Script Prak APG 9
Wisnu Aimariyadi
2024-12-05
Importing Data (Indonesia tanpa Pulau Papua)
## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13
## 1 99.17 1.52 9.89 66.23 14.38 98.97 84.85 71.70 99.08 94.55 74.46 99.43 97.72
## 2 99.31 0.79 10.07 56.10 13.48 97.95 82.09 68.67 98.75 94.35 74.43 99.51 96.76
## 3 99.18 0.63 9.59 77.31 14.11 98.89 80.22 69.18 95.81 90.65 68.64 99.76 96.79
## 4 98.16 0.75 9.60 66.88 13.30 98.13 80.76 64.81 98.09 90.52 67.79 99.65 95.89
## 5 98.73 1.70 9.16 62.84 13.13 99.33 80.23 60.60 97.76 89.35 66.62 99.49 96.01
## 6 97.89 1.16 8.90 68.64 12.63 98.12 79.12 61.24 97.58 87.95 64.81 99.41 95.27
## 7 97.33 1.92 9.35 59.83 13.74 98.61 81.08 67.09 97.10 89.25 63.41 99.42 97.91
## 8 98.24 2.42 8.72 59.25 12.77 99.22 80.64 62.84 98.67 87.67 64.54 99.61 95.93
## 9 99.05 1.67 8.66 77.50 12.31 98.11 77.00 60.72 96.01 87.11 68.96 99.51 93.20
## 10 99.69 0.86 10.52 62.52 13.05 99.29 86.78 74.11 97.92 95.51 78.97 99.29 99.07
## 11 98.51 0.28 11.42 70.99 13.33 98.44 84.95 60.81 98.66 95.85 88.10 99.49 98.17
## 12 94.34 1.36 9.16 60.02 12.68 98.20 83.61 59.01 99.09 91.42 66.47 99.40 95.75
## 13 95.59 5.18 8.44 64.40 12.85 98.46 81.56 61.46 98.42 90.64 58.35 99.57 97.08
## 14 93.70 4.12 10.16 85.09 15.66 99.36 85.62 76.37 98.95 97.02 89.69 99.63 98.88
## 15 98.23 5.83 8.53 75.18 13.38 98.04 83.91 62.59 98.78 90.74 68.65 99.28 97.64
## 16 95.61 1.62 9.48 52.50 13.09 97.97 85.43 60.42 97.15 90.86 70.07 99.43 96.65
## 17 89.11 4.03 9.74 62.70 13.97 97.77 84.78 75.60 98.43 93.03 76.51 99.61 97.95
## 18 95.11 9.79 8.39 66.32 13.22 98.76 84.03 68.04 98.11 92.95 63.66 99.46 97.95
## 19 94.79 4.37 8.31 60.53 12.67 95.98 73.47 58.15 93.41 82.48 43.46 98.62 94.89
## 20 99.03 4.72 8.17 67.08 12.76 97.70 70.85 54.76 95.33 81.56 55.58 98.81 92.92
## 21 98.37 0.92 9.07 66.68 12.86 99.05 79.07 55.63 97.47 88.92 63.93 99.13 95.21
## 22 99.01 1.49 8.95 71.29 14.02 99.14 77.44 59.83 95.99 88.19 68.35 99.30 94.12
## 23 97.78 0.89 10.17 68.77 13.20 98.53 83.36 69.89 97.88 94.85 73.63 99.64 98.71
## 24 99.79 2.02 9.53 65.39 12.96 94.73 80.53 66.70 96.41 88.08 59.50 99.22 96.96
## 25 98.14 0.21 9.94 59.15 13.33 95.68 76.56 63.86 96.18 92.07 67.57 99.34 95.00
## 26 93.83 1.70 9.22 63.94 13.54 93.31 76.80 66.18 97.56 90.05 55.69 98.34 93.13
## 27 96.03 5.62 9.12 86.74 13.70 98.41 77.98 60.57 98.37 88.74 67.41 99.49 93.22
## 28 98.49 3.57 9.62 67.53 13.16 98.48 76.54 64.00 97.83 89.55 68.28 99.20 95.00
## 29 94.33 1.45 8.48 70.39 12.88 98.69 73.55 60.18 93.69 83.71 46.19 98.69 91.85
## 30 99.47 5.10 8.48 62.73 14.08 95.92 72.39 61.17 95.13 84.04 54.79 98.31 89.47
## 31 98.81 0.48 10.38 63.97 13.74 97.27 78.58 66.16 98.69 93.90 75.01 99.59 97.97
## 32 97.84 1.08 9.61 57.00 13.34 97.36 78.53 65.75 98.30 93.46 64.61 99.12 97.51
## X14 X15
## 1 83.41 33.10
## 2 79.25 28.61
## 3 84.33 38.08
## 4 78.15 30.07
## 5 72.46 23.98
## 6 71.71 19.79
## 7 79.57 30.74
## 8 71.74 21.66
## 9 69.53 17.59
## 10 84.97 20.51
## 11 72.50 26.52
## 12 68.58 24.72
## 13 70.87 24.59
## 14 91.17 51.60
## 15 74.07 26.53
## 16 69.64 23.72
## 17 84.73 30.92
## 18 77.46 26.42
## 19 75.93 30.68
## 20 69.25 25.08
## 21 66.32 23.27
## 22 69.95 27.18
## 23 81.50 32.33
## 24 77.03 27.63
## 25 74.55 23.57
## 26 76.29 27.58
## 27 71.00 34.47
## 28 74.60 31.73
## 29 71.70 33.20
## 30 71.57 23.98
## 31 79.90 37.41
## 32 78.38 28.78Metadata Variabel:
| Variabel | Label Variabel |
|---|---|
| X1 | Angka Melek Aksara |
| X2 | Angka Buta Aksara |
| X3 | RLS |
| X4 | Indeks Pembangunan Literasi Masyarakat |
| X5 | Angka Harapan Lama Sekolah |
| X6 | APM SD |
| X7 | APM SMP |
| X8 | APM SMA |
| X9 | Penyelesaian Pendidikan SD |
| X10 | Penyelesaian Pendidikan SMP |
| X11 | Penyelesaian Pendidikan SMA |
| X12 | APS 7-12 |
| X13 | APS 13-15 |
| X14 | APS 16-19 |
| X15 | APS 19-24 |
Assumption Checking
Multivariate Normal
mvn <- mvn(dat, mvnTest = "mardia")
mvn## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 760.699031721101 0.0167874243434867 NO
## 2 Mardia Kurtosis 0.288150597581361 0.77323146301757 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling X1 1.8123 1e-04 NO
## 2 Anderson-Darling X2 1.8798 1e-04 NO
## 3 Anderson-Darling X3 0.2858 0.6028 YES
## 4 Anderson-Darling X4 0.6537 0.08 YES
## 5 Anderson-Darling X5 0.7029 0.0601 YES
## 6 Anderson-Darling X6 2.0609 <0.001 NO
## 7 Anderson-Darling X7 0.3281 0.5054 YES
## 8 Anderson-Darling X8 0.5291 0.1635 YES
## 9 Anderson-Darling X9 1.2898 0.002 NO
## 10 Anderson-Darling X10 0.3499 0.4513 YES
## 11 Anderson-Darling X11 0.6271 0.0934 YES
## 12 Anderson-Darling X12 2.0160 <0.001 NO
## 13 Anderson-Darling X13 0.6258 0.0941 YES
## 14 Anderson-Darling X14 0.5593 0.1365 YES
## 15 Anderson-Darling X15 0.6438 0.0848 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## X1 32 97.270625 2.3908966 98.195 89.11 99.79 95.6050 99.0150 -1.42210460
## X2 32 2.476562 2.1661123 1.645 0.21 9.79 0.9125 4.0525 1.39969550
## X3 32 9.338437 0.7518755 9.285 8.17 11.42 8.7050 9.7775 0.51955090
## X4 32 66.421563 7.6989656 65.810 52.50 86.74 62.0225 69.1750 0.83054032
## X5 32 13.353750 0.6516666 13.260 12.31 15.66 12.8750 13.7100 1.33487048
## X6 32 97.933437 1.4019194 98.305 93.31 99.36 97.7525 98.7925 -1.60786131
## X7 32 80.072187 4.1282127 80.380 70.85 86.78 77.3300 83.6850 -0.36569509
## X8 32 64.315313 5.4018300 63.350 54.76 76.37 60.5925 67.3275 0.51306067
## X9 32 97.393750 1.5088251 97.855 93.41 99.09 96.3525 98.4875 -1.06189679
## X10 32 90.281875 3.8520363 90.580 81.56 97.02 88.1625 93.1375 -0.41960723
## X11 32 66.816563 9.8554896 67.490 43.46 89.69 63.5975 70.9600 -0.03408319
## X12 32 99.304688 0.3705095 99.425 98.31 99.76 99.2150 99.5250 -1.36113922
## X13 32 95.955625 2.2550430 96.330 89.47 99.07 94.9725 97.7675 -0.83785609
## X14 32 75.690938 5.8534954 74.575 66.32 91.17 71.4275 79.3300 0.64294236
## X15 32 28.313750 6.4843985 27.380 17.59 51.60 23.9800 31.1225 1.33603932
## Kurtosis
## X1 1.92850516
## X2 1.77608215
## X3 -0.08839996
## X4 0.52284354
## X5 2.67461141
## X6 2.18173124
## X7 -0.72432879
## X8 -0.43556667
## X9 0.27584587
## X10 -0.40109611
## X11 0.51888890
## X12 0.96027080
## X13 0.22592896
## X14 -0.31947020
## X15 3.00979677Berdasarkan hasil pengujian tersebut, dapat dipahami bahwa data tidak berdistribusi multivariate normal. Sehingga, dalam proses analisis faktor tidak dapat dilanjutkan menggunakan metode maximum likelihood.
Tes Independensi
Matriks Korelasi
#Peninjauan nilai Korelasi
r <- round(cor(dat), 3)
r## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
## X1 1.000 -0.339 0.136 -0.009 -0.157 0.101 -0.166 -0.212 -0.062 -0.066 0.077
## X2 -0.339 1.000 -0.565 0.241 0.083 0.016 -0.061 -0.030 -0.010 -0.221 -0.250
## X3 0.136 -0.565 1.000 -0.022 0.377 0.088 0.546 0.548 0.476 0.792 0.792
## X4 -0.009 0.241 -0.022 1.000 0.354 0.279 -0.017 0.069 0.014 0.016 0.251
## X5 -0.157 0.083 0.377 0.354 1.000 0.104 0.266 0.612 0.250 0.449 0.487
## X6 0.101 0.016 0.088 0.279 0.104 1.000 0.414 0.082 0.311 0.255 0.433
## X7 -0.166 -0.061 0.546 -0.017 0.266 0.414 1.000 0.597 0.734 0.820 0.730
## X8 -0.212 -0.030 0.548 0.069 0.612 0.082 0.597 1.000 0.417 0.703 0.558
## X9 -0.062 -0.010 0.476 0.014 0.250 0.311 0.734 0.417 1.000 0.772 0.694
## X10 -0.066 -0.221 0.792 0.016 0.449 0.255 0.820 0.703 0.772 1.000 0.840
## X11 0.077 -0.250 0.792 0.251 0.487 0.433 0.730 0.558 0.694 0.840 1.000
## X12 0.059 -0.162 0.428 0.194 0.149 0.608 0.669 0.377 0.597 0.603 0.686
## X13 -0.060 -0.109 0.591 -0.092 0.228 0.349 0.834 0.623 0.627 0.793 0.644
## X14 -0.166 -0.051 0.534 0.125 0.659 0.067 0.463 0.936 0.269 0.607 0.481
## X15 -0.290 0.074 0.316 0.452 0.763 0.118 0.126 0.497 0.115 0.317 0.288
## X12 X13 X14 X15
## X1 0.059 -0.060 -0.166 -0.290
## X2 -0.162 -0.109 -0.051 0.074
## X3 0.428 0.591 0.534 0.316
## X4 0.194 -0.092 0.125 0.452
## X5 0.149 0.228 0.659 0.763
## X6 0.608 0.349 0.067 0.118
## X7 0.669 0.834 0.463 0.126
## X8 0.377 0.623 0.936 0.497
## X9 0.597 0.627 0.269 0.115
## X10 0.603 0.793 0.607 0.317
## X11 0.686 0.644 0.481 0.288
## X12 1.000 0.681 0.305 0.181
## X13 0.681 1.000 0.615 0.277
## X14 0.305 0.615 1.000 0.656
## X15 0.181 0.277 0.656 1.000Berdasarkan matriks korelasi yang diberikan, terdapat beberapa variabel yang memiliki nilai korelasi yang sangat rendah. Sehingga perlu diidentifikasi terlebih dahulu apakah nilai korelasi memiliki nilai yang sama seperti matriks identitas melalui uji hipotesis Bartlett Sphericity test.
Tes Bartlett
#Uji Bartlett
cortest.bartlett(r, n=32)## $chisq
## [1] 422.925
##
## $p.value
## [1] 9.666755e-40
##
## $df
## [1] 105qchisq(p = 1-0.05, df = 119)## [1] 145.4607Hipotesis
\[ H_0: \rho=I\\ H_1:\rho\neq I \]
Tingkat Signifikansi
\[ \alpha =5\% \]
Statistik Uji
\[ Statistik~Uji=422.925 \]
Wilayah Kritis
\[ Tolak~H_0~jika~statistik~uji>\chi^2_{(p+2)(p-1)/2;\alpha}\\ \chi^2_{(17)(14)/2;0.05}=145.461\\ \]
Kesimpulan
Dengan tingkat signifikansi 5% dari sampel yang ada, dapat disimpulkan bahwa matriks korelasi dari ke delapan variabel tersebut memiliki nilai tidak sama dengan matriks identitas. Sehingga dapat dilanjutkan ke proses pengujian.
Factor Analysis
Penentuan Jumlah Faktor
#Eigen Values of Data
eigen <- eigen(cor(dat))
values <- eigen$values
vector <- eigen$vectors
#Scree Plot
scree.plot(dat)
Berdasarkan scree plot, terlihat bahwa terjadi elbow pada dimension ketiga. Sehingga, akan dilakukan exploratory factor analysis (EFA) pada dengan jumlah faktor 3.
Model Estimation
Minimum Residual Method
#Minres
fact1 <- fa(r, nfactors = 3, rotate = "varimax")
fact1$communalities## X1 X2 X3 X4 X5 X6 X7 X8
## 0.1081202 0.3293917 0.8079957 0.3202874 0.6933247 0.4652497 0.7770787 0.7673605
## X9 X10 X11 X12 X13 X14 X15
## 0.5896575 0.9124809 0.7945529 0.7289746 0.7127850 0.8389558 0.7306806#Loadings
fact1$loadings##
## Loadings:
## MR1 MR2 MR3
## X1 -0.250 -0.209
## X2 -0.136 0.556
## X3 0.541 0.428 -0.576
## X4 0.104 0.236 0.504
## X5 0.176 0.792 0.189
## X6 0.583 -0.100 0.340
## X7 0.849 0.211 -0.108
## X8 0.414 0.757 -0.150
## X9 0.754 0.128
## X10 0.789 0.440 -0.310
## X11 0.816 0.335 -0.131
## X12 0.848
## X13 0.764 0.303 -0.193
## X14 0.298 0.858 -0.119
## X15 0.795 0.301
##
## MR1 MR2 MR3
## SS loadings 4.842 3.342 1.393
## Proportion Var 0.323 0.223 0.093
## Cumulative Var 0.323 0.546 0.638load1 <- round(matrix(fact1$loadings[1:45], ncol = 3, nrow = 15, byrow = F),3)
rownames(load1) <- c("X1","X2","X3","X4","X5","X6","X7","X8","X9","X10","X11","X12","X13","X14","X15")Principal Component Solution Method
#Penghitungan nilai eigen
eigen <- eigen(r)
values <- eigen$values
vectors <- eigen$vectors
#Penghitungan Matriks Loading
loadings1 <- sqrt(values[1])*vectors[,1]
loadings2 <- sqrt(values[2])*vectors[,2]
loadings3 <- sqrt(values[3])*vectors[,3]
#Factor 3 Princomp Method
fact2 <- cbind(loadings1,loadings2,loadings3)
fact2 <- varimax(fact2) #rotation loadings matriks factor analysis dengan 3 faktor
load2 <- round(matrix(fact2$loadings[1:45], ncol = 3, nrow = 15, byrow = F),3)
rownames(load2) <- c("X1","X2","X3","X4","X5","X6","X7","X8","X9","X10","X11","X12","X13","X14","X15")
load2## [,1] [,2] [,3]
## X1 -0.091 0.350 0.331
## X2 0.151 -0.031 -0.743
## X3 -0.561 -0.451 0.547
## X4 -0.123 -0.228 -0.668
## X5 -0.166 -0.824 -0.202
## X6 -0.668 0.193 -0.418
## X7 -0.858 -0.225 0.080
## X8 -0.417 -0.786 0.123
## X9 -0.798 -0.123 0.041
## X10 -0.787 -0.457 0.262
## X11 -0.831 -0.338 0.112
## X12 -0.874 -0.014 -0.095
## X13 -0.785 -0.317 0.178
## X14 -0.305 -0.864 0.095
## X15 -0.080 -0.815 -0.309Interpretasi
Minimum Residual
Nilai Komunalitas
as.matrix(fact1$communalities)## [,1]
## X1 0.1081202
## X2 0.3293917
## X3 0.8079957
## X4 0.3202874
## X5 0.6933247
## X6 0.4652497
## X7 0.7770787
## X8 0.7673605
## X9 0.5896575
## X10 0.9124809
## X11 0.7945529
## X12 0.7289746
## X13 0.7127850
## X14 0.8389558
## X15 0.7306806Sebagian besar dari variabel sudah memiliki nilai communalities yang lebih dari 0,5. Hal ini bermakna bahwa dari main factor yang disusun, dapat menjelaskan sebagian besar variasi dari masing-masing variabel pada data.
Loadings
load1## [,1] [,2] [,3]
## X1 0.040 -0.250 -0.209
## X2 -0.136 0.037 0.556
## X3 0.541 0.428 -0.576
## X4 0.104 0.236 0.504
## X5 0.176 0.792 0.189
## X6 0.583 -0.100 0.340
## X7 0.849 0.211 -0.108
## X8 0.414 0.757 -0.150
## X9 0.754 0.128 -0.070
## X10 0.789 0.440 -0.310
## X11 0.816 0.335 -0.131
## X12 0.848 0.036 0.093
## X13 0.764 0.303 -0.193
## X14 0.298 0.858 -0.119
## X15 0.093 0.795 0.301Principal Component Method
Communalities
as.matrix(rowSums(load2^2))## [,1]
## X1 0.240342
## X2 0.575811
## X3 0.817331
## X4 0.513337
## X5 0.747336
## X6 0.658197
## X7 0.793189
## X8 0.806814
## X9 0.653614
## X10 0.896862
## X11 0.817349
## X12 0.773097
## X13 0.748398
## X14 0.848546
## X15 0.766106Loadings
load2## [,1] [,2] [,3]
## X1 -0.091 0.350 0.331
## X2 0.151 -0.031 -0.743
## X3 -0.561 -0.451 0.547
## X4 -0.123 -0.228 -0.668
## X5 -0.166 -0.824 -0.202
## X6 -0.668 0.193 -0.418
## X7 -0.858 -0.225 0.080
## X8 -0.417 -0.786 0.123
## X9 -0.798 -0.123 0.041
## X10 -0.787 -0.457 0.262
## X11 -0.831 -0.338 0.112
## X12 -0.874 -0.014 -0.095
## X13 -0.785 -0.317 0.178
## X14 -0.305 -0.864 0.095
## X15 -0.080 -0.815 -0.309