.020769 1.010141 1.012760 1.006878
## [79,] 1.004254 1.008251 1.005476 1.013076
## [80,] 1.019937 1.017848 1.011916 1.006485
## [81,] 1.000000 1.000000 1.000887 1.014426
## [82,] 1.008402 1.013789 1.013520 1.003826
## [83,] 1.005251 1.007835 1.000000 1.015543
## [84,] 1.008402 1.003134 1.002028 1.009565
## [85,] 1.004201 1.008148 1.014196 1.008609
## [86,] 1.000000 1.015670 1.010816 1.004783
## [87,] 1.010503 1.020057 1.028391 1.007174
## [88,] 1.010503 1.005641 1.011492 1.007174
## [89,] 1.010503 1.013789 1.006084 1.006696
## [90,] 1.012603 1.005641 1.012168 1.011478
## [91,] 1.023106 1.008148 1.009464 1.002391
## [92,] 1.012603 1.008148 1.014196 1.002391
## [93,] 1.023106 1.025072 1.025011 1.001435
## [94,] 1.010373 1.011143 1.010015 1.008975
## [95,] 1.012603 1.016923 1.029743 1.001435
## [96,] 1.006302 1.011282 1.008788 1.001435
## [97,] 1.004201 1.009402 1.006760 1.003348
## [98,] 1.000000 1.005641 1.004056 1.003348
## [99,] 1.007638 1.009801 1.007866 1.002261
## [100,] 1.006302 1.020057 1.016224 1.005261
## [101,] 1.004201 1.010655 1.004056 1.003348
## [102,] 1.023106 1.017550 1.020280 1.002391
## [103,] 1.002848 1.004249 1.000000 1.012970
## [104,] 1.018905 1.009402 1.009464 1.003826
## [105,] 1.027307 1.010029 1.021631 1.002391
## [106,] 1.032949 1.021631 1.023328 1.002251
## [107,] 1.008618 1.022500 1.022186 1.001472
## [108,] 1.000000 1.008775 1.004056 1.007652#Fórmula de entropía
entropy<-function(x){
return(x*log(x))
}
apply(data_NormPos,2,entropy)->data_norm_2
print(data_norm_2)## X2 X3 X4 X7
## [1,] 0.006321392 0.0069184383 0.0040641192 0.016878361
## [2,] 0.000000000 0.0031388713 0.0016913876 0.024196573
## [3,] 0.000000000 0.0000000000 0.0000000000 0.023080614
## [4,] 0.006321392 0.0043971630 0.0033856264 0.016392276
## [5,] 0.000000000 0.0103767576 0.0015918153 0.012454747
## [6,] 0.009741579 0.0077440563 0.0031247889 0.014077122
## [7,] 0.004209865 0.0018821461 0.0013528819 0.019312158
## [8,] 0.008852121 0.0115495907 0.0161047786 0.008328571
## [9,] 0.000000000 0.0000000000 0.0000000000 0.017364671
## [10,] 0.000000000 0.0000000000 0.0000000000 0.019029691
## [11,] 0.007667375 0.0074349233 0.0049283136 0.021085718
## [12,] 0.006321392 0.0196181492 0.0095084195 0.007681335
## [13,] 0.023370695 0.0151556179 0.0204837788 0.007681335
## [14,] 0.000000000 0.0031388713 0.0000000000 0.019312158
## [15,] 0.019082315 0.0081814181 0.0067826382 0.002873663
## [16,] 0.004209865 0.0012543716 0.0020300074 0.009610766
## [17,] 0.002102731 0.0037678214 0.0020300074 0.007681335
## [18,] 0.004209865 0.0069184383 0.0074634035 0.009128068
## [19,] 0.006321392 0.0069184383 0.0101909972 0.013965228
## [20,] 0.003506998 0.0010452006 0.0000000000 0.016068344
## [21,] 0.002102731 0.0037678214 0.0067826382 0.017851205
## [22,] 0.012682246 0.0145196597 0.0184171286 0.007199544
## [23,] 0.014811257 0.0025103128 0.0061023269 0.010576841
## [24,] 0.003116728 0.0027896237 0.0020049206 0.022928094
## [25,] 0.014811257 0.0088134926 0.0122414434 0.007199544
## [26,] 0.006321392 0.0126141098 0.0122414434 0.008645597
## [27,] 0.008437304 0.0031388713 0.0013528819 0.016392276
## [28,] 0.008298422 0.0049442855 0.0044424930 0.008187064
## [29,] 0.014811257 0.0100788098 0.0101909972 0.007681335
## [30,] 0.000000000 0.0071889455 0.0000000000 0.008232230
## [31,] 0.019963803 0.0284103201 0.0339532945 0.002253158
## [32,] 0.004209865 0.0132489054 0.0054224697 0.010093690
## [33,] 0.003059974 0.0036534378 0.0078968539 0.018249447
## [34,] 0.011522803 0.0057143227 0.0148569777 0.007856588
## [35,] 0.002438356 0.0007269806 0.0015687274 0.013958202
## [36,] 0.000000000 0.0006269895 0.0006762126 0.010093690
## [37,] 0.019151345 0.0228999222 0.0238255760 0.008054490
## [38,] 0.002102731 0.0031388713 0.0027075891 0.015906416
## [39,] 0.008437304 0.0062875336 0.0136106654 0.005274655
## [40,] 0.004209865 0.0081814181 0.0074634035 0.007199544
## [41,] 0.016733721 0.0099537709 0.0107390719 0.010445592
## [42,] 0.006321392 0.0145196597 0.0054224697 0.007681335
## [43,] 0.006321392 0.0018821461 0.0020300074 0.012027651
## [44,] 0.014627097 0.0124574298 0.0040138448 0.005209367
## [45,] 0.000000000 0.0062875336 0.0045167005 0.019312158
## [46,] 0.008437304 0.0056570193 0.0033856264 0.012027651
## [47,] 0.002901471 0.0025969872 0.0028010844 0.015286852
## [48,] 0.004209865 0.0031388713 0.0054224697 0.010093690
## [49,] 0.019082315 0.0221766508 0.0267078827 0.007681335
## [50,] 0.002102731 0.0088134926 0.0101909972 0.006717981
## [51,] 0.000000000 0.0165445062 0.0098806785 0.007681335
## [52,] 0.007496358 0.0078304339 0.0096600643 0.004260208
## [53,] 0.002102731 0.0056570193 0.0020300074 0.006717981
## [54,] 0.025521358 0.0081814181 0.0095084195 0.005755536
## [55,] 0.019082315 0.0113456828 0.0129258288 0.007681335
## [56,] 0.002102731 0.0025103128 0.0047430670 0.011060218
## [57,] 0.008437304 0.0025103128 0.0067826382 0.009128068
## [58,] 0.014627097 0.0112048423 0.0073709272 0.008538412
## [59,] 0.017423723 0.0152666035 0.0188738906 0.007057002
## [60,] 0.029835587 0.0164286952 0.0191055637 0.008163352
## [61,] 0.002102731 0.0075497332 0.0081446223 0.005755536
## [62,] 0.006321392 0.0012543716 0.0054224697 0.012027651
## [63,] 0.014811257 0.0107120519 0.0115575095 0.004794001
## [64,] 0.007667375 0.0034247092 0.0036939758 0.008733302
## [65,] 0.025521358 0.0145196597 0.0218637855 0.005274655
## [66,] 0.020367014 0.0073813498 0.0057850036 0.009739523
## [67,] 0.000000000 0.0018821461 0.0027075891 0.013965228
## [68,] 0.006210150 0.0071509753 0.0054224697 0.013786616
## [69,] 0.034166960 0.0253834257 0.0239371494 0.006236645
## [70,] 0.011265325 0.0179867782 0.0169652398 0.007681335
## [71,] 0.012682246 0.0088134926 0.0142959528 0.003833376
## [72,] 0.006321392 0.0234582091 0.0149816908 0.010576841
## [73,] 0.008437304 0.0107120519 0.0047430670 0.002394148
## [74,] 0.008437304 0.0031388713 0.0074634035 0.012511707
## [75,] 0.006321392 0.0062875336 0.0101909972 0.005274655
## [76,] 0.002102731 0.0145196597 0.0129258288 0.009610766
## [77,] 0.012682246 0.0119797022 0.0108740273 0.006236645
## [78,] 0.020983451 0.0101926224 0.0128412174 0.006901922
## [79,] 0.004263267 0.0082854036 0.0054912953 0.013161554
## [80,] 0.020134636 0.0180059986 0.0119863644 0.006505839
## [81,] 0.000000000 0.0000000000 0.0008869295 0.014529710
## [82,] 0.008437304 0.0138840888 0.0136106654 0.003833376
## [83,] 0.005265080 0.0078655269 0.0000000000 0.015663570
## [84,] 0.008437304 0.0031388713 0.0020300074 0.009610766
## [85,] 0.004209865 0.0081814181 0.0142959528 0.008645597
## [86,] 0.000000000 0.0157919631 0.0108740273 0.004794001
## [87,] 0.010557592 0.0202571971 0.0287906085 0.007199544
## [88,] 0.010557592 0.0056570193 0.0115575095 0.007199544
## [89,] 0.010557592 0.0138840888 0.0061023269 0.006717981
## [90,] 0.012682246 0.0056570193 0.0122414434 0.011543821
## [91,] 0.023370695 0.0081814181 0.0095084195 0.002394148
## [92,] 0.012682246 0.0081814181 0.0142959528 0.002394148
## [93,] 0.023370695 0.0253834257 0.0253216244 0.001435803
## [94,] 0.010426583 0.0112048423 0.0100645598 0.009014875
## [95,] 0.012682246 0.0170658138 0.0301813145 0.001435803
## [96,] 0.006321392 0.0113456828 0.0088262944 0.001435803
## [97,] 0.004209865 0.0094459566 0.0067826382 0.003353405
## [98,] 0.000000000 0.0056570193 0.0040641192 0.003353405
## [99,] 0.007667375 0.0098486363 0.0078968539 0.002263411
## [100,] 0.006321392 0.0202571971 0.0163545172 0.005274655
## [101,] 0.004209865 0.0107120519 0.0040641192 0.003353405
## [102,] 0.023370695 0.0177033188 0.0204837788 0.002394148
## [103,] 0.002852223 0.0042584609 0.0000000000 0.013053460
## [104,] 0.019082315 0.0094459566 0.0095084195 0.003833376
## [105,] 0.027676325 0.0100788098 0.0218637855 0.002394148
## [106,] 0.033486398 0.0218627779 0.0235980896 0.002253158
## [107,] 0.008654568 0.0227515189 0.0224304598 0.001472646
## [108,] 0.000000000 0.0088134926 0.0040641192 0.007681335#Número de variables en el factor:
ncol(data_norm)->m
#Constante de entropía:
-1/log(m)->K
print(K)## [1] -0.7213475#Cálculo de las entropías
K*colSums(data_norm_2)->Ej
print(Ej)## X2 X3 X4 X7
## -0.7271061 -0.7262614 -0.7268258 -0.7257437#Cálculo de las especificidades:
1-Ej->vj
print(vj)## X2 X3 X4 X7
## 1.727106 1.726261 1.726826 1.725744#Calculo de los ponderados normalizados
prop.table(vj)->wj
print(wj)## X2 X3 X4 X7
## 0.2500900 0.2499677 0.2500495 0.2498928#3. Metodo critic para factor 2
norm_directa <- function(x){
return((x-min(x)) / (max(x)-min(x)))
}
norm_inverza <- function(x){
return((max(x)-x) / (max(x)-min(x)))
}
# Normalizaci?n de los datos
library(dplyr)
datos_ejer %>% dplyr::select(X5, X8, X9, X10, X11) %>% dplyr::transmute(X5=norm_directa(X5),X8=norm_directa(X8), X9=norm_directa(X9), X10=norm_directa(X10), X11=norm_directa(X11)) ->data_factor_1
print(data_factor_1)## # A tibble: 108 x 5
## X5 X8 X9 X10 X11
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.498 0.975 0.881 0.265 1
## 2 0.0160 0.774 0.814 0.292 0.391
## 3 0.159 1 0.976 0.193 0.658
## 4 0.536 0.830 0.746 0.922 0.828
## 5 0.0613 0.833 0.599 0.274 0.441
## 6 0.145 0.838 0.898 0.0489 0.0962
## 7 0.122 0.814 0.932 0.180 0.312
## 8 0.530 0.578 0.623 0.489 0.299
## 9 0.423 0.846 0.678 0.106 0.188
## 10 0.0404 0.800 0.785 0.418 0.199
## # ... with 98 more rows#Cálculo de las desviaciones estándar de cada variable
data_factor_1 %>% dplyr::summarise(S5=sd(X5),S8=sd(X8),S9=sd(X9),S10=sd(X10), S11=sd(X11))-> sd_vector
print(sd_vector)## # A tibble: 1 x 5
## S5 S8 S9 S10 S11
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.256 0.185 0.236 0.200 0.183#Calculo de la matriz de correlaciin
cor(data_factor_1)->mat_R_F1
print(mat_R_F1)## X5 X8 X9 X10 X11
## X5 1.00000000 0.06386425 -0.0613244 0.09029485 0.1687878
## X8 0.06386425 1.00000000 0.6988972 0.18389026 0.3720139
## X9 -0.06132440 0.69889722 1.0000000 0.26598819 0.4806005
## X10 0.09029485 0.18389026 0.2659882 1.00000000 0.5526752
## X11 0.16878781 0.37201388 0.4806005 0.55267522 1.0000000#Cálculo de los ponderadores brutos
1-mat_R_F1->sum_data
colSums(sum_data)->sum_vector
sd_vector*sum_vector->vj
print(vj)## S5 S8 S9 S10 S11
## 1 0.957998 0.4954271 0.6163074 0.5808737 0.4439521#Cálculo de los ponderadores netos
vj/sum(vj)->wj
print(wj)## S5 S8 S9 S10 S11
## 1 0.309575 0.1600962 0.1991584 0.1877081 0.1434622#PONDERADORES NORMALIZADOS DE CADA VARIABLE DEL FACTOR 2
print(round(wj*100,2))## S5 S8 S9 S10 S11
## 1 30.96 16.01 19.92 18.77 14.35