PCA y FA
Luis Saucedo
24 de marzo de 2019
Análisis de componentes
prcomp y princomp
pca_prcomp(datos, t=TRUE, n=11, w=TRUE, q=TRUE, m=11)## Standard deviations (1, .., p=11):
## [1] 2.3314342 1.4399034 1.1896948 0.8180625 0.6477702 0.5073144 0.4921281
## [8] 0.4242908 0.3821780 0.3137094 0.2506634
##
## Rotation (n x k) = (11 x 11):
## PC1 PC2 PC3 PC4 PC5
## V1 -0.3821641 0.12218707 -0.014056290 -0.01399090 -0.45040647
## V2 -0.3825994 -0.03246375 0.020596338 0.12168423 -0.50160567
## V3 0.1135163 -0.07102210 0.748462737 -0.28112277 -0.14551431
## V4 0.3185078 0.36956111 -0.035427309 -0.28133267 -0.18546059
## V5 0.2515746 0.30962429 0.461138374 0.03612228 -0.18121642
## V6 -0.2973952 0.44790378 -0.019041506 -0.06843929 -0.02615058
## V7 -0.2981321 0.35685649 0.001941143 -0.33119936 0.47685381
## V8 0.2007606 0.57076656 -0.172157282 0.03799432 0.02418820
## V9 -0.2276497 0.24693541 0.332158621 0.74848726 0.22629198
## V10 -0.3429979 -0.16251083 0.288074137 -0.25820884 0.37998114
## V11 -0.3779443 0.07351183 -0.044243799 -0.28773043 -0.18128464
## PC6 PC7 PC8 PC9 PC10
## V1 0.10872118 -0.058766226 0.07269904 -0.71377358 -0.325106443
## V2 -0.31040509 0.242360223 -0.21878837 0.15627378 0.588707133
## V3 0.07875158 0.451997356 -0.17652047 0.08736735 -0.264553974
## V4 0.48586631 0.040299607 -0.04823410 -0.13254604 0.462776583
## V5 -0.36584593 -0.652186368 0.11398169 -0.01476997 0.105554201
## V6 -0.26393022 0.192630211 0.44281233 0.34556115 -0.233611303
## V7 -0.24709329 -0.056420568 -0.58977760 -0.18023693 0.028838416
## V8 0.02288744 0.343598022 0.16432572 -0.02197933 -0.006208564
## V9 0.37200145 0.005648358 -0.12625079 0.01976721 0.050422895
## V10 0.11148208 0.007228604 0.55245969 -0.20112214 0.418533978
## V11 0.48338993 -0.384840084 -0.09107352 0.49745784 -0.138850465
## PC11
## V1 0.005981733
## V2 0.108482896
## V3 0.048828928
## V4 -0.418845205
## V5 0.102509603
## V6 -0.477883734
## V7 -0.035935648
## V8 0.675385771
## V9 -0.090213436
## V10 0.169072324
## V11 0.278096752
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.3314 1.4399 1.1897 0.81806 0.64777 0.5073 0.49213
## Proportion of Variance 0.4941 0.1885 0.1287 0.06084 0.03815 0.0234 0.02202
## Cumulative Proportion 0.4941 0.6826 0.8113 0.87214 0.91028 0.9337 0.95570
## PC8 PC9 PC10 PC11
## Standard deviation 0.42429 0.38218 0.31371 0.25066
## Proportion of Variance 0.01637 0.01328 0.00895 0.00571
## Cumulative Proportion 0.97206 0.98534 0.99429 1.00000
pca_princomp(datos, f=TRUE, w=TRUE, q=TRUE, m=11)## Call:
## princomp(x = datos, cor = f)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
## 2.3314342 1.4399034 1.1896948 0.8180625 0.6477702 0.5073144 0.4921281
## Comp.8 Comp.9 Comp.10 Comp.11
## 0.4242908 0.3821780 0.3137094 0.2506634
##
## 11 variables and 50 observations.
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 2.3314342 1.4399034 1.1896948 0.81806252 0.64777020
## Proportion of Variance 0.4941441 0.1884838 0.1286703 0.06083875 0.03814602
## Cumulative Proportion 0.4941441 0.6826279 0.8112983 0.87213704 0.91028306
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.50731439 0.49212810 0.4242908 0.38217799
## Proportion of Variance 0.02339708 0.02201728 0.0163657 0.01327818
## Cumulative Proportion 0.93368014 0.95569742 0.9720631 0.98534130
## Comp.10 Comp.11
## Standard deviation 0.31370941 0.250663389
## Proportion of Variance 0.00894669 0.005712012
## Cumulative Proportion 0.99428799 1.000000000
Análisis Factorial
Con solución de factor principal; varimax, none y quartimax. scores=regression
FA(D1, n=3, r="varimax", B=FALSE)## $varianza_acumulada
## X1 X2 X3 X4 X5 X6 X7
## 0.4511991 0.4455733 0.2191468 0.3100766 0.2036984 0.1730550 0.8528584
## X8 X9 X10 X11
## 0.8140632 0.8164366 0.1198478 0.2735050
##
## $comunalidad
## X1 X2 X3 X4 X5 X6 X7
## 0.5488009 0.5544267 0.7808532 0.6899234 0.7963016 0.8269450 0.1471416
## X8 X9 X10 X11
## 0.1859368 0.1835634 0.8801522 0.7264950
##
## $pesos_factoriales
##
## Loadings:
## PA1 PA3 PA2
## X1 -0.438 -0.274 -0.531
## X2 -0.717 -0.176
## X3 0.125 0.872
## X4 0.243 0.792
## X5 0.140 0.881
## X6 0.848 0.247 0.218
## X7 0.137 0.163 -0.319
## X8 0.426
## X9 -0.400 -0.136
## X10 0.925 -0.129
## X11 0.826 -0.205
##
## PA1 PA3 PA2
## SS loadings 3.230 1.641 1.450
## Proportion Var 0.294 0.149 0.132
## Cumulative Var 0.294 0.443 0.575FA(D1, n=3, r="none", B=FALSE)## $varianza_acumulada
## X1 X2 X3 X4 X5 X6 X7
## 0.4511991 0.4455733 0.2191468 0.3100766 0.2036984 0.1730550 0.8528584
## X8 X9 X10 X11
## 0.8140632 0.8164366 0.1198478 0.2735050
##
## $comunalidad
## X1 X2 X3 X4 X5 X6 X7
## 0.5488009 0.5544267 0.7808532 0.6899234 0.7963016 0.8269450 0.1471416
## X8 X9 X10 X11
## 0.1859368 0.1835634 0.8801522 0.7264950
##
## $pesos_factoriales
##
## Loadings:
## PA1 PA2 PA3
## X1 -0.579 -0.421 0.189
## X2 -0.728 0.134
## X3 0.232 0.770 -0.366
## X4 0.570 0.300 0.525
## X5 0.512 0.338 0.648
## X6 0.891 -0.182
## X7 0.151 -0.249 0.249
## X8 0.394 -0.175
## X9 -0.406 0.137
## X10 0.844 -0.377 -0.161
## X11 0.731 -0.423 -0.115
##
## PA1 PA2 PA3
## SS loadings 3.733 1.538 1.049
## Proportion Var 0.339 0.140 0.095
## Cumulative Var 0.339 0.479 0.575FA(D1, n=3, r="quartimax", B=FALSE)## $varianza_acumulada
## X1 X2 X3 X4 X5 X6 X7
## 0.4511991 0.4455733 0.2191468 0.3100766 0.2036984 0.1730550 0.8528584
## X8 X9 X10 X11
## 0.8140632 0.8164366 0.1198478 0.2735050
##
## $comunalidad
## X1 X2 X3 X4 X5 X6 X7
## 0.5488009 0.5544267 0.7808532 0.6899234 0.7963016 0.8269450 0.1471416
## X8 X9 X10 X11
## 0.1859368 0.1835634 0.8801522 0.7264950
##
## $pesos_factoriales
##
## Loadings:
## PA1 PA3 PA2
## X1 -0.421 -0.232 -0.563
## X2 -0.719 -0.137 -0.139
## X3 0.879
## X4 0.276 0.776 0.107
## X5 0.180 0.871
## X6 0.845 0.196 0.272
## X7 0.162 0.168 -0.305
## X8 0.423
## X9 -0.409 -0.118
## X10 0.934
## X11 0.837 -0.159
##
## PA1 PA3 PA2
## SS loadings 3.292 1.525 1.504
## Proportion Var 0.299 0.139 0.137
## Cumulative Var 0.299 0.438 0.575Gráfico de codo
scree.plot(D1,type = 'R')