# Mengimpor pustaka yang diperlukan
library(biotools)
## Loading required package: MASS
## ---
## biotools version 4.2
library(candisc)
## Loading required package: heplots
## Loading required package: broom
## Warning in rgl.init(initValue, onlyNULL): RGL: unable to open X11 display
## Warning: 'rgl.init' failed, running with 'rgl.useNULL = TRUE'.
##
## Attaching package: 'heplots'
## The following object is masked from 'package:biotools':
##
## boxM
##
## Attaching package: 'candisc'
## The following object is masked from 'package:stats':
##
## cancor
library(MASS)
library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
library(readxl)
library(moments)
library(ggplot2)
# Membaca Data dari File Excel
datadiskriminan <- read_excel('data simulasi.xlsx')
head(datadiskriminan)
## # A tibble: 6 × 7
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah Usia
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 205 300 104 52
## 2 2 168 300 113 58
## 3 2 210 300 100 70
## 4 2 158 340 100 46
## 5 2 245 347 117 61
## 6 2 158 390 115 60
## # ℹ 2 more variables: Berat_Badan <dbl>, Diabetes_Melitus <dbl>
# Menghitung Standar Deviasi untuk Setiap Variabel
std_dev <- apply(datadiskriminan[, 1:6], 2, sd)
print(std_dev)
## Jenis_Kelamin Gula_Darah_Puasa
## 0.4963042 73.8878098
## Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 63.3469012 6.9684026
## Usia Berat_Badan
## 8.0512877 9.7076650
# Pembakuan Data (Z-Score)
z_score <- scale(datadiskriminan[, 1:6])
z_score_data <- as.data.frame(z_score)
z_score_data$Diabetes_Melitus <- datadiskriminan$Diabetes_Melitus
head(z_score_data)
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
# Uji Asumsi Normalitas Multivariat secara Manual
shapiro_results <- apply(z_score_data[, 1:6], 2, shapiro.test)
print(shapiro_results)
## $Jenis_Kelamin
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.62939, p-value < 2.2e-16
##
##
## $Gula_Darah_Puasa
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.90498, p-value = 1.697e-10
##
##
## $Gula_Darah_Jam_Pos_Prandial
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97961, p-value = 0.003215
##
##
## $Tekanan_Darah
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.99309, p-value = 0.4105
##
##
## $Usia
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.98728, p-value = 0.05114
##
##
## $Berat_Badan
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.95367, p-value = 1.916e-06
kurtosis_values <- apply(z_score_data[, 1:6], 2, kurtosis)
skewness_values <- apply(z_score_data[, 1:6], 2, skewness)
print(kurtosis_values)
## Jenis_Kelamin Gula_Darah_Puasa
## 1.078678 2.446707
## Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 3.062940 2.638613
## Usia Berat_Badan
## 2.440338 3.253544
print(skewness_values)
## Jenis_Kelamin Gula_Darah_Puasa
## -0.28049636 0.72089751
## Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 0.03989887 0.06512175
## Usia Berat_Badan
## 0.06757823 0.73741438
# Fungsi untuk Uji Mardia
mardiaTest <- function(data) {
n <- nrow(data)
p <- ncol(data)
S <- cov(data)
D <- mahalanobis(data, colMeans(data), S)
skewness <- sum(D^3) / n^2
kurtosis <- sum((D^2 - p*(p+2))^2) / (6*n)
skewness_test <- 1 - pchisq(skewness, df = p * (p + 1) * (p + 2) / 6)
kurtosis_test <- 1 - pchisq(kurtosis, df = p * (p + 1) / 2)
return(list(
skewness = skewness,
kurtosis = kurtosis,
skewness_p_value = skewness_test,
kurtosis_p_value = kurtosis_test
))
}
mardia_results <- mardiaTest(z_score_data[, 1:6])
print(mardia_results)
## $skewness
## [1] 1.791149
##
## $kurtosis
## [1] 344.4244
##
## $skewness_p_value
## [1] 1
##
## $kurtosis_p_value
## [1] 0
# Menghitung Jarak Mahalanobis
mahalanobis_distances <- mahalanobis(z_score_data[, 1:6], colMeans(z_score_data[, 1:6]), cov(z_score_data[, 1:6]))
# Menampilkan Jarak Mahalanobis
print(mahalanobis_distances)
## [1] 3.302903 10.403062 7.563359 4.013743 2.841154 6.927135 7.330482
## [8] 5.824415 13.855559 10.561243 2.709230 6.343351 5.258432 10.367384
## [15] 6.371304 2.702129 2.434439 4.079689 10.613354 9.381816 5.047701
## [22] 9.359773 3.826247 4.987148 3.953331 3.161660 2.557219 10.718360
## [29] 3.940927 14.239956 5.433777 8.727231 4.459528 5.003449 2.371802
## [36] 3.663036 10.438842 3.637564 3.082724 3.814762 7.272961 7.981521
## [43] 11.209582 4.542734 8.603207 3.018609 5.609909 3.982150 6.069442
## [50] 2.891201 4.183997 4.324541 6.205996 5.685525 3.226490 6.536451
## [57] 4.952103 3.446623 5.781965 6.870296 4.795004 6.775750 2.093067
## [64] 2.884114 5.721607 8.826378 4.559201 2.870625 2.487784 2.329662
## [71] 6.341268 3.030197 6.243308 3.334498 6.823348 8.270301 2.703203
## [78] 9.740442 11.119249 5.126365 2.973501 12.576820 4.040471 4.126404
## [85] 2.184335 5.650509 7.166263 6.678123 10.613844 4.160122 6.740284
## [92] 8.445388 3.756144 7.784593 4.780416 4.936509 6.116217 4.546096
## [99] 3.730742 5.977770 8.961600 3.978433 2.378394 2.436968 2.921181
## [106] 11.378657 9.963123 9.234962 3.110419 2.587634 7.059587 7.044857
## [113] 8.333633 3.344155 5.759270 3.637244 5.679935 1.975011 7.412179
## [120] 9.096477 7.637605 10.009306 3.900205 4.182347 3.143620 5.238443
## [127] 3.769393 7.107146 7.168686 5.237983 7.843095 8.745535 2.784300
## [134] 12.229576 6.053905 7.602616 4.413651 5.998367 4.674470 6.641800
## [141] 3.262199 2.195322 7.169116 13.791371 4.106467 3.970720 5.646608
## [148] 9.151876 7.948018 4.377479 6.831316 2.196440 13.600791 4.424593
## [155] 3.230557 7.836566 2.907931 3.661100 6.516647 4.557561 9.660268
## [162] 3.337381 3.912317 2.008576 6.439764 5.170457 3.991131 3.622865
## [169] 5.937997 4.995275 4.871745 3.398749 5.682312 7.486796 5.068760
## [176] 9.691410 5.381175 4.911998 6.055570 4.271717 6.195223 2.878715
## [183] 3.085791 6.065180 10.050922 5.207102 12.987982 6.589241 5.111616
## [190] 8.193395 11.427626 6.455140 6.596590 5.986297 10.040599 6.182185
## [197] 4.096309 5.682430 8.107261 4.507613 7.321020 10.270993 5.415660
## [204] 3.051097 8.612455 6.573726 19.289445 1.477415 10.031991 5.931815
## [211] 8.372399 4.329661 7.380865 4.369650 4.912342 2.493091
# Menghitung Jarak Mahalanobis dan Menentukan Outlier
cutoff <- qchisq(0.975, df = 6)
outliers <- which(mahalanobis_distances > cutoff)
databaru <- z_score_data[-outliers,]
# Uji Normalitas Univariatif dan Multivariat pada Data Baru
shapiro_results_new <- apply(databaru[, 1:6], 2, shapiro.test)
print(shapiro_results_new)
## $Jenis_Kelamin
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.62884, p-value < 2.2e-16
##
##
## $Gula_Darah_Puasa
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.90379, p-value = 1.512e-10
##
##
## $Gula_Darah_Jam_Pos_Prandial
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97941, p-value = 0.003098
##
##
## $Tekanan_Darah
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.99303, p-value = 0.4063
##
##
## $Usia
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.98713, p-value = 0.04928
##
##
## $Berat_Badan
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.95802, p-value = 5.873e-06
mardia_results_new <- mardiaTest(databaru[, 1:6])
print(mardia_results_new)
## $skewness
## [1] 1.71385
##
## $kurtosis
## [1] 279.0904
##
## $skewness_p_value
## [1] 1
##
## $kurtosis_p_value
## [1] 0
# Membuat Q-Q Plot Chi-Square
qqplot_chisquare <- function(distances, df) {
chi2_quantiles <- qchisq((1:length(distances) - 0.5) / length(distances), df)
plot <- ggplot(data = data.frame(distances = sort(distances), chi2_quantiles = chi2_quantiles), aes(x = chi2_quantiles, y = distances)) +
geom_point() +
geom_abline(slope = 1, intercept = 0, color = "red") +
labs(title = "Adjusted Chi-Square Q-Q Plot", x = "Chi-Square Quantile", y = "Robust Squared Mahalanobis Distance") +
theme_minimal()
return(plot)
}
# Menampilkan plot
print(qqplot_chisquare(mahalanobis_distances, df = 6))
uji_bart <- function(x) {
method = "Bartlett's test of sphericity"
data.name = deparse(substitute(x))
x = subset(x, complete.cases(x))
n = nrow(x)
p = ncol(x)
chisq = (1 - n + (2 * p + 5) / 6) * log(det(cor(x)))
df = p * (p - 1) / 2
p.value = pchisq(chisq, df, lower.tail = FALSE)
names(chisq) = "Khi-squared"
names(df) = "df"
return(structure(list(statistic = chisq, parameter = df, p.value = p.value,
method = method, data.name = data.name), class = "htest"))
}
print(uji_bart(databaru[, 1:6]))
##
## Bartlett's test of sphericity
##
## data: databaru[, 1:6]
## Khi-squared = 142.94, df = 15, p-value < 2.2e-16
X <- as.matrix(databaru[, 1:6])
X.manova <- manova(X ~ databaru$Diabetes_Melitus)
X.wilks <- summary(X.manova, test = "Wilks")
print(X.wilks)
## Df Wilks approx F num Df den Df Pr(>F)
## databaru$Diabetes_Melitus 1 0.26852 94.435 6 208 < 2.2e-16 ***
## Residuals 213
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
cc <- candisc(X.manova)
print(cc)
##
## Canonical Discriminant Analysis for databaru$Diabetes_Melitus:
##
## CanRsq Eigenvalue Difference Percent Cumulative
## 1 0.73148 2.7241 100 100
##
## Test of H0: The canonical correlations in the
## current row and all that follow are zero
##
## LR test stat approx F numDF denDF Pr(> F)
## 1 0.26852 94.435 6 208 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
set.seed(123) # untuk reprodusibilitas
folds <- createFolds(databaru$Diabetes_Melitus, k = 10)
accuracy <- c()
for(i in 1:10) {
cat("\nFold", i, "\n")
# Data latih dan uji
train_indices <- folds[[i]]
test_indices <- setdiff(seq_len(nrow(databaru)), train_indices)
train_data <- databaru[train_indices, ]
test_data <- databaru[test_indices, ]
cat("Train Indices:\n", train_indices, "\n")
cat("Test Indices:\n", test_indices, "\n")
cat("Train Data (first 6 rows):\n")
print(head(train_data))
cat("Test Data (first 6 rows):\n")
print(head(test_data))
# Membuat model LDA
model_lda <- lda(Diabetes_Melitus ~ ., data = train_data)
# Prediksi pada data uji
predictions <- predict(model_lda, test_data)$class
# Menghitung akurasi
conf_matrix <- table(test_data$Diabetes_Melitus, predictions)
cat("Confusion Matrix:\n")
print(conf_matrix)
accuracy[i] <- sum(diag(conf_matrix)) / sum(conf_matrix)
}
##
## Fold 1
## Train Indices:
## 6 20 28 44 49 50 75 82 99 112 129 136 138 151 161 165 169 182 191 193 199
## Test Indices:
## 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 47 48 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 76 77 78 79 80 81 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 100 101 102 103 104 105 106 107 108 109 110 111 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 130 131 132 133 134 135 137 139 140 141 142 143 144 145 146 147 148 149 150 152 153 154 155 156 157 158 159 160 162 163 164 166 167 168 170 171 172 173 174 175 176 177 178 179 180 181 183 184 185 186 187 188 189 190 192 194 195 196 197 198 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 6 0.8675235 -1.0749530 0.8718892 0.9852675
## 20 0.8675235 -0.7095342 -2.3011152 0.9852675
## 28 -1.1473699 2.2002828 2.4504984 -1.3825635
## 44 0.8675235 -1.1832253 0.2404456 0.2677430
## 49 0.8675235 -0.3711834 -0.8014365 -0.7367914
## 50 0.8675235 0.8468795 0.7140283 0.1242380
## Usia Berat_Badan Diabetes_Melitus
## 6 0.4962399 0.01144571 1
## 20 -1.2426124 -0.09156567 2
## 28 0.8688511 -0.50361121 2
## 44 -1.3668161 -0.91565674 1
## 49 1.6140735 -0.19457706 2
## 50 0.3720362 0.93854816 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 7 -1.1473699 2.2002828 1.58226337 0.9135151
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 7 1.8624810 0.01144571 2
## Confusion Matrix:
## predictions
## 1 2
## 1 69 10
## 2 6 109
##
## Fold 2
## Train Indices:
## 10 13 26 36 42 60 67 68 72 79 92 97 107 109 110 114 149 158 160 189 207 209
## Test Indices:
## 1 2 3 4 5 6 7 8 9 11 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 61 62 63 64 65 66 69 70 71 73 74 75 76 77 78 80 81 82 83 84 85 86 87 88 89 90 91 93 94 95 96 98 99 100 101 102 103 104 105 106 108 111 112 113 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 150 151 152 153 154 155 156 157 159 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 208 210 211 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 10 0.8675235 -0.7772043 1.0297502 -0.09101932
## 13 0.8675235 -0.6553980 -0.2331372 -1.95658317
## 26 0.8675235 -0.8990106 -1.3381636 -0.80854388
## 36 0.8675235 -1.0478850 -0.5488590 -1.52606844
## 42 -1.1473699 -0.6824661 1.0297502 -1.88483072
## 60 -1.1473699 -0.1005027 -1.3223775 -1.31081107
## Usia Berat_Badan Diabetes_Melitus
## 10 -0.9942049 1.76263923 1
## 13 0.3720362 0.01144571 1
## 26 -0.8700012 0.62951401 1
## 36 -0.7457974 0.11445709 1
## 42 -0.3731862 -0.91565674 1
## 60 0.2478325 -0.60662259 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## Confusion Matrix:
## predictions
## 1 2
## 1 71 4
## 2 8 110
##
## Fold 3
## Train Indices:
## 1 4 22 25 32 34 37 41 43 51 64 86 102 106 117 124 141 155 171 183 195 212
## Test Indices:
## 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 23 24 26 27 28 29 30 31 33 35 36 38 39 40 42 44 45 46 47 48 49 50 52 53 54 55 56 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 103 104 105 107 108 109 110 111 112 113 114 115 116 118 119 120 121 122 123 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 142 143 144 145 146 147 148 149 150 151 152 153 154 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 172 173 174 175 176 177 178 179 180 181 182 184 185 186 187 188 189 190 191 192 193 194 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.59328651
## 4 0.8675235 -1.0749530 0.08258465 -1.16730616
## 22 -1.1473699 -0.3711834 -0.95929741 -1.02380125
## 25 0.8675235 -1.0208169 0.55616740 0.05248559
## 32 0.8675235 -0.9802148 -0.23313719 2.06155436
## 34 0.8675235 0.5085287 -0.31206765 1.12877243
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 4 -1.2426124 -0.09156567 1
## 22 1.1172586 1.96866199 2
## 25 -0.8700012 -1.01866812 1
## 32 -0.9942049 -1.22469089 1
## 34 -0.4973900 1.45360508 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 2 0.8675235 -0.9396127 -0.5488590 0.6982577
## 3 0.8675235 -0.3711834 -0.5488590 -1.1673062
## 5 0.8675235 0.1025078 0.1930873 1.2722773
## 6 0.8675235 -1.0749530 0.8718892 0.9852675
## 7 -1.1473699 2.2002828 1.5822634 0.9135151
## 8 -1.1473699 -0.5065237 -1.4960245 1.3440298
## Usia Berat_Badan Diabetes_Melitus
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## 7 1.8624810 0.01144571 2
## 8 -0.1247788 0.62951401 2
## Confusion Matrix:
## predictions
## 1 2
## 1 68 10
## 2 15 100
##
## Fold 4
## Train Indices:
## 2 18 31 39 55 63 77 88 89 94 96 101 108 139 163 164 166 184 200 206 215
## Test Indices:
## 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 56 57 58 59 60 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 80 81 82 83 84 85 86 87 90 91 92 93 95 97 98 99 100 102 103 104 105 106 107 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 165 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 201 202 203 204 205 207 208 209 210 211 212 213 214
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 2 0.8675235 -0.9396127 -0.5488590 0.6982577
## 18 0.8675235 -0.7772043 0.7929588 0.6265052
## 31 -1.1473699 -0.5065237 -1.1803027 0.4112479
## 39 0.8675235 -0.8584085 0.5561674 0.2677430
## 55 -1.1473699 -0.6824661 0.3509482 0.6982577
## 63 0.8675235 0.1025078 -0.5488590 -0.2345242
## Usia Berat_Badan Diabetes_Melitus
## 2 0.2478325 2.68974168 1
## 18 -0.6215937 0.01144571 1
## 31 -1.3668161 1.04155954 2
## 39 -0.3731862 -0.81264536 1
## 55 -0.1247788 -0.09156567 1
## 63 0.2478325 -0.50361121 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## 7 -1.1473699 2.2002828 1.58226337 0.9135151
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## 7 1.8624810 0.01144571 2
## Confusion Matrix:
## predictions
## 1 2
## 1 77 0
## 2 30 87
##
## Fold 5
## Train Indices:
## 9 17 33 35 70 71 81 95 98 115 119 121 122 134 153 157 159 181 185 202 210
## Test Indices:
## 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 92 93 94 96 97 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 116 117 118 120 123 124 125 126 127 128 129 130 131 132 133 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 154 155 156 158 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 182 183 184 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 203 204 205 206 207 208 209 211 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 9 -1.1473699 0.8468795 -0.2331372 0.19599050
## 17 0.8675235 1.1040261 0.6982422 -0.01926686
## 33 0.8675235 -0.8854766 0.3983065 0.19599050
## 35 0.8675235 -0.5065237 -0.7067199 0.12423805
## 70 0.8675235 0.7115392 -0.3909981 -0.23452423
## 71 -1.1473699 -0.9802148 0.8718892 0.98526752
## Usia Berat_Badan Diabetes_Melitus
## 9 -2.6088534290 -0.60662259 2
## 17 0.3720361844 -0.29758844 2
## 33 -0.9942048884 0.83553678 1
## 35 0.7446473861 0.01144571 1
## 70 -0.0005750173 0.21746848 2
## 71 0.1236287166 -0.81264536 1
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## Confusion Matrix:
## predictions
## 1 2
## 1 77 2
## 2 13 102
##
## Fold 6
## Train Indices:
## 14 21 24 38 53 54 56 57 65 84 90 93 100 118 123 132 133 156 167 175 194 214
## Test Indices:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20 22 23 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 42 43 44 45 46 47 48 49 50 51 52 55 58 59 60 61 62 63 64 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 85 86 87 88 89 91 92 94 95 96 97 98 99 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 119 120 121 122 124 125 126 127 128 129 130 131 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 157 158 159 160 161 162 163 164 165 166 168 169 170 171 172 173 174 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 14 -1.14737 -0.77720433 -1.9696073 1.2005249
## 21 -1.14737 0.33258631 -0.2331372 0.1959905
## 24 -1.14737 -0.50652369 -0.7067199 -0.2345242
## 38 -1.14737 1.38824083 0.7929588 -0.3780291
## 53 -1.14737 -0.03283256 -0.5488590 0.3394954
## 54 -1.14737 -0.50652369 -0.5488590 -1.2390586
## Usia Berat_Badan Diabetes_Melitus
## 14 -1.1184086223 1.9686620 2
## 21 1.7382772572 -0.4005998 2
## 24 -1.2426123562 -1.1216795 2
## 38 -0.0005750173 0.1144571 2
## 53 1.7382772572 0.8355368 2
## 54 0.6204436522 -1.0186681 1
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## Confusion Matrix:
## predictions
## 1 2
## 1 66 14
## 2 9 104
##
## Fold 7
## Train Indices:
## 7 11 15 23 45 62 66 78 83 91 103 104 113 120 125 126 127 131 152 180 213
## Test Indices:
## 1 2 3 4 5 6 8 9 10 12 13 14 16 17 18 19 20 21 22 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 63 64 65 67 68 69 70 71 72 73 74 75 76 77 79 80 81 82 84 85 86 87 88 89 90 92 93 94 95 96 97 98 99 100 101 102 105 106 107 108 109 110 111 112 114 115 116 117 118 119 121 122 123 124 128 129 130 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 7 -1.1473699 2.2002828 1.5822634 0.91351506
## 11 0.8675235 0.1701779 -0.7067199 -0.44978160
## 15 -1.1473699 0.1701779 -0.2804955 -0.80854388
## 23 -1.1473699 -0.5065237 -0.5488590 -0.59328651
## 45 -1.1473699 -0.6418640 -0.2331372 0.69825770
## 62 0.8675235 -0.7095342 0.4298787 -0.01926686
## Usia Berat_Badan Diabetes_Melitus
## 7 1.8624810 0.01144571 2
## 11 -0.7457974 0.01144571 2
## 15 1.2414623 -1.32770227 2
## 23 0.8688511 -0.09156567 2
## 45 1.9866847 -0.40059982 1
## 62 -0.4973900 1.76263923 1
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## Confusion Matrix:
## predictions
## 1 2
## 1 67 14
## 2 15 98
##
## Fold 8
## Train Indices:
## 3 19 46 48 85 105 130 135 142 144 147 154 168 170 177 178 187 190 197 198 203 208
## Test Indices:
## 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 47 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 131 132 133 134 136 137 138 139 140 141 143 145 146 148 149 150 151 152 153 155 156 157 158 159 160 161 162 163 164 165 166 167 169 171 172 173 174 175 176 179 180 181 182 183 184 185 186 188 189 191 192 193 194 195 196 199 200 201 202 204 205 206 207 209 210 211 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 3 0.8675235 -0.37118337 -0.5488590 -1.1673062
## 19 0.8675235 -0.50652369 -1.4960245 -1.0238012
## 46 -1.1473699 -0.70953417 0.3983065 0.4112479
## 48 -1.1473699 0.84687954 0.2404456 -0.4497816
## 85 0.8675235 -0.50652369 -0.5488590 0.1959905
## 105 -1.1473699 0.02130357 -0.3909981 -0.2345242
## Usia Berat_Badan Diabetes_Melitus
## 3 1.7382773 0.9385482 2
## 19 -2.1120385 -1.0186681 2
## 46 -0.1247788 -0.6066226 1
## 48 -0.8700012 -0.1945771 2
## 85 -0.2489825 1.1445709 2
## 105 -0.8700012 -0.5036112 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## 7 -1.1473699 2.2002828 1.58226337 0.9135151
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## 7 1.8624810 0.01144571 2
## Confusion Matrix:
## predictions
## 1 2
## 1 71 9
## 2 6 107
##
## Fold 9
## Train Indices:
## 12 27 29 30 40 58 59 69 80 128 145 146 148 150 172 188 192 196 204 205 211
## Test Indices:
## 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 31 32 33 34 35 36 37 38 39 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 60 61 62 63 64 65 66 67 68 70 71 72 73 74 75 76 77 78 79 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 147 149 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 189 190 191 193 194 195 197 198 199 200 201 202 203 206 207 208 209 210 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 12 -1.1473699 -0.7772043 0.4772369 -0.37802914
## 27 0.8675235 -0.7230682 0.2404456 0.26774296
## 29 -1.1473699 -0.5065237 -0.6277895 0.69825770
## 30 0.8675235 1.3882408 0.8718892 -1.16730616
## 40 -1.1473699 -1.0614190 0.2404456 0.19599050
## 58 0.8675235 0.8468795 1.2665415 0.05248559
## Usia Berat_Badan Diabetes_Melitus
## 12 -0.7457974 1.1445709 1
## 27 0.4962399 -0.4005998 1
## 29 0.3720362 -0.9156567 2
## 30 -0.7457974 2.5867303 2
## 40 -0.6215937 -0.8126454 1
## 58 0.6204437 0.5265026 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 5 0.8675235 0.1025078 0.19308729 1.2722773
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 5 0.6204437 0.11445709 2
## 6 0.4962399 0.01144571 1
## Confusion Matrix:
## predictions
## 1 2
## 1 62 16
## 2 3 113
##
## Fold 10
## Train Indices:
## 5 8 16 47 52 61 73 74 76 87 111 116 137 140 143 162 173 174 176 179 186 201
## Test Indices:
## 1 2 3 4 6 7 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 50 51 53 54 55 56 57 58 59 60 62 63 64 65 66 67 68 69 70 71 72 75 77 78 79 80 81 82 83 84 85 86 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 112 113 114 115 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 138 139 141 142 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 163 164 165 166 167 168 169 170 171 172 175 177 178 180 181 182 183 184 185 187 188 189 190 191 192 193 194 195 196 197 198 199 200 202 203 204 205 206 207 208 209 210 211 212 213 214 215
## Train Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 5 0.8675235 0.1025078 0.1930873 1.27227734
## 8 -1.1473699 -0.5065237 -1.4960245 1.34402980
## 16 0.8675235 0.0348376 -0.7067199 0.33949542
## 47 0.8675235 -0.9531468 1.1876111 -0.09101932
## 52 -1.1473699 -0.9666808 -0.6277895 0.62650524
## 61 0.8675235 1.1852303 0.5561674 -0.59328651
## Usia Berat_Badan Diabetes_Melitus
## 5 0.6204436522 0.1144571 2
## 8 -0.1247787512 0.6295140 2
## 16 -0.0005750173 1.3505937 2
## 47 -0.0005750173 -1.0186681 1
## 52 -0.7457974206 -1.0186681 1
## 61 -0.1247787512 -1.0186681 2
## Test Data (first 6 rows):
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.4388535 -0.54885903 -0.5932865
## 2 0.8675235 -0.9396127 -0.54885903 0.6982577
## 3 0.8675235 -0.3711834 -0.54885903 -1.1673062
## 4 0.8675235 -1.0749530 0.08258465 -1.1673062
## 6 0.8675235 -1.0749530 0.87188924 0.9852675
## 7 -1.1473699 2.2002828 1.58226337 0.9135151
## Usia Berat_Badan Diabetes_Melitus
## 1 -0.4973900 -0.91565674 1
## 2 0.2478325 2.68974168 1
## 3 1.7382773 0.93854816 2
## 4 -1.2426124 -0.09156567 1
## 6 0.4962399 0.01144571 1
## 7 1.8624810 0.01144571 2
## Confusion Matrix:
## predictions
## 1 2
## 1 65 11
## 2 8 109
# Menghitung rata-rata akurasi
mean_accuracy <- mean(accuracy)
cat("\nMean Accuracy:", mean_accuracy, "\n")
##
## Mean Accuracy: 0.8951098
# Membuat model diskriminan linear
modellda <- lda(Diabetes_Melitus ~ ., data = databaru)
print(modellda)
## Call:
## lda(Diabetes_Melitus ~ ., data = databaru)
##
## Prior probabilities of groups:
## 1 2
## 0.4046512 0.5953488
##
## Group means:
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 0.03377455 -0.8156285 0.1382896 -0.14462748
## 2 -0.01399232 0.5477563 -0.1038886 0.09620975
## Usia Berat_Badan
## 1 -0.354627 -0.3177171
## 2 0.238129 0.1893013
##
## Coefficients of linear discriminants:
## LD1
## Jenis_Kelamin 0.09172254
## Gula_Darah_Puasa 2.13669096
## Gula_Darah_Jam_Pos_Prandial -1.29933671
## Tekanan_Darah 0.10879640
## Usia 0.04068888
## Berat_Badan 0.14446796
# Menampilkan Koefisien Fungsi Diskriminan
print(modellda$scaling)
## LD1
## Jenis_Kelamin 0.09172254
## Gula_Darah_Puasa 2.13669096
## Gula_Darah_Jam_Pos_Prandial -1.29933671
## Tekanan_Darah 0.10879640
## Usia 0.04068888
## Berat_Badan 0.14446796
eigen_values <- eigen(cov(databaru[, 1:6]))$values
canonical_correlations <- sqrt(eigen_values / (1 + eigen_values))
print(eigen_values)
## [1] 1.8763986 1.1146046 0.9969639 0.9138895 0.6776039 0.3758966
print(canonical_correlations)
## [1] 0.8076776 0.7260154 0.7065690 0.6910165 0.6355405 0.5226865
centroids <- aggregate(. ~ Diabetes_Melitus, data = databaru, FUN = mean)
print(centroids)
## Diabetes_Melitus Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial
## 1 1 0.03377455 -0.8156285 0.1382896
## 2 2 -0.01399232 0.5477563 -0.1038886
## Tekanan_Darah Usia Berat_Badan
## 1 -0.14462748 -0.354627 -0.3177171
## 2 0.09620975 0.238129 0.1893013
cutting_score <- mean(modellda$means %*% modellda$scaling)
print(cutting_score)
## [1] -0.3219021
pred_LDA1 <- predict(modellda, databaru)
conf_matrix <- table(actual = databaru$Diabetes_Melitus, predicted = pred_LDA1$class)
print(conf_matrix)
## predicted
## actual 1 2
## 1 82 5
## 2 4 124
# Menghitung Hit Ratio
hit_ratio <- sum(diag(conf_matrix)) / sum(conf_matrix)
print(hit_ratio)
## [1] 0.9581395
# Menghitung Press's Q Statistik
n <- sum(conf_matrix)
press_q <- (n - sum(diag(conf_matrix)))^2 / n
p_value <- 1 - pchisq(press_q, 1)
print(p_value)
## [1] 0.5393509
# Kesimpulan berdasarkan p-value
if (p_value < 0.05) {
print("Model diskriminan baik")
} else {
print("Model diskriminan tidak baik")
}
## [1] "Model diskriminan tidak baik"
# Menampilkan tabel pembakuan data
print(z_score_data)
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 1 -1.1473699 -0.43885353 -0.54885903 -0.59328651
## 2 0.8675235 -0.93961272 -0.54885903 0.69825770
## 3 0.8675235 -0.37118337 -0.54885903 -1.16730616
## 4 0.8675235 -1.07495304 0.08258465 -1.16730616
## 5 0.8675235 0.10250776 0.19308729 1.27227734
## 6 0.8675235 -1.07495304 0.87188924 0.98526752
## 7 -1.1473699 2.20028276 1.58226337 0.91351506
## 8 -1.1473699 -0.50652369 -1.49602454 1.34402980
## 9 -1.1473699 0.84687954 -0.23313719 0.19599050
## 10 0.8675235 -0.77720433 1.02975016 -0.09101932
## 11 0.8675235 0.17017792 -0.70671995 -0.44978160
## 12 -1.1473699 -0.77720433 0.47723694 -0.37802914
## 13 0.8675235 -0.65539804 -0.23313719 -1.95658317
## 14 -1.1473699 -0.77720433 -1.96960729 1.20052489
## 15 -1.1473699 0.17017792 -0.28049547 -0.80854388
## 16 0.8675235 0.03483760 -0.70671995 0.33949542
## 17 0.8675235 1.10402615 0.69824223 -0.01926686
## 18 0.8675235 -0.77720433 0.79295878 0.62650524
## 19 0.8675235 -0.50652369 -1.49602454 -1.02380125
## 20 0.8675235 -0.70953417 -2.30111522 0.98526752
## 21 -1.1473699 0.33258631 -0.23313719 0.19599050
## 22 -1.1473699 -0.37118337 -0.95929741 -1.02380125
## 23 -1.1473699 -0.50652369 -0.54885903 -0.59328651
## 24 -1.1473699 -0.50652369 -0.70671995 -0.23452423
## 25 0.8675235 -1.02081691 0.55616740 0.05248559
## 26 0.8675235 -0.89901062 -1.33816362 -0.80854388
## 27 0.8675235 -0.72306820 0.24044557 0.26774296
## 28 -1.1473699 2.20028276 2.45049842 -1.38256352
## 29 -1.1473699 -0.50652369 -0.62778949 0.69825770
## 30 0.8675235 1.38824083 0.87188924 -1.16730616
## 31 -1.1473699 -0.50652369 -1.18030270 0.41124787
## 32 0.8675235 -0.98021482 -0.23313719 2.06155436
## 33 0.8675235 -0.88547659 0.39830648 0.19599050
## 34 0.8675235 0.50852873 -0.31206765 1.12877243
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## Usia Berat_Badan Diabetes_Melitus
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## 176 2.2350921927 -0.29758844 2
## 177 1.7382772572 0.73252539 2
## 178 -1.1184086223 0.93854816 2
## 179 -1.6152235579 -1.12167951 1
## 180 1.3656660555 -0.81264536 2
## 181 1.7382772572 -0.40059982 2
## 182 -0.6215936867 -0.40059982 2
## 183 -0.4973899528 -0.29758844 1
## 184 -0.7457974206 1.14457093 1
## 185 -1.9878347595 -0.50361121 1
## 186 -0.9942048884 0.62951401 1
## 187 -0.7457974206 -1.94577057 1
## 188 -0.8700011545 1.14457093 2
## 189 0.3720361844 -0.91565674 2
## 190 -0.7457974206 2.58673029 2
## 191 1.9866847250 -1.43071366 2
## 192 -0.3731862190 0.21746848 2
## 193 0.4962399183 1.24758231 2
## 194 1.3656660555 -1.43071366 1
## 195 1.2414623216 -1.01866812 2
## 196 -0.6215936867 -0.91565674 2
## 197 -0.4973899528 1.14457093 2
## 198 1.4898697894 0.01144571 1
## 199 -0.9942048884 0.83553678 2
## 200 1.3656660555 0.83553678 2
## 201 0.4962399183 -1.94577057 1
## 202 -1.6152235579 -1.12167951 2
## 203 -0.2489824851 -0.60662259 1
## 204 0.1236287166 -0.09156567 2
## 205 0.4962399183 -0.40059982 2
## 206 0.7446473861 -0.60662259 2
## 207 0.3720361844 3.41082136 2
## 208 0.3720361844 0.01144571 1
## 209 -1.7394272918 -1.43071366 1
## 210 1.6140735233 0.62951401 2
## 211 -0.2489824851 2.17468476 2
## 212 -0.8700011545 -0.81264536 1
## 213 1.1172585877 2.17468476 2
## 214 -0.4973899528 -0.60662259 2
## 215 0.6204436522 0.52650263 2
## 216 -0.6215936867 -0.40059982 1
# Mengimpor pustaka yang diperlukan
library(ICSNP)
## Loading required package: mvtnorm
## Loading required package: ICS
# Uji Hotelling's T-squared untuk vektor nilai rata-rata
hotelling_test <- function(data, group) {
# Memisahkan data berdasarkan kelompok
group1 <- data[group == levels(group)[1], ]
group2 <- data[group == levels(group)[2], ]
# Menghitung uji Hotelling's T-squared
result <- HotellingsT2(group1, group2)
return(result)
}
# Melakukan uji Hotelling's T-squared pada data
hotelling_results <- hotelling_test(databaru[, 1:6], as.factor(databaru$Diabetes_Melitus))
print(hotelling_results)
##
## Hotelling's two sample T2-test
##
## data: group1 and group2
## T.2 = 94.435, df1 = 6, df2 = 208, p-value < 2.2e-16
## alternative hypothesis: true location difference is not equal to c(0,0,0,0,0,0)
# Fungsi untuk Menghitung Jarak Mahalanobis
mahalanobis_distance <- function(data) {
means <- colMeans(data)
cov_matrix <- cov(data)
inv_cov_matrix <- solve(cov_matrix)
distances <- apply(data, 1, function(x) {
diff <- x - means
dist <- t(diff) %*% inv_cov_matrix %*% diff
return(as.numeric(dist))
})
return(distances)
}
# Menghitung Jarak Mahalanobis
mahalanobis_distances <- mahalanobis_distance(databaru[, 1:6])
# Mengurutkan Nilai Jarak Mahalanobis
sorted_distances <- sort(mahalanobis_distances)
# Menghitung Nilai Chi-Square Quantiles
chi_square_quantiles <- qchisq((1:length(sorted_distances) - 0.5) / length(sorted_distances), df = 6)
# Membuat Plot Pasangan
plot(chi_square_quantiles, sorted_distances, xlab = "Chi-Square Quantiles", ylab = "Mahalanobis Distances",
main = "Uji Distribusi Normal Ganda")
abline(0, 1, col = "red")
# Menghitung Proporsi yang Lebih dari Nilai Chi-Square
alpha <- 0.05
cutoff <- qchisq(1 - alpha, df = 6)
prop_greater_than_cutoff <- mean(sorted_distances > cutoff)
# Menentukan Hasil Uji
if (prop_greater_than_cutoff <= 0.5) {
print("Terima H0: Data berdistribusi normal ganda")
} else {
print("Tolak H0: Data tidak berdistribusi normal ganda")
}
## [1] "Terima H0: Data berdistribusi normal ganda"
# Menampilkan Proporsi
print(paste("Proporsi yang lebih besar dari cutoff:", prop_greater_than_cutoff))
## [1] "Proporsi yang lebih besar dari cutoff: 0.027906976744186"
# Menghitung nilai Chi-square untuk uji goodness-of-fit
observed <- table(databaru$Diabetes_Melitus)
expected <- rep(sum(observed) / length(observed), length(observed))
chi_square_value <- sum((observed - expected)^2 / expected)
p_value <- 1 - pchisq(chi_square_value, df = length(observed) - 1)
# Menampilkan nilai Chi-square dan p-value
print(paste("Chi-square value:", chi_square_value))
## [1] "Chi-square value: 7.81860465116279"
print(paste("P-value:", p_value))
## [1] "P-value: 0.00517111046832897"
# Kesimpulan berdasarkan p-value
if (p_value < 0.05) {
print("Tolak H0: Data tidak sesuai dengan distribusi yang diharapkan")
} else {
print("Terima H0: Data sesuai dengan distribusi yang diharapkan")
}
## [1] "Tolak H0: Data tidak sesuai dengan distribusi yang diharapkan"
# Fungsi untuk melakukan uji kestabilan
stability_test <- function(data, dependent_var, k_values) {
results <- data.frame(k = integer(), Experiment = integer(), QPress = numeric(), Status = character())
for (k in k_values) {
folds <- createFolds(data[[dependent_var]], k = k)
for (i in 1:k) {
train_indices <- folds[[i]]
test_indices <- setdiff(seq_len(nrow(data)), train_indices)
train_data <- data[train_indices, ]
test_data <- data[test_indices, ]
model_lda <- lda(as.formula(paste(dependent_var, "~ .")), data = train_data)
predictions <- predict(model_lda, test_data)$class
conf_matrix <- table(test_data[[dependent_var]], predictions)
n <- sum(conf_matrix)
press_q <- (n - sum(diag(conf_matrix)))^2 / n
results <- rbind(results, data.frame(
k = k,
Experiment = i,
QPress = press_q,
Status = ifelse(press_q < qchisq(0.95, df = 1), "Konsisten", "Tidak Konsisten")
))
}
}
return(results)
}
# Melakukan uji kestabilan dengan k = 2, 3, dan 4
k_values <- c(2, 3, 4)
stability_results <- stability_test(databaru, "Diabetes_Melitus", k_values)
# Menampilkan hasil uji kestabilan
print(stability_results)
## k Experiment QPress Status
## 1 2 1 0.3364486 Konsisten
## 2 2 2 0.1481481 Konsisten
## 3 3 1 0.0625000 Konsisten
## 4 3 2 0.5664336 Konsisten
## 5 3 3 0.6993007 Konsisten
## 6 4 1 0.5000000 Konsisten
## 7 4 2 2.4844720 Konsisten
## 8 4 3 0.6211180 Konsisten
## 9 4 4 1.0496894 Konsisten
# Fungsi untuk mendeteksi pencilan peubah ganda
detect_outliers <- function(data, dependent_var, alpha = 0.05) {
independent_vars <- setdiff(names(data), dependent_var)
cov_matrix <- cov(data[, independent_vars])
inv_cov_matrix <- solve(cov_matrix)
mean_vector <- colMeans(data[, independent_vars])
mahalanobis_distances <- apply(data[, independent_vars], 1, function(row) {
diff <- row - mean_vector
dist <- t(diff) %*% inv_cov_matrix %*% diff
return(as.numeric(dist))
})
cutoff <- qchisq(1 - alpha, df = length(independent_vars))
outliers <- which(mahalanobis_distances > cutoff)
result <- data.frame(
Observation = 1:nrow(data),
MahalanobisDistance = mahalanobis_distances,
IsOutlier = mahalanobis_distances > cutoff
)
return(list(outliers = outliers, result = result))
}
# Melakukan deteksi pencilan peubah ganda
outlier_detection <- detect_outliers(databaru, "Diabetes_Melitus")
# Menampilkan hasil deteksi pencilan peubah ganda
print(outlier_detection$result)
## Observation MahalanobisDistance IsOutlier
## 1 1 3.320235 FALSE
## 2 2 10.950204 FALSE
## 3 3 7.556543 FALSE
## 4 4 3.991435 FALSE
## 5 5 2.827670 FALSE
## 6 6 6.946771 FALSE
## 7 7 7.436734 FALSE
## 8 8 5.805944 FALSE
## 9 9 13.796821 TRUE
## 10 10 11.131270 FALSE
## 11 11 2.718866 FALSE
## 12 12 6.767070 FALSE
## 13 13 5.230380 FALSE
## 14 14 10.518488 FALSE
## 15 15 6.430366 FALSE
## 16 16 2.755922 FALSE
## 17 17 2.419332 FALSE
## 18 18 4.096973 FALSE
## 19 19 10.928576 FALSE
## 20 20 9.540569 FALSE
## 21 21 5.019708 FALSE
## 22 22 9.688322 FALSE
## 23 23 3.808278 FALSE
## 24 24 5.038900 FALSE
## 25 25 3.954709 FALSE
## 26 26 3.143855 FALSE
## 27 27 2.542652 FALSE
## 28 28 10.807446 FALSE
## 29 29 3.956357 FALSE
## 30 30 14.942425 TRUE
## 31 31 5.494261 FALSE
## 32 32 8.816512 FALSE
## 33 33 4.580373 FALSE
## 34 34 5.102657 FALSE
## 35 35 2.370728 FALSE
## 36 36 3.642734 FALSE
## 37 37 10.414821 FALSE
## 38 38 3.701566 FALSE
## 39 39 3.073810 FALSE
## 40 40 3.794058 FALSE
## 41 41 7.397835 FALSE
## 42 42 7.956641 FALSE
## 43 43 11.291783 FALSE
## 44 44 4.548099 FALSE
## 45 45 8.561197 FALSE
## 46 46 3.013717 FALSE
## 47 47 5.580381 FALSE
## 48 48 3.972582 FALSE
## 49 49 6.084458 FALSE
## 50 50 3.014039 FALSE
## 51 51 4.217760 FALSE
## 52 52 4.340191 FALSE
## 53 53 6.284034 FALSE
## 54 54 5.705849 FALSE
## 55 55 3.279025 FALSE
## 56 56 6.818571 FALSE
## 57 57 4.926481 FALSE
## 58 58 3.554071 FALSE
## 59 59 5.861380 FALSE
## 60 60 6.911335 FALSE
## 61 61 4.852535 FALSE
## 62 62 7.181976 FALSE
## 63 63 2.161240 FALSE
## 64 64 3.007729 FALSE
## 65 65 5.690391 FALSE
## 66 66 8.872803 FALSE
## 67 67 4.533602 FALSE
## 68 68 2.869503 FALSE
## 69 69 2.498039 FALSE
## 70 70 2.318645 FALSE
## 71 71 6.335633 FALSE
## 72 72 3.052898 FALSE
## 73 73 6.523525 FALSE
## 74 74 3.316083 FALSE
## 75 75 6.787016 FALSE
## 76 76 8.597070 FALSE
## 77 77 2.691437 FALSE
## 78 78 9.761324 FALSE
## 79 79 11.843140 FALSE
## 80 80 5.262061 FALSE
## 81 81 3.053735 FALSE
## 82 82 12.817097 TRUE
## 83 83 4.058725 FALSE
## 84 84 4.108120 FALSE
## 85 85 2.239734 FALSE
## 86 86 5.619656 FALSE
## 87 87 7.191361 FALSE
## 88 88 6.642488 FALSE
## 89 89 10.581560 FALSE
## 90 90 4.250780 FALSE
## 91 91 6.756259 FALSE
## 92 92 8.403876 FALSE
## 93 93 3.877679 FALSE
## 94 94 7.743855 FALSE
## 95 95 4.755166 FALSE
## 96 96 5.078869 FALSE
## 97 97 6.084175 FALSE
## 98 98 4.530411 FALSE
## 99 99 3.824412 FALSE
## 100 100 5.969575 FALSE
## 101 101 8.944533 FALSE
## 102 102 3.973888 FALSE
## 103 103 2.401012 FALSE
## 104 104 2.441905 FALSE
## 105 105 2.906249 FALSE
## 106 106 11.562074 FALSE
## 107 107 9.919982 FALSE
## 108 108 9.278897 FALSE
## 109 109 3.190429 FALSE
## 110 110 2.650346 FALSE
## 111 111 7.024227 FALSE
## 112 112 7.026265 FALSE
## 113 113 8.290501 FALSE
## 114 114 3.326733 FALSE
## 115 115 6.094169 FALSE
## 116 116 3.795444 FALSE
## 117 117 5.649845 FALSE
## 118 118 1.969925 FALSE
## 119 119 7.442717 FALSE
## 120 120 9.111281 FALSE
## 121 121 7.660619 FALSE
## 122 122 9.989517 FALSE
## 123 123 3.948443 FALSE
## 124 124 4.158312 FALSE
## 125 125 3.133046 FALSE
## 126 126 5.259081 FALSE
## 127 127 3.844059 FALSE
## 128 128 7.084001 FALSE
## 129 129 7.237239 FALSE
## 130 130 5.416407 FALSE
## 131 131 7.821826 FALSE
## 132 132 8.857921 FALSE
## 133 133 2.794580 FALSE
## 134 134 12.179030 FALSE
## 135 135 6.039407 FALSE
## 136 136 7.562733 FALSE
## 137 137 4.497013 FALSE
## 138 138 5.984687 FALSE
## 139 139 4.752249 FALSE
## 140 140 6.609871 FALSE
## 141 141 3.333422 FALSE
## 142 142 2.233003 FALSE
## 143 143 7.146752 FALSE
## 144 144 13.914206 TRUE
## 145 145 4.197360 FALSE
## 146 146 4.017704 FALSE
## 147 147 5.971855 FALSE
## 148 148 9.106015 FALSE
## 149 149 7.915925 FALSE
## 150 150 4.479002 FALSE
## 151 151 6.796159 FALSE
## 152 152 2.184582 FALSE
## 153 153 13.857832 TRUE
## 154 154 4.429790 FALSE
## 155 155 3.214434 FALSE
## 156 156 7.806530 FALSE
## 157 157 2.902586 FALSE
## 158 158 3.787183 FALSE
## 159 159 6.538310 FALSE
## 160 160 4.628854 FALSE
## 161 161 9.635759 FALSE
## 162 162 3.324660 FALSE
## 163 163 3.894551 FALSE
## 164 164 2.014087 FALSE
## 165 165 6.411924 FALSE
## 166 166 5.252562 FALSE
## 167 167 4.108940 FALSE
## 168 168 3.604446 FALSE
## 169 169 6.068543 FALSE
## 170 170 5.083957 FALSE
## 171 171 4.845874 FALSE
## 172 172 3.393456 FALSE
## 173 173 5.766107 FALSE
## 174 174 7.870290 FALSE
## 175 175 5.098004 FALSE
## 176 176 9.642474 FALSE
## 177 177 5.475982 FALSE
## 178 178 4.885705 FALSE
## 179 179 6.064158 FALSE
## 180 180 4.262883 FALSE
## 181 181 6.226945 FALSE
## 182 182 2.937573 FALSE
## 183 183 3.067033 FALSE
## 184 184 6.116222 FALSE
## 185 185 10.035219 FALSE
## 186 186 5.482198 FALSE
## 187 187 12.930018 TRUE
## 188 188 6.709485 FALSE
## 189 189 5.267104 FALSE
## 190 190 8.596937 FALSE
## 191 191 11.413515 FALSE
## 192 192 6.420967 FALSE
## 193 193 6.896334 FALSE
## 194 194 5.989211 FALSE
## 195 195 10.045910 FALSE
## 196 196 6.251218 FALSE
## 197 197 4.229160 FALSE
## 198 198 5.667414 FALSE
## 199 199 8.152712 FALSE
## 200 200 4.503142 FALSE
## 201 201 7.530825 FALSE
## 202 202 10.321638 FALSE
## 203 203 5.403016 FALSE
## 204 204 3.106391 FALSE
## 205 205 8.826985 FALSE
## 206 206 6.544879 FALSE
## 208 207 1.466640 FALSE
## 209 208 10.198502 FALSE
## 210 209 6.136077 FALSE
## 211 210 8.648165 FALSE
## 212 211 4.317444 FALSE
## 213 212 7.657243 FALSE
## 214 213 4.350592 FALSE
## 215 214 4.895985 FALSE
## 216 215 2.533024 FALSE
# Menampilkan pengamatan yang merupakan outliers
outlier_indices <- outlier_detection$outliers
print(databaru[outlier_indices, ])
## Jenis_Kelamin Gula_Darah_Puasa Gula_Darah_Jam_Pos_Prandial Tekanan_Darah
## 9 -1.1473699 0.8468795 -0.2331372 0.1959905
## 30 0.8675235 1.3882408 0.8718892 -1.1673062
## 82 0.8675235 -0.9125447 -2.2853291 0.6265052
## 144 -1.1473699 -0.3711834 -1.3381636 2.7790789
## 153 -1.1473699 0.6438691 -2.1274682 0.1242380
## 187 0.8675235 -0.6012619 2.4504984 0.4830003
## Usia Berat_Badan Diabetes_Melitus
## 9 -2.6088534 -0.6066226 2
## 30 -0.7457974 2.5867303 2
## 82 -0.2489825 3.1017872 2
## 144 0.8688511 1.5566165 2
## 153 0.2478325 -0.9156567 2
## 187 -0.7457974 -1.9457706 1
# Fungsi untuk menghitung Cpro dan Cmax
accuracy_test <- function(data, dependent_var) {
# Menghitung proporsi sampel pada setiap kelompok
group_counts <- table(data[[dependent_var]])
p <- group_counts[1] / sum(group_counts)
q <- 1 - p
# Menghitung nilai Cpro
Cpro <- p^2 + q^2
# Menghitung nilai Cmax
n_max <- max(group_counts)
N <- sum(group_counts)
Cmax <- (n_max / N) * 100
return(list(Cpro = Cpro, Cmax = Cmax))
}
# Melakukan uji keakuratan
accuracy_results <- accuracy_test(databaru, "Diabetes_Melitus")
# Menampilkan hasil uji keakuratan
print(accuracy_results)
## $Cpro
## 1
## 0.5181828
##
## $Cmax
## [1] 59.53488
# Membandingkan dengan akurasi aktual dari model LDA
actual_accuracy <- mean_accuracy * 100 # Mengkonversi ke persen
Cpro <- accuracy_results$Cpro * 100 # Mengkonversi ke persen
cat("Akurasi Aktual:", actual_accuracy, "%\n")
## Akurasi Aktual: 89.51098 %
cat("Cpro:", Cpro, "%\n")
## Cpro: 51.81828 %
cat("Cmax:", accuracy_results$Cmax, "%\n")
## Cmax: 59.53488 %
# Menentukan hasil uji keakuratan berdasarkan Cpro
if (actual_accuracy > Cpro) {
print("H0 ditolak: Klasifikasi akurat")
} else {
print("H0 diterima: Klasifikasi tidak akurat")
}
## [1] "H0 ditolak: Klasifikasi akurat"