library(psych)
library(GPArotation)
# Import Data dari Packages Sandwich
data(Investment, package = "sandwich")
Investment <- as.data.frame(Investment[,1:6])
Investment
## GNP Investment Price Interest RealGNP RealInv
## 1 596.7 90.9 0.7167 3.23 832.5659 126.8313
## 2 637.7 97.4 0.7277 3.55 876.3227 133.8464
## 3 691.1 113.5 0.7436 4.04 929.3975 152.6358
## 4 756.0 125.7 0.7676 4.50 984.8880 163.7572
## 5 799.6 122.8 0.7906 4.19 1011.3838 155.3251
## 6 873.4 133.3 0.8254 5.16 1058.1536 161.4975
## 7 944.0 149.3 0.8679 5.87 1087.6829 172.0244
## 8 992.7 144.2 0.9145 5.95 1085.5112 157.6818
## 9 1077.6 166.4 0.9601 4.88 1122.3831 173.3153
## 10 1185.9 195.0 1.0000 4.50 1185.9000 195.0000
## 11 1326.4 229.8 1.0575 6.44 1254.2790 217.3050
## 12 1434.2 228.7 1.1508 7.83 1246.2635 198.7313
## 13 1549.2 206.1 1.2579 6.25 1231.5764 163.8445
## 14 1718.0 257.9 1.3234 5.50 1298.1714 194.8768
## 15 1918.3 324.1 1.4005 5.46 1369.7251 231.4174
## 16 2163.9 386.6 1.5042 7.46 1438.5720 257.0137
## 17 2417.8 423.0 1.6342 10.28 1479.5007 258.8422
## 18 2631.7 401.9 1.7842 11.77 1475.0028 225.2550
## 19 2954.1 474.9 1.9514 13.42 1513.8362 243.3637
## 20 3073.0 414.5 2.0688 11.02 1485.4022 200.3577
#Transformasi Normal Baku
zinvestment <- data.frame(scale(Investment))
zinvestment
## GNP Investment Price Interest RealGNP RealInv
## 1 -1.12491819 -1.14784022 -1.06818487 -1.15272905 -1.6976136 -1.5795163
## 2 -1.07311736 -1.09581120 -1.04239746 -1.04212236 -1.4945241 -1.4017030
## 3 -1.00564994 -0.96693932 -1.00512293 -0.87275588 -1.2481860 -0.9254396
## 4 -0.92365302 -0.86928486 -0.94885949 -0.71375877 -0.9906364 -0.6435429
## 5 -0.86856726 -0.89249780 -0.89494036 -0.82090899 -0.8676606 -0.8572743
## 6 -0.77532576 -0.80845092 -0.81335837 -0.48563248 -0.6505861 -0.7008206
## 7 -0.68612726 -0.68037949 -0.71372519 -0.24022389 -0.5135309 -0.4339895
## 8 -0.62459798 -0.72120226 -0.60448034 -0.21257222 -0.5236105 -0.7975376
## 9 -0.51733236 -0.54350315 -0.49757980 -0.58241333 -0.3524758 -0.4012698
## 10 -0.38050236 -0.31457546 -0.40404183 -0.71375877 -0.0576727 0.1483809
## 11 -0.20298976 -0.03602009 -0.26924401 -0.04320574 0.2596968 0.7137532
## 12 -0.06679148 -0.04482500 -0.05051988 0.43724205 0.2224942 0.2429600
## 13 0.07850353 -0.22572590 0.20055572 -0.10887846 0.1543268 -0.6413291
## 14 0.29177133 0.18890536 0.35410803 -0.36811287 0.4634161 0.1452589
## 15 0.54483734 0.71880092 0.53485433 -0.38193871 0.7955207 1.0714651
## 16 0.85513694 1.21907996 0.77795928 0.30935307 1.1150621 1.7202652
## 17 1.17592306 1.51044247 1.08271959 1.28407449 1.3050256 1.7666141
## 18 1.44617178 1.34154827 1.43436609 1.79908687 1.2841495 0.9152661
## 19 1.85350318 1.92587418 1.82633473 2.36940259 1.4643883 1.3742746
## 20 2.00372559 1.44240452 2.10155673 1.53985245 1.3324164 0.2841844
#Mengecek Bentuk Histogram dan Kurva
par(mfrow=c(1,3))
for (i in 1:3) {
hist(zinvestment[,i], prob=TRUE, main=paste("x",i,sep = ""), xlab=paste("x",i,sep = ""))
lines(density(zinvestment[,i]))
}
par(mfrow=c(1,3))
for (i in 4:6) {
hist(zinvestment[,i], prob=TRUE, main=paste("x",i,sep = ""), xlab=paste("x",i,sep = ""))
lines(density(zinvestment[,i]))
}
#Uji Kenormalan Menggunakan Shapiro-Wilks
shapiro.test(zinvestment$GNP)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$GNP
## W = 0.89545, p-value = 0.03391
shapiro.test(zinvestment$Investment)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$Investment
## W = 0.88116, p-value = 0.01857
shapiro.test(zinvestment$Price)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$Price
## W = 0.89299, p-value = 0.03054
shapiro.test(zinvestment$Interest)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$Interest
## W = 0.8667, p-value = 0.01029
shapiro.test(zinvestment$RealGNP)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$RealGNP
## W = 0.94756, p-value = 0.3316
shapiro.test(zinvestment$RealInv)
##
## Shapiro-Wilk normality test
##
## data: zinvestment$RealInv
## W = 0.94862, p-value = 0.3466
#Uji Multivariat Normal
library(MVN)
mvn(data = Investment,mvnTest ="mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 81.2646154516567 0.0153260019440204 NO
## 2 Mardia Kurtosis -0.298396533551169 0.765400534453533 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling GNP 0.7245 0.0493 NO
## 2 Anderson-Darling Investment 0.9209 0.0154 NO
## 3 Anderson-Darling Price 0.7279 0.0483 NO
## 4 Anderson-Darling Interest 1.0673 0.0065 NO
## 5 Anderson-Darling RealGNP 0.3130 0.5204 YES
## 6 Anderson-Darling RealInv 0.3923 0.3449 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th
## GNP 20 1487.06500 791.4931115 1256.15000 596.7000 3073.0000 854.9500
## Investment 20 234.30000 124.9302795 200.55000 90.9000 474.9000 131.4000
## Price 20 1.17235 0.4265647 1.02875 0.7167 2.0688 0.8167
## Interest 20 6.56500 2.8931343 5.68500 3.2300 13.4200 4.5000
## RealGNP 20 1198.32589 215.4553672 1208.73822 832.5659 1513.8362 1046.4612
## RealInv 20 189.14610 39.4518207 184.09606 126.8313 258.8422 160.5435
## 75th Skew Kurtosis
## GNP 1979.700000 0.67604403 -0.9542482
## Investment 339.725000 0.58362449 -1.2362325
## Price 1.426425 0.70003321 -0.8708394
## Interest 7.552500 0.99777586 -0.2452418
## RealGNP 1386.936823 -0.02656484 -1.3519458
## RealInv 219.292477 0.29791744 -1.1619473
#Uji Korelasi dan Kecukupan Sampel "Barlett Test of Sphericity"
bartlett.test(zinvestment)
##
## Bartlett test of homogeneity of variances
##
## data: zinvestment
## Bartlett's K-squared = -6.2013e-15, df = 5, p-value = 1
#Penentuan Jumlah Faktor
library(nFactors)
## Loading required package: lattice
##
## Attaching package: 'nFactors'
## The following object is masked from 'package:lattice':
##
## parallel
R = cov(zinvestment)
eigen_data = eigen(R)
eigen_data
## eigen() decomposition
## $values
## [1] 5.5173791599 0.3300284791 0.1151570916 0.0361705689 0.0010496037
## [6] 0.0002150969
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.4194705 -0.22343018 0.32000450 0.13760165 0.33486088 0.73529214
## [2,] 0.4230439 0.05771685 0.07624479 0.53240938 -0.72647463 -0.02577197
## [3,] 0.4155335 -0.28516498 0.41772067 0.06975269 0.33813839 -0.67254686
## [4,] 0.3931743 -0.48686777 -0.77062786 -0.11413025 0.02673516 -0.02767562
## [5,] 0.4165632 0.21444001 0.18394897 -0.80469596 -0.31224573 0.04025371
## [6,] 0.3798674 0.76315392 -0.29931383 0.17938590 0.38412637 -0.06305315
ap = parallel(subject = 20, var = 6, rep = 100, cent = 0.05)
nfaktor = nScree(eigen$values, ap$eigen$qevpea)
plotnScree(nfaktor)
#Analisis Faktor Menggunakan Metode Estimasi Principal Component
library(psych)
R = cov(zinvestment)
Solution_pa = fa(R, nfactors = 1, rotate = "varimax", fm = "pa")
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
Solution_pa
## Factor Analysis using method = pa
## Call: fa(r = R, nfactors = 1, rotate = "varimax", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 h2 u2 com
## GNP 0.99 0.98 0.0214 1
## Investment 1.00 1.00 -0.0033 1
## Price 0.98 0.95 0.0488 1
## Interest 0.90 0.81 0.1919 1
## RealGNP 0.98 0.96 0.0434 1
## RealInv 0.86 0.73 0.2659 1
##
## PA1
## SS loadings 5.43
## Proportion Var 0.91
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 20.19
## The degrees of freedom for the model are 9 and the objective function was 9.56
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## Fit based upon off diagonal values = 1