Implementasi Principal Component Analysis (PCA) dan Factor Analysis (FA) pada Dataset Gallstone dari UCI Machine Learning
Ivan Andika Setyawan (24031554085); Anggoro Daru Prasetyo (24031554070)
2026-03-03
1 Load Library
library(car)## Loading required package: carDatalibrary(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha## The following object is masked from 'package:car':
##
## logitlibrary(corrplot)## corrplot 0.95 loadedlibrary(sjPlot)##
## Attaching package: 'sjPlot'## The following object is masked from 'package:ggplot2':
##
## set_themelibrary(readxl)
library(FactoMineR)
library(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinelibrary(ggcorrplot)2 Baca Data dan Rapikan Data
data <- read_excel("D:/.tugas semester 4 dika/analisis multivariat/gallstone-1/dataset-uci/dataset-uci.xlsx")names(data)## [1] "Gallstone Status"
## [2] "Age"
## [3] "Gender"
## [4] "Comorbidity"
## [5] "Coronary Artery Disease (CAD)"
## [6] "Hypothyroidism"
## [7] "Hyperlipidemia"
## [8] "Diabetes Mellitus (DM)"
## [9] "Height"
## [10] "Weight"
## [11] "Body Mass Index (BMI)"
## [12] "Total Body Water (TBW)"
## [13] "Extracellular Water (ECW)"
## [14] "Intracellular Water (ICW)"
## [15] "Extracellular Fluid/Total Body Water (ECF/TBW)"
## [16] "Total Body Fat Ratio (TBFR) (%)"
## [17] "Lean Mass (LM) (%)"
## [18] "Body Protein Content (Protein) (%)"
## [19] "Visceral Fat Rating (VFR)"
## [20] "Bone Mass (BM)"
## [21] "Muscle Mass (MM)"
## [22] "Obesity (%)"
## [23] "Total Fat Content (TFC)"
## [24] "Visceral Fat Area (VFA)"
## [25] "Visceral Muscle Area (VMA) (Kg)"
## [26] "Hepatic Fat Accumulation (HFA)"
## [27] "Glucose"
## [28] "Total Cholesterol (TC)"
## [29] "Low Density Lipoprotein (LDL)"
## [30] "High Density Lipoprotein (HDL)"
## [31] "Triglyceride"
## [32] "Aspartat Aminotransferaz (AST)"
## [33] "Alanin Aminotransferaz (ALT)"
## [34] "Alkaline Phosphatase (ALP)"
## [35] "Creatinine"
## [36] "Glomerular Filtration Rate (GFR)"
## [37] "C-Reactive Protein (CRP)"
## [38] "Hemoglobin (HGB)"
## [39] "Vitamin D"data <- data %>%
rename(
Status = `Gallstone Status`,
Age = `Age`,
Gender = `Gender`,
Comorbidity = `Comorbidity`,
CAD = `Coronary Artery Disease (CAD)`,
Hypothyroid = `Hypothyroidism`,
Hyperlipid = `Hyperlipidemia`,
DM = `Diabetes Mellitus (DM)`,
Height = `Height`,
Weight = `Weight`,
BMI = `Body Mass Index (BMI)`,
TBW = `Total Body Water (TBW)`,
ECW = `Extracellular Water (ECW)`,
ICW = `Intracellular Water (ICW)`,
ECF_TBW = `Extracellular Fluid/Total Body Water (ECF/TBW)`,
TBFR = `Total Body Fat Ratio (TBFR) (%)`,
LeanMass = `Lean Mass (LM) (%)`,
Protein = `Body Protein Content (Protein) (%)`,
VFR = `Visceral Fat Rating (VFR)`,
BoneMass = `Bone Mass (BM)`,
MuscleMass = `Muscle Mass (MM)`,
Obesity = `Obesity (%)`,
TFC = `Total Fat Content (TFC)`,
VFA = `Visceral Fat Area (VFA)`,
VMA = `Visceral Muscle Area (VMA) (Kg)`,
HFA = `Hepatic Fat Accumulation (HFA)`,
Glucose = `Glucose`,
TotalChol = `Total Cholesterol (TC)`,
LDL = `Low Density Lipoprotein (LDL)`,
HDL = `High Density Lipoprotein (HDL)`,
Triglyceride = `Triglyceride`,
AST = `Aspartat Aminotransferaz (AST)`,
ALT = `Alanin Aminotransferaz (ALT)`,
ALP = `Alkaline Phosphatase (ALP)`,
Creatinine = `Creatinine`,
GFR = `Glomerular Filtration Rate (GFR)`,
CRP = `C-Reactive Protein (CRP)`,
HGB = `Hemoglobin (HGB)`,
VitaminD = `Vitamin D`
) %>%
mutate(Status = factor(Status, levels=c(0,1),
labels=c("Batu Empedu","Normal")))head(data)## # A tibble: 6 × 39
## Status Age Gender Comorbidity CAD Hypothyroid Hyperlipid DM Height
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Batu Empedu 50 0 0 0 0 0 0 185
## 2 Batu Empedu 47 0 1 0 0 0 0 176
## 3 Batu Empedu 61 0 0 0 0 0 0 171
## 4 Batu Empedu 41 0 0 0 0 0 0 168
## 5 Batu Empedu 42 0 0 0 0 0 0 178
## 6 Batu Empedu 96 0 0 0 0 0 0 155
## # ℹ 30 more variables: Weight <dbl>, BMI <dbl>, TBW <dbl>, ECW <dbl>,
## # ICW <dbl>, ECF_TBW <dbl>, TBFR <dbl>, LeanMass <dbl>, Protein <dbl>,
## # VFR <dbl>, BoneMass <dbl>, MuscleMass <dbl>, Obesity <dbl>, TFC <dbl>,
## # VFA <dbl>, VMA <dbl>, HFA <dbl>, Glucose <dbl>, TotalChol <dbl>, LDL <dbl>,
## # HDL <dbl>, Triglyceride <dbl>, AST <dbl>, ALT <dbl>, ALP <dbl>,
## # Creatinine <dbl>, GFR <dbl>, CRP <dbl>, HGB <dbl>, VitaminD <dbl>data_num <- data[,-26]
data_num <- data_num[,9:38]
head(data_num)## # A tibble: 6 × 30
## Height Weight BMI TBW ECW ICW ECF_TBW TBFR LeanMass Protein VFR
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 185 92.8 27.1 52.9 21.2 31.7 40 19.2 80.8 18.9 9
## 2 176 94.5 30.5 43.1 19.5 23.6 45 32.8 67.2 16.7 15
## 3 171 91.1 31.2 47.2 20.1 27.1 43 27.3 72.7 16.4 15
## 4 168 67.7 24 41.4 17 24.4 41 15.8 84.2 16.9 6
## 5 178 89.6 28.3 51.4 20 31.4 39 20 80.0 16.8 8
## 6 155 49 20.4 34 15.7 18.3 46 6.3 93.7 18.5 12
## # ℹ 19 more variables: BoneMass <dbl>, MuscleMass <dbl>, Obesity <dbl>,
## # TFC <dbl>, VFA <dbl>, VMA <dbl>, Glucose <dbl>, TotalChol <dbl>, LDL <dbl>,
## # HDL <dbl>, Triglyceride <dbl>, AST <dbl>, ALT <dbl>, ALP <dbl>,
## # Creatinine <dbl>, GFR <dbl>, CRP <dbl>, HGB <dbl>, VitaminD <dbl>3 Statistika Deskriptif
hasil_desc <- describe(data_num)
hasil <- select(hasil_desc,n,mean,median,sd,min,max,skew,kurtosis)
hasil## n mean median sd min max skew kurtosis
## Height 319 167.16 168.00 10.05 145.00 191.00 -0.08 -0.70
## Weight 319 80.56 78.80 15.71 42.90 143.50 0.43 0.31
## BMI 319 28.88 28.30 5.31 17.40 49.70 0.66 1.13
## TBW 319 40.59 39.80 7.93 13.00 66.20 0.21 -0.38
## ECW 319 17.07 17.10 3.16 9.00 27.80 0.02 -0.37
## ICW 319 23.63 23.00 5.35 13.80 57.10 0.94 3.47
## ECF_TBW 319 42.21 42.00 3.24 29.23 52.00 -0.51 1.37
## TBFR 319 28.27 27.82 8.44 6.30 50.92 0.13 -0.52
## LeanMass 319 71.64 72.11 8.44 48.99 93.67 -0.12 -0.51
## Protein 319 15.94 15.87 2.33 5.56 24.81 -0.05 1.82
## VFR 319 9.08 9.00 4.33 1.00 31.00 0.79 2.13
## BoneMass 319 2.80 2.80 0.51 1.40 4.00 0.20 -0.83
## MuscleMass 319 54.27 53.90 10.60 4.70 78.80 -0.10 0.36
## Obesity 319 35.85 25.60 109.80 0.40 1954.00 16.71 288.97
## TFC 319 23.49 22.60 9.61 3.10 62.50 0.80 1.11
## VFA 319 12.17 11.59 5.26 0.90 41.00 1.05 2.92
## VMA 319 30.40 30.41 4.46 18.90 41.10 -0.06 -0.47
## Glucose 319 108.69 98.00 44.85 69.00 575.00 5.88 45.42
## TotalChol 319 203.50 198.00 45.76 60.00 360.00 0.43 0.49
## LDL 319 126.65 122.00 38.54 11.00 293.00 0.54 1.08
## HDL 319 49.48 46.50 17.72 25.00 273.00 6.47 77.18
## Triglyceride 319 144.50 119.00 97.90 1.39 838.00 2.76 12.65
## AST 319 21.68 18.00 16.70 8.00 195.00 6.93 60.06
## ALT 319 26.86 19.00 27.88 3.00 372.00 7.21 76.92
## ALP 319 73.11 71.00 24.18 7.00 197.00 0.79 2.51
## Creatinine 319 0.80 0.79 0.18 0.46 1.46 0.61 0.14
## GFR 319 100.82 104.00 16.97 10.60 132.00 -1.80 6.39
## CRP 319 1.85 0.22 4.99 0.00 43.40 5.36 33.23
## HGB 319 14.42 14.40 1.78 8.50 18.80 -0.38 0.13
## VitaminD 319 21.40 22.00 9.98 3.50 53.10 0.28 -0.244 Karakteristik Data menggunakan Plot
data %>%
count(Status) %>%
mutate(label = paste0(Status, "\nn=", n, " (", round(n/sum(n)*100,1), "%)")) %>%
ggplot(aes(x=2, y=n, fill=Status)) +
geom_col(color="white") +
coord_polar(theta="y") +
xlim(0.5, 2.5) +
geom_text(aes(label=label), position=position_stack(vjust=0.5),
color="white", fontface="bold", size=4) +
scale_fill_manual(values=c("Batu Empedu"="#E74C3C","Normal"="#2980B9")) +
theme_void() +
theme(legend.position="none",
plot.title=element_text(face="bold", hjust=0.5))
vars_plot <- c("Height","Weight","BMI","TBW","ECW","ICW",
"TBFR","LeanMass","Protein","VFR","BoneMass",
"MuscleMass","Obesity","TFC","VFA","VMA",
"Glucose","HDL","Triglyceride","AST","ALT",
"ALP","Creatinine","GFR","CRP","HGB","VitaminD")
daftar_plot <- lapply(vars_plot, function(v) {
rata2 <- data %>%
group_by(Status) %>%
summarise(nilai = mean(.data[[v]], na.rm=TRUE), .groups="drop")
ggplot(data, aes(x=.data[[v]], fill=Status, color=Status)) +
geom_histogram(aes(y=after_stat(density)), bins=25,
alpha=0.4, position="identity", linewidth=0.2) +
geom_density(linewidth=0.9, fill=NA) +
geom_vline(data=rata2, aes(xintercept=nilai, color=Status),
linetype="dashed", linewidth=0.7) +
scale_fill_manual(values=c("Batu Empedu"="#E74C3C","Normal"="#2980B9")) +
scale_color_manual(values=c("Batu Empedu"="#E74C3C","Normal"="#2980B9")) +
labs(title=v, x=NULL, y=NULL) +
theme_minimal(base_size=9) +
theme(legend.position="none",
plot.title=element_text(face="bold", size=9))
})
leg <- cowplot::get_legend(
ggplot(data, aes(x=BMI, fill=Status)) +
geom_density(alpha=0.4) +
scale_fill_manual(values=c("Batu Empedu"="#E74C3C","Normal"="#2980B9")) +
theme_minimal() +
theme(legend.title=element_blank(), legend.position="bottom")
)
grid.arrange(grobs=c(daftar_plot, list(leg)), ncol=4)
5 Uji Asumsi Korelasi , Bartlet Test , KMO
5.1 Matriks Correlation
matriks_corr <- cor(data_num)
corrplot(matriks_corr)
5.2 Uji KMO
kmo <- KMO(data_num)
print(kmo)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_num)
## Overall MSA = 0.8
## MSA for each item =
## Height Weight BMI TBW ECW ICW
## 0.78 0.80 0.77 0.82 0.77 0.83
## ECF_TBW TBFR LeanMass Protein VFR BoneMass
## 0.47 0.86 0.84 0.79 0.84 0.97
## MuscleMass Obesity TFC VFA VMA Glucose
## 0.97 0.86 0.92 0.85 0.98 0.74
## TotalChol LDL HDL Triglyceride AST ALT
## 0.39 0.40 0.67 0.64 0.60 0.66
## ALP Creatinine GFR CRP HGB VitaminD
## 0.52 0.87 0.46 0.57 0.95 0.77data_num1 <- data_num[,-19]kmo <- KMO(data_num1)
print(kmo)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_num1)
## Overall MSA = 0.83
## MSA for each item =
## Height Weight BMI TBW ECW ICW
## 0.78 0.80 0.77 0.82 0.77 0.83
## ECF_TBW TBFR LeanMass Protein VFR BoneMass
## 0.47 0.85 0.83 0.79 0.84 0.98
## MuscleMass Obesity TFC VFA VMA Glucose
## 0.98 0.85 0.92 0.85 0.98 0.72
## LDL HDL Triglyceride AST ALT ALP
## 0.37 0.92 0.85 0.59 0.66 0.51
## Creatinine GFR CRP HGB VitaminD
## 0.87 0.45 0.57 0.95 0.76data_num2 <- data_num1[,-19]kmo <- KMO(data_num2)
print(kmo)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_num2)
## Overall MSA = 0.83
## MSA for each item =
## Height Weight BMI TBW ECW ICW
## 0.78 0.80 0.77 0.82 0.77 0.83
## ECF_TBW TBFR LeanMass Protein VFR BoneMass
## 0.47 0.85 0.84 0.79 0.84 0.98
## MuscleMass Obesity TFC VFA VMA Glucose
## 0.98 0.86 0.92 0.85 0.98 0.72
## HDL Triglyceride AST ALT ALP Creatinine
## 0.93 0.85 0.59 0.66 0.51 0.87
## GFR CRP HGB VitaminD
## 0.46 0.57 0.95 0.77data_num3 <- data_num2[,-7]kmo <- KMO(data_num3)
print(kmo)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_num3)
## Overall MSA = 0.84
## MSA for each item =
## Height Weight BMI TBW ECW ICW
## 0.76 0.78 0.76 0.87 0.87 0.85
## TBFR LeanMass Protein VFR BoneMass MuscleMass
## 0.84 0.83 0.71 0.79 0.98 0.97
## Obesity TFC VFA VMA Glucose HDL
## 0.85 0.91 0.83 0.98 0.72 0.93
## Triglyceride AST ALT ALP Creatinine GFR
## 0.85 0.59 0.66 0.52 0.87 0.45
## CRP HGB VitaminD
## 0.56 0.94 0.715.3 Uji Bartlet
bartlet_test <- cortest.bartlett(cor(data_num3), n = nrow(data_num3))
print(bartlet_test)## $chisq
## [1] 10972.26
##
## $p.value
## [1] 0
##
## $df
## [1] 3516 Principal Component Analysis
6.1 Manual PCA
scale_data <- scale(data_num3)
r <- cov(scale_data)
pc <- eigen(r)
print(pc)## eigen() decomposition
## $values
## [1] 8.543020116 5.909418055 1.767097501 1.548861969 1.312008248 1.082754767
## [7] 1.004615498 0.918128477 0.862861127 0.743264160 0.613419767 0.558760336
## [13] 0.396786097 0.354203219 0.267787216 0.236783770 0.213971445 0.197460719
## [19] 0.127368589 0.118080201 0.074695297 0.056775299 0.041017532 0.023099247
## [25] 0.018565507 0.005410330 0.003785511
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.23545404 0.21739162 -0.0037080070 0.159297609 -4.764273e-02
## [2,] -0.29643149 -0.18668585 -0.0019815092 0.099540530 3.499169e-03
## [3,] -0.15837712 -0.34424799 -0.0006168793 0.001001541 3.038913e-02
## [4,] -0.32016947 0.05125864 -0.0091479125 0.088126444 3.114604e-02
## [5,] -0.31536101 -0.00581424 0.0030269525 0.088530519 7.111574e-02
## [6,] -0.30056274 0.09504513 0.0113295489 0.114935532 -1.874966e-02
## [7,] 0.02897468 -0.39736411 0.0184905790 -0.013751353 -3.262792e-03
## [8,] -0.03066373 0.39743338 -0.0177179259 0.020391258 8.990578e-03
## [9,] -0.01034868 0.30409955 -0.1060017585 -0.088361470 1.215771e-03
## [10,] -0.23064175 -0.20969875 -0.1042019954 -0.137706904 1.523130e-01
## [11,] -0.29538715 0.05989780 -0.0329191254 0.109635196 1.252728e-02
## [12,] -0.32320327 0.06783934 -0.0079500131 0.101319044 4.704108e-03
## [13,] -0.00892062 -0.08537336 0.0235484157 -0.124989920 -1.529563e-01
## [14,] -0.11025679 -0.37407809 0.0141845791 0.041477852 4.196625e-05
## [15,] -0.21465074 -0.29718709 -0.0137875377 0.051602083 3.439374e-02
## [16,] -0.29935240 0.06364837 -0.0106835797 0.073550970 -1.175211e-02
## [17,] -0.06574309 -0.03518461 -0.2151597501 -0.384762663 -3.903055e-01
## [18,] 0.14510027 -0.07452986 0.0542479806 0.057143661 2.977579e-01
## [19,] -0.14460036 0.00485697 -0.0997808553 -0.280151290 -4.174899e-01
## [20,] -0.09610112 0.05474895 0.6014574692 -0.297276996 1.514606e-01
## [21,] -0.13100755 0.05244508 0.5713748644 -0.320363343 1.320284e-01
## [22,] -0.01983034 -0.06297339 0.0393821566 -0.377716562 -1.756683e-01
## [23,] -0.16440493 0.18033049 -0.2648574601 -0.275450669 2.683504e-01
## [24,] 0.02573697 0.03364893 0.3755609435 0.456652736 -4.460369e-01
## [25,] 0.01687440 -0.08164519 -0.1036946558 -0.048913634 1.924508e-01
## [26,] -0.20864638 0.16298786 -0.0124251704 -0.093428634 -7.504613e-02
## [27,] 0.00122398 0.06472836 -0.0611320368 0.042771378 3.769220e-01
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.1360202508 0.0213757059 -0.096588012 -0.0279727359 0.094037310
## [2,] -0.0555381966 0.0065104896 -0.038060342 -0.0058103241 0.020676223
## [3,] 0.0122069214 -0.0150835613 0.036851378 -0.0005271727 -0.045512188
## [4,] -0.0060919643 0.0003081984 0.013937776 -0.0772807221 0.009521554
## [5,] 0.1060885213 -0.0394572575 0.018193150 -0.0910516525 -0.027119804
## [6,] -0.0669530502 0.0307733090 0.012273501 -0.0775786948 0.025942546
## [7,] -0.0009865401 -0.0160417147 -0.032618264 0.1001337779 -0.005087421
## [8,] 0.0063323807 0.0232487979 0.036373254 -0.0983423344 0.020231002
## [9,] -0.1792256009 0.0775367701 -0.138731647 0.0417120340 0.065141061
## [10,] 0.1215901927 -0.0102352461 -0.076085760 0.0131206223 -0.045933913
## [11,] 0.0322030485 0.0153001874 0.018675552 -0.0957945872 0.072995917
## [12,] -0.0605425920 0.0304118624 -0.025698098 -0.0495480408 0.038830053
## [13,] 0.2361361620 0.7551329814 0.313331751 -0.3899567675 -0.164065391
## [14,] -0.0294964441 -0.0075243944 -0.053331424 0.0577360504 0.010202920
## [15,] -0.0094032619 -0.0021873921 -0.075931734 0.0242650545 0.017321013
## [16,] -0.1008442836 0.0187702595 -0.006464326 0.0167799871 0.050186145
## [17,] 0.2066579968 -0.0587838054 -0.021218315 -0.1721854251 0.563753587
## [18,] -0.0109034933 0.2164086724 -0.485846708 -0.2226472177 0.575425361
## [19,] 0.0354243774 -0.1043015343 0.189055502 0.4206995129 0.155529182
## [20,] 0.0378861664 0.0172161356 0.096585466 0.1321196990 0.074677536
## [21,] -0.0364953891 0.0170471603 -0.001915481 0.0597955604 0.068388810
## [22,] -0.2649887178 -0.3767288117 -0.225091240 -0.6221874373 -0.331258111
## [23,] 0.0100900502 0.1160201691 -0.054350095 0.1293645374 -0.184739759
## [24,] 0.0392899383 -0.1183126254 0.085579659 -0.1596123491 0.089059741
## [25,] -0.6483690504 0.0003950853 0.585917562 -0.1414825544 0.291519394
## [26,] 0.1310454060 0.0229409601 -0.115852074 0.0035240990 -0.069939970
## [27,] 0.5363619511 -0.4317319526 0.390757659 -0.2505864136 0.136568863
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.012041336 0.092978708 -0.299316478 0.479375672 0.135161452
## [2,] -0.110304952 0.032306750 -0.083136895 0.065004074 -0.052930834
## [3,] -0.122888631 -0.017341724 0.093131663 -0.243168952 -0.148850835
## [4,] -0.003494525 -0.055983473 0.182505663 0.014799875 0.040699621
## [5,] 0.159455097 -0.097459910 0.262760668 -0.002422531 0.101624999
## [6,] 0.005467107 0.045722487 -0.004904177 -0.020289256 -0.122178716
## [7,] -0.044131716 0.075036868 -0.205196203 0.128001633 -0.002814619
## [8,] 0.042492675 -0.091784324 0.201920694 -0.129450233 0.019291012
## [9,] -0.626476246 0.066228992 -0.353678246 -0.354090863 -0.100961336
## [10,] -0.029309594 -0.120154829 0.077874815 -0.522443055 0.014025617
## [11,] -0.025689500 -0.089818173 0.226549884 -0.007174512 0.189299354
## [12,] -0.103056689 -0.012229174 0.032184864 -0.002715459 -0.027568377
## [13,] -0.115665430 0.162078546 -0.027951164 0.060318733 0.026391894
## [14,] -0.078891490 0.036998520 -0.157989060 0.115535010 -0.075460271
## [15,] 0.066304600 0.023642478 -0.190852697 0.070811250 -0.065319909
## [16,] -0.243703041 0.024749150 -0.054150455 0.078277371 0.132744903
## [17,] 0.059453811 -0.457703138 -0.149717654 0.073591939 -0.072734613
## [18,] 0.055074658 0.385472773 0.227286640 -0.028518397 -0.068382841
## [19,] -0.088447578 0.574474910 0.335991814 0.027233861 0.026171773
## [20,] -0.039753513 -0.085016254 -0.042629551 0.026148917 0.038812290
## [21,] -0.005335826 -0.050267936 -0.012942965 0.035104550 -0.050896123
## [22,] -0.058878659 0.188323121 0.092306520 0.072055004 0.008889710
## [23,] 0.156957537 0.001530598 0.049756111 0.227472310 -0.726940494
## [24,] 0.054125031 0.051250474 -0.015415291 -0.179617106 -0.535111713
## [25,] 0.204706377 0.043967083 -0.061799951 -0.128751714 -0.032782244
## [26,] 0.574623383 0.320070492 -0.479235283 -0.355300605 0.146419933
## [27,] -0.190353787 0.255053085 -0.165195934 0.075163166 -0.045723570
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.327508392 -0.1889480400 0.083787864 0.0216984436 -0.081699049
## [2,] -0.038508741 0.0215472973 0.039452624 -0.0374354387 0.167663282
## [3,] -0.294717245 0.1351191051 -0.062378195 -0.0392394039 0.244815942
## [4,] 0.215432325 0.0619809842 -0.205324985 -0.2786539271 0.438676933
## [5,] 0.212297849 0.0009776405 -0.109834706 -0.0502582606 0.103553023
## [6,] -0.355825946 0.2419521056 0.632573935 0.2610676059 -0.086318751
## [7,] -0.083487221 -0.0717665744 -0.134652303 -0.0178382994 -0.011158336
## [8,] 0.062985432 0.0564170680 0.120117310 0.0223680686 -0.000334363
## [9,] 0.025631804 -0.2126522170 -0.036729530 -0.0851044012 0.136889429
## [10,] 0.460105184 -0.0864955753 0.105622641 0.1189909910 -0.372541205
## [11,] -0.481255765 -0.6655529657 -0.177720800 0.0095104279 -0.248709740
## [12,] 0.018619889 0.0801384025 0.144558503 -0.0293083578 0.294285189
## [13,] 0.064596454 -0.0127231144 0.005684504 -0.0065316495 -0.025532719
## [14,] -0.046208205 -0.0811932452 0.007564407 -0.0925106026 0.057933513
## [15,] 0.231153372 -0.1401813095 0.211978208 0.1082025786 -0.133673076
## [16,] -0.091527208 0.5553049679 -0.496715561 0.1327349492 -0.447522082
## [17,] -0.039348415 0.0607572249 -0.010211416 0.0003021102 0.040684306
## [18,] 0.006118770 0.0345829342 -0.047679847 0.0478518720 0.011350308
## [19,] 0.085919243 -0.0525919670 0.062309461 0.0032934360 -0.012559094
## [20,] 0.042787424 -0.1013368296 -0.143974607 0.6042771557 0.255853668
## [21,] -0.061853241 0.0550709128 0.169684102 -0.6379465735 -0.263609089
## [22,] 0.013902135 -0.0276154333 -0.023270026 0.0773235950 -0.004160230
## [23,] -0.038220882 -0.0729712305 -0.183040664 0.0431173029 -0.063672368
## [24,] 0.124984324 -0.0903800211 -0.161788904 0.0172485229 -0.123776825
## [25,] 0.051071506 -0.0416874194 -0.049245987 -0.0083776960 -0.016706875
## [26,] -0.168569974 0.0309883609 -0.157393923 -0.0547324812 0.097983981
## [27,] -0.004227577 0.0098523301 0.025741372 -0.0391431403 -0.015483611
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.097970737 -0.0672698627 0.004709907 0.4437955216 0.185311340
## [2,] 0.022876951 -0.0748532743 0.107335186 0.2331420682 0.228110052
## [3,] 0.005852499 -0.1130343346 0.077454856 0.2951324826 0.519327459
## [4,] -0.416517207 0.1005592031 0.351411531 0.0734243106 -0.390283428
## [5,] 0.726108469 -0.1360192766 0.151669714 -0.3284272605 0.050102950
## [6,] 0.102496911 0.0319118706 0.259030099 0.0430141459 -0.326411229
## [7,] 0.205761573 0.3835611838 0.092603069 0.0247024822 -0.266523994
## [8,] -0.206597647 -0.3628137836 -0.072479739 -0.0623478611 0.143859732
## [9,] 0.177504997 -0.0369647878 0.164508442 -0.1784647694 -0.028592861
## [10,] -0.019618005 0.0586125252 -0.112325002 0.3304403788 -0.152661230
## [11,] -0.105951419 0.0517252821 -0.024265488 -0.0054603671 -0.023472926
## [12,] -0.006616124 0.3987358825 -0.746090527 -0.1590310155 0.038849229
## [13,] 0.005875118 -0.0046963884 -0.003003255 -0.0042171771 0.001877854
## [14,] -0.034809611 -0.7017620045 -0.328272605 -0.0918936888 -0.387357446
## [15,] -0.370719221 0.0581652637 0.217047251 -0.5954945241 0.328885433
## [16,] -0.082204763 -0.0233560543 -0.027607141 -0.1047494783 0.001864987
## [17,] 0.018183062 0.0036268452 0.010942875 0.0043126868 0.002102103
## [18,] 0.007165899 -0.0013193927 0.003930012 0.0081957061 0.000352813
## [19,] 0.001449447 -0.0186901864 0.003812208 -0.0144737287 0.015051997
## [20,] -0.031424207 -0.0411867137 0.006275874 0.0139574782 -0.036991252
## [21,] 0.025056548 0.0364268784 0.001604572 -0.0102488695 0.053973468
## [22,] -0.011508211 0.0015498719 -0.012645810 -0.0114751954 -0.009223695
## [23,] 0.015612087 0.0182768697 -0.017182319 0.0157819058 -0.018873454
## [24,] 0.021360062 0.0318448193 -0.014449417 0.0224436817 -0.035140096
## [25,] 0.035231202 -0.0009527924 -0.011703370 -0.0066132353 -0.014658271
## [26,] -0.012845435 -0.0328822272 -0.034063217 -0.0071284137 -0.002839603
## [27,] -0.027586100 0.0013167622 -0.017956093 0.0003324248 0.002188838
## [,26] [,27]
## [1,] -0.0016012928 0.2875894479
## [2,] -0.1084673138 -0.8163012888
## [3,] -0.0096955250 0.4473543035
## [4,] 0.0453628190 0.1098362784
## [5,] 0.0076286783 0.0398027479
## [6,] 0.0369363755 0.0888452361
## [7,] -0.6700740328 0.1178914672
## [8,] -0.7304102671 0.0212097902
## [9,] 0.0133917384 0.0386546859
## [10,] 0.0010777182 -0.0114552420
## [11,] 0.0249185776 -0.0066474831
## [12,] -0.0047395121 0.0341045915
## [13,] -0.0001528412 0.0002482526
## [14,] 0.0287530206 0.0756458790
## [15,] -0.0037687292 0.0764706940
## [16,] 0.0100805572 0.0110461609
## [17,] 0.0071776527 -0.0007167878
## [18,] 0.0011495481 0.0021567621
## [19,] -0.0098332779 0.0039923647
## [20,] 0.0064163087 -0.0050569152
## [21,] -0.0046192832 0.0038810164
## [22,] -0.0117645196 -0.0059065642
## [23,] -0.0058914753 -0.0046337065
## [24,] -0.0012134038 -0.0015015100
## [25,] 0.0022065482 -0.0105892736
## [26,] -0.0012660659 -0.0129652820
## [27,] -0.0002277842 -0.0017883147sumvar <- sum(pc$values)
propvar <- sapply(pc$values, function(x) x/sumvar)*100
cumvar <- data.frame(cbind(pc$values, propvar)) %>% mutate(cum = cumsum(propvar))
colnames(cumvar)[1] <- "eigen_value"
row.names(cumvar) <- paste0("PC",c(1:ncol(data_num3)))
print(cumvar)## eigen_value propvar cum
## PC1 8.543020116 31.64081525 31.64082
## PC2 5.909418055 21.88673354 53.52755
## PC3 1.767097501 6.54480556 60.07235
## PC4 1.548861969 5.73652581 65.80888
## PC5 1.312008248 4.85928981 70.66817
## PC6 1.082754767 4.01020284 74.67837
## PC7 1.004615498 3.72079814 78.39917
## PC8 0.918128477 3.40047584 81.79965
## PC9 0.862861127 3.19578195 84.99543
## PC10 0.743264160 2.75283022 87.74826
## PC11 0.613419767 2.27192506 90.02018
## PC12 0.558760336 2.06948273 92.08967
## PC13 0.396786097 1.46957814 93.55924
## PC14 0.354203219 1.31186377 94.87111
## PC15 0.267787216 0.99180450 95.86291
## PC16 0.236783770 0.87697692 96.73989
## PC17 0.213971445 0.79248683 97.53238
## PC18 0.197460719 0.73133600 98.26371
## PC19 0.127368589 0.47173552 98.73545
## PC20 0.118080201 0.43733408 99.17278
## PC21 0.074695297 0.27664925 99.44943
## PC22 0.056775299 0.21027888 99.65971
## PC23 0.041017532 0.15191679 99.81163
## PC24 0.023099247 0.08555277 99.89718
## PC25 0.018565507 0.06876114 99.96594
## PC26 0.005410330 0.02003826 99.98598
## PC27 0.003785511 0.01402041 100.00000print('eigen vectors:')## [1] "eigen vectors:"pc$vectors## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.23545404 0.21739162 -0.0037080070 0.159297609 -4.764273e-02
## [2,] -0.29643149 -0.18668585 -0.0019815092 0.099540530 3.499169e-03
## [3,] -0.15837712 -0.34424799 -0.0006168793 0.001001541 3.038913e-02
## [4,] -0.32016947 0.05125864 -0.0091479125 0.088126444 3.114604e-02
## [5,] -0.31536101 -0.00581424 0.0030269525 0.088530519 7.111574e-02
## [6,] -0.30056274 0.09504513 0.0113295489 0.114935532 -1.874966e-02
## [7,] 0.02897468 -0.39736411 0.0184905790 -0.013751353 -3.262792e-03
## [8,] -0.03066373 0.39743338 -0.0177179259 0.020391258 8.990578e-03
## [9,] -0.01034868 0.30409955 -0.1060017585 -0.088361470 1.215771e-03
## [10,] -0.23064175 -0.20969875 -0.1042019954 -0.137706904 1.523130e-01
## [11,] -0.29538715 0.05989780 -0.0329191254 0.109635196 1.252728e-02
## [12,] -0.32320327 0.06783934 -0.0079500131 0.101319044 4.704108e-03
## [13,] -0.00892062 -0.08537336 0.0235484157 -0.124989920 -1.529563e-01
## [14,] -0.11025679 -0.37407809 0.0141845791 0.041477852 4.196625e-05
## [15,] -0.21465074 -0.29718709 -0.0137875377 0.051602083 3.439374e-02
## [16,] -0.29935240 0.06364837 -0.0106835797 0.073550970 -1.175211e-02
## [17,] -0.06574309 -0.03518461 -0.2151597501 -0.384762663 -3.903055e-01
## [18,] 0.14510027 -0.07452986 0.0542479806 0.057143661 2.977579e-01
## [19,] -0.14460036 0.00485697 -0.0997808553 -0.280151290 -4.174899e-01
## [20,] -0.09610112 0.05474895 0.6014574692 -0.297276996 1.514606e-01
## [21,] -0.13100755 0.05244508 0.5713748644 -0.320363343 1.320284e-01
## [22,] -0.01983034 -0.06297339 0.0393821566 -0.377716562 -1.756683e-01
## [23,] -0.16440493 0.18033049 -0.2648574601 -0.275450669 2.683504e-01
## [24,] 0.02573697 0.03364893 0.3755609435 0.456652736 -4.460369e-01
## [25,] 0.01687440 -0.08164519 -0.1036946558 -0.048913634 1.924508e-01
## [26,] -0.20864638 0.16298786 -0.0124251704 -0.093428634 -7.504613e-02
## [27,] 0.00122398 0.06472836 -0.0611320368 0.042771378 3.769220e-01
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.1360202508 0.0213757059 -0.096588012 -0.0279727359 0.094037310
## [2,] -0.0555381966 0.0065104896 -0.038060342 -0.0058103241 0.020676223
## [3,] 0.0122069214 -0.0150835613 0.036851378 -0.0005271727 -0.045512188
## [4,] -0.0060919643 0.0003081984 0.013937776 -0.0772807221 0.009521554
## [5,] 0.1060885213 -0.0394572575 0.018193150 -0.0910516525 -0.027119804
## [6,] -0.0669530502 0.0307733090 0.012273501 -0.0775786948 0.025942546
## [7,] -0.0009865401 -0.0160417147 -0.032618264 0.1001337779 -0.005087421
## [8,] 0.0063323807 0.0232487979 0.036373254 -0.0983423344 0.020231002
## [9,] -0.1792256009 0.0775367701 -0.138731647 0.0417120340 0.065141061
## [10,] 0.1215901927 -0.0102352461 -0.076085760 0.0131206223 -0.045933913
## [11,] 0.0322030485 0.0153001874 0.018675552 -0.0957945872 0.072995917
## [12,] -0.0605425920 0.0304118624 -0.025698098 -0.0495480408 0.038830053
## [13,] 0.2361361620 0.7551329814 0.313331751 -0.3899567675 -0.164065391
## [14,] -0.0294964441 -0.0075243944 -0.053331424 0.0577360504 0.010202920
## [15,] -0.0094032619 -0.0021873921 -0.075931734 0.0242650545 0.017321013
## [16,] -0.1008442836 0.0187702595 -0.006464326 0.0167799871 0.050186145
## [17,] 0.2066579968 -0.0587838054 -0.021218315 -0.1721854251 0.563753587
## [18,] -0.0109034933 0.2164086724 -0.485846708 -0.2226472177 0.575425361
## [19,] 0.0354243774 -0.1043015343 0.189055502 0.4206995129 0.155529182
## [20,] 0.0378861664 0.0172161356 0.096585466 0.1321196990 0.074677536
## [21,] -0.0364953891 0.0170471603 -0.001915481 0.0597955604 0.068388810
## [22,] -0.2649887178 -0.3767288117 -0.225091240 -0.6221874373 -0.331258111
## [23,] 0.0100900502 0.1160201691 -0.054350095 0.1293645374 -0.184739759
## [24,] 0.0392899383 -0.1183126254 0.085579659 -0.1596123491 0.089059741
## [25,] -0.6483690504 0.0003950853 0.585917562 -0.1414825544 0.291519394
## [26,] 0.1310454060 0.0229409601 -0.115852074 0.0035240990 -0.069939970
## [27,] 0.5363619511 -0.4317319526 0.390757659 -0.2505864136 0.136568863
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.012041336 0.092978708 -0.299316478 0.479375672 0.135161452
## [2,] -0.110304952 0.032306750 -0.083136895 0.065004074 -0.052930834
## [3,] -0.122888631 -0.017341724 0.093131663 -0.243168952 -0.148850835
## [4,] -0.003494525 -0.055983473 0.182505663 0.014799875 0.040699621
## [5,] 0.159455097 -0.097459910 0.262760668 -0.002422531 0.101624999
## [6,] 0.005467107 0.045722487 -0.004904177 -0.020289256 -0.122178716
## [7,] -0.044131716 0.075036868 -0.205196203 0.128001633 -0.002814619
## [8,] 0.042492675 -0.091784324 0.201920694 -0.129450233 0.019291012
## [9,] -0.626476246 0.066228992 -0.353678246 -0.354090863 -0.100961336
## [10,] -0.029309594 -0.120154829 0.077874815 -0.522443055 0.014025617
## [11,] -0.025689500 -0.089818173 0.226549884 -0.007174512 0.189299354
## [12,] -0.103056689 -0.012229174 0.032184864 -0.002715459 -0.027568377
## [13,] -0.115665430 0.162078546 -0.027951164 0.060318733 0.026391894
## [14,] -0.078891490 0.036998520 -0.157989060 0.115535010 -0.075460271
## [15,] 0.066304600 0.023642478 -0.190852697 0.070811250 -0.065319909
## [16,] -0.243703041 0.024749150 -0.054150455 0.078277371 0.132744903
## [17,] 0.059453811 -0.457703138 -0.149717654 0.073591939 -0.072734613
## [18,] 0.055074658 0.385472773 0.227286640 -0.028518397 -0.068382841
## [19,] -0.088447578 0.574474910 0.335991814 0.027233861 0.026171773
## [20,] -0.039753513 -0.085016254 -0.042629551 0.026148917 0.038812290
## [21,] -0.005335826 -0.050267936 -0.012942965 0.035104550 -0.050896123
## [22,] -0.058878659 0.188323121 0.092306520 0.072055004 0.008889710
## [23,] 0.156957537 0.001530598 0.049756111 0.227472310 -0.726940494
## [24,] 0.054125031 0.051250474 -0.015415291 -0.179617106 -0.535111713
## [25,] 0.204706377 0.043967083 -0.061799951 -0.128751714 -0.032782244
## [26,] 0.574623383 0.320070492 -0.479235283 -0.355300605 0.146419933
## [27,] -0.190353787 0.255053085 -0.165195934 0.075163166 -0.045723570
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.327508392 -0.1889480400 0.083787864 0.0216984436 -0.081699049
## [2,] -0.038508741 0.0215472973 0.039452624 -0.0374354387 0.167663282
## [3,] -0.294717245 0.1351191051 -0.062378195 -0.0392394039 0.244815942
## [4,] 0.215432325 0.0619809842 -0.205324985 -0.2786539271 0.438676933
## [5,] 0.212297849 0.0009776405 -0.109834706 -0.0502582606 0.103553023
## [6,] -0.355825946 0.2419521056 0.632573935 0.2610676059 -0.086318751
## [7,] -0.083487221 -0.0717665744 -0.134652303 -0.0178382994 -0.011158336
## [8,] 0.062985432 0.0564170680 0.120117310 0.0223680686 -0.000334363
## [9,] 0.025631804 -0.2126522170 -0.036729530 -0.0851044012 0.136889429
## [10,] 0.460105184 -0.0864955753 0.105622641 0.1189909910 -0.372541205
## [11,] -0.481255765 -0.6655529657 -0.177720800 0.0095104279 -0.248709740
## [12,] 0.018619889 0.0801384025 0.144558503 -0.0293083578 0.294285189
## [13,] 0.064596454 -0.0127231144 0.005684504 -0.0065316495 -0.025532719
## [14,] -0.046208205 -0.0811932452 0.007564407 -0.0925106026 0.057933513
## [15,] 0.231153372 -0.1401813095 0.211978208 0.1082025786 -0.133673076
## [16,] -0.091527208 0.5553049679 -0.496715561 0.1327349492 -0.447522082
## [17,] -0.039348415 0.0607572249 -0.010211416 0.0003021102 0.040684306
## [18,] 0.006118770 0.0345829342 -0.047679847 0.0478518720 0.011350308
## [19,] 0.085919243 -0.0525919670 0.062309461 0.0032934360 -0.012559094
## [20,] 0.042787424 -0.1013368296 -0.143974607 0.6042771557 0.255853668
## [21,] -0.061853241 0.0550709128 0.169684102 -0.6379465735 -0.263609089
## [22,] 0.013902135 -0.0276154333 -0.023270026 0.0773235950 -0.004160230
## [23,] -0.038220882 -0.0729712305 -0.183040664 0.0431173029 -0.063672368
## [24,] 0.124984324 -0.0903800211 -0.161788904 0.0172485229 -0.123776825
## [25,] 0.051071506 -0.0416874194 -0.049245987 -0.0083776960 -0.016706875
## [26,] -0.168569974 0.0309883609 -0.157393923 -0.0547324812 0.097983981
## [27,] -0.004227577 0.0098523301 0.025741372 -0.0391431403 -0.015483611
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.097970737 -0.0672698627 0.004709907 0.4437955216 0.185311340
## [2,] 0.022876951 -0.0748532743 0.107335186 0.2331420682 0.228110052
## [3,] 0.005852499 -0.1130343346 0.077454856 0.2951324826 0.519327459
## [4,] -0.416517207 0.1005592031 0.351411531 0.0734243106 -0.390283428
## [5,] 0.726108469 -0.1360192766 0.151669714 -0.3284272605 0.050102950
## [6,] 0.102496911 0.0319118706 0.259030099 0.0430141459 -0.326411229
## [7,] 0.205761573 0.3835611838 0.092603069 0.0247024822 -0.266523994
## [8,] -0.206597647 -0.3628137836 -0.072479739 -0.0623478611 0.143859732
## [9,] 0.177504997 -0.0369647878 0.164508442 -0.1784647694 -0.028592861
## [10,] -0.019618005 0.0586125252 -0.112325002 0.3304403788 -0.152661230
## [11,] -0.105951419 0.0517252821 -0.024265488 -0.0054603671 -0.023472926
## [12,] -0.006616124 0.3987358825 -0.746090527 -0.1590310155 0.038849229
## [13,] 0.005875118 -0.0046963884 -0.003003255 -0.0042171771 0.001877854
## [14,] -0.034809611 -0.7017620045 -0.328272605 -0.0918936888 -0.387357446
## [15,] -0.370719221 0.0581652637 0.217047251 -0.5954945241 0.328885433
## [16,] -0.082204763 -0.0233560543 -0.027607141 -0.1047494783 0.001864987
## [17,] 0.018183062 0.0036268452 0.010942875 0.0043126868 0.002102103
## [18,] 0.007165899 -0.0013193927 0.003930012 0.0081957061 0.000352813
## [19,] 0.001449447 -0.0186901864 0.003812208 -0.0144737287 0.015051997
## [20,] -0.031424207 -0.0411867137 0.006275874 0.0139574782 -0.036991252
## [21,] 0.025056548 0.0364268784 0.001604572 -0.0102488695 0.053973468
## [22,] -0.011508211 0.0015498719 -0.012645810 -0.0114751954 -0.009223695
## [23,] 0.015612087 0.0182768697 -0.017182319 0.0157819058 -0.018873454
## [24,] 0.021360062 0.0318448193 -0.014449417 0.0224436817 -0.035140096
## [25,] 0.035231202 -0.0009527924 -0.011703370 -0.0066132353 -0.014658271
## [26,] -0.012845435 -0.0328822272 -0.034063217 -0.0071284137 -0.002839603
## [27,] -0.027586100 0.0013167622 -0.017956093 0.0003324248 0.002188838
## [,26] [,27]
## [1,] -0.0016012928 0.2875894479
## [2,] -0.1084673138 -0.8163012888
## [3,] -0.0096955250 0.4473543035
## [4,] 0.0453628190 0.1098362784
## [5,] 0.0076286783 0.0398027479
## [6,] 0.0369363755 0.0888452361
## [7,] -0.6700740328 0.1178914672
## [8,] -0.7304102671 0.0212097902
## [9,] 0.0133917384 0.0386546859
## [10,] 0.0010777182 -0.0114552420
## [11,] 0.0249185776 -0.0066474831
## [12,] -0.0047395121 0.0341045915
## [13,] -0.0001528412 0.0002482526
## [14,] 0.0287530206 0.0756458790
## [15,] -0.0037687292 0.0764706940
## [16,] 0.0100805572 0.0110461609
## [17,] 0.0071776527 -0.0007167878
## [18,] 0.0011495481 0.0021567621
## [19,] -0.0098332779 0.0039923647
## [20,] 0.0064163087 -0.0050569152
## [21,] -0.0046192832 0.0038810164
## [22,] -0.0117645196 -0.0059065642
## [23,] -0.0058914753 -0.0046337065
## [24,] -0.0012134038 -0.0015015100
## [25,] 0.0022065482 -0.0105892736
## [26,] -0.0012660659 -0.0129652820
## [27,] -0.0002277842 -0.00178831476.2 With Function PCA for Visualisation
pca_result <- PCA(scale_data,
scale.unit = TRUE,
graph = FALSE,
ncp=ncol(data_num3))
pca_result$eig## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 8.543020116 31.64081525 31.64082
## comp 2 5.909418055 21.88673354 53.52755
## comp 3 1.767097501 6.54480556 60.07235
## comp 4 1.548861969 5.73652581 65.80888
## comp 5 1.312008248 4.85928981 70.66817
## comp 6 1.082754767 4.01020284 74.67837
## comp 7 1.004615498 3.72079814 78.39917
## comp 8 0.918128477 3.40047584 81.79965
## comp 9 0.862861127 3.19578195 84.99543
## comp 10 0.743264160 2.75283022 87.74826
## comp 11 0.613419767 2.27192506 90.02018
## comp 12 0.558760336 2.06948273 92.08967
## comp 13 0.396786097 1.46957814 93.55924
## comp 14 0.354203219 1.31186377 94.87111
## comp 15 0.267787216 0.99180450 95.86291
## comp 16 0.236783770 0.87697692 96.73989
## comp 17 0.213971445 0.79248683 97.53238
## comp 18 0.197460719 0.73133600 98.26371
## comp 19 0.127368589 0.47173552 98.73545
## comp 20 0.118080201 0.43733408 99.17278
## comp 21 0.074695297 0.27664925 99.44943
## comp 22 0.056775299 0.21027888 99.65971
## comp 23 0.041017532 0.15191679 99.81163
## comp 24 0.023099247 0.08555277 99.89718
## comp 25 0.018565507 0.06876114 99.96594
## comp 26 0.005410330 0.02003826 99.98598
## comp 27 0.003785511 0.01402041 100.00000fviz_eig(pca_result,
choice = "eigenvalue",
addlabels = TRUE,
ncp = ncol(data_num3),
barfill = "skyblue",
barcolor = "darkblue",
linecolor = "red")+
geom_hline(yintercept = 1, linetype = "dashed", color = "black", size = 1)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Warning in geom_bar(stat = "identity", fill = barfill, color = barcolor, :
## Ignoring empty aesthetic: `width`.
fviz_pca_biplot(pca_result,
col.ind = data$Status,
palette = c("Batu Empedu" = "#E74C3C", "Normal" = "#2980B9"),
addEllipses = TRUE,
ellipse.type = "confidence",
col.var = "black",
label = "var",
repel = TRUE,
legend.title = "Status") +
labs(title = "Biplot PCA — Gallstone Disease") +
theme_minimal(base_size = 11)## Ignoring unknown labels:
## • linetype : "Status"
fviz_pca_var(pca_result,
col.var = "cos2",
gradient.cols = c("#2980B9", "#F39C12", "#E74C3C"),
repel = TRUE,
legend.title = "cos²") +
labs(title = "Correlation Circle PCA — Gallstone Disease") +
theme_minimal(base_size = 11)## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Ignoring unknown labels:
## • fill : "cos²"
## • linetype : "cos²"
## • shape : "cos²"
contrib_PC1 <- fviz_contrib(pca_result, choice = "var", axes = 1, top = 10) + ggtitle("Kontribusi Variabel — PC1 (31.64%)")
contrib_PC2 <- fviz_contrib(pca_result, choice = "var", axes = 2, top = 10) + ggtitle("Kontribusi Variabel — PC2 (21.89%)")
contrib_PC3 <- fviz_contrib(pca_result, choice = "var", axes = 3, top = 10) + ggtitle("Kontribusi Variabel — PC3 (6.54%)")
contrib_PC4 <- fviz_contrib(pca_result, choice = "var", axes = 4, top = 10) + ggtitle("Kontribusi Variabel — PC4 (5.74%)")
contrib_PC5 <- fviz_contrib(pca_result, choice = "var", axes = 5, top = 10) + ggtitle("Kontribusi Variabel — PC5 (4.86%)")
contrib_PC6 <- fviz_contrib(pca_result, choice = "var", axes = 6, top = 10) + ggtitle("Kontribusi Variabel — PC6 (4.01%)")
contrib_PC7 <- fviz_contrib(pca_result, choice = "var", axes = 7, top = 10) + ggtitle("Kontribusi Variabel — PC7 (3.72%)")
grid.arrange(contrib_PC1, contrib_PC2, contrib_PC3,
contrib_PC4, contrib_PC5, contrib_PC6, contrib_PC7,
ncol = 3)
pc <- principal(data_num3,nfactors = 7, rotate= "none")
pc## Principal Components Analysis
## Call: principal(r = data_num3, nfactors = 7, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 h2 u2 com
## Height 0.69 -0.53 0.00 -0.20 -0.05 0.14 0.02 0.82 0.184 2.2
## Weight 0.87 0.45 0.00 -0.12 0.00 0.06 0.01 0.98 0.025 1.6
## BMI 0.46 0.84 0.00 0.00 0.03 -0.01 -0.02 0.92 0.084 1.6
## TBW 0.94 -0.12 -0.01 -0.11 0.04 0.01 0.00 0.90 0.095 1.1
## ECW 0.92 0.01 0.00 -0.11 0.08 -0.11 -0.04 0.88 0.118 1.1
## ICW 0.88 -0.23 0.02 -0.14 -0.02 0.07 0.03 0.85 0.148 1.2
## TBFR -0.08 0.97 0.02 0.02 0.00 0.00 -0.02 0.94 0.059 1.0
## LeanMass 0.09 -0.97 -0.02 -0.03 0.01 -0.01 0.02 0.94 0.057 1.0
## Protein 0.03 -0.74 -0.14 0.11 0.00 0.19 0.08 0.62 0.380 1.3
## VFR 0.67 0.51 -0.14 0.17 0.17 -0.13 -0.01 0.81 0.191 2.4
## BoneMass 0.86 -0.15 -0.04 -0.14 0.01 -0.03 0.02 0.79 0.211 1.1
## MuscleMass 0.94 -0.16 -0.01 -0.13 0.01 0.06 0.03 0.94 0.059 1.1
## Obesity 0.03 0.21 0.03 0.16 -0.18 -0.25 0.76 0.73 0.267 1.6
## TFC 0.32 0.91 0.02 -0.05 0.00 0.03 -0.01 0.93 0.065 1.3
## VFA 0.63 0.72 -0.02 -0.06 0.04 0.01 0.00 0.92 0.078 2.0
## VMA 0.87 -0.15 -0.01 -0.09 -0.01 0.10 0.02 0.81 0.190 1.1
## Glucose 0.19 0.09 -0.29 0.48 -0.45 -0.22 -0.06 0.60 0.395 3.6
## HDL -0.42 0.18 0.07 -0.07 0.34 0.01 0.22 0.39 0.614 3.0
## Triglyceride 0.42 -0.01 -0.13 0.35 -0.48 -0.04 -0.10 0.56 0.441 3.1
## AST 0.28 -0.13 0.80 0.37 0.17 -0.04 0.02 0.90 0.095 1.9
## ALT 0.38 -0.13 0.76 0.40 0.15 0.04 0.02 0.92 0.077 2.2
## ALP 0.06 0.15 0.05 0.47 -0.20 0.28 -0.38 0.51 0.490 3.4
## Creatinine 0.48 -0.44 -0.35 0.34 0.31 -0.01 0.12 0.77 0.227 4.6
## GFR -0.08 -0.08 0.50 -0.57 -0.51 -0.04 -0.12 0.86 0.139 3.2
## CRP -0.05 0.20 -0.14 0.06 0.22 0.67 0.00 0.57 0.432 1.5
## HGB 0.61 -0.40 -0.02 0.12 -0.09 -0.14 0.02 0.57 0.431 2.0
## VitaminD 0.00 -0.16 -0.08 -0.05 0.43 -0.56 -0.43 0.72 0.281 3.1
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## SS loadings 8.54 5.91 1.77 1.55 1.31 1.08 1.00
## Proportion Var 0.32 0.22 0.07 0.06 0.05 0.04 0.04
## Cumulative Var 0.32 0.54 0.60 0.66 0.71 0.75 0.78
## Proportion Explained 0.40 0.28 0.08 0.07 0.06 0.05 0.05
## Cumulative Proportion 0.40 0.68 0.77 0.84 0.90 0.95 1.00
##
## Mean item complexity = 2
## Test of the hypothesis that 7 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.03
## with the empirical chi square 226.72 with prob < 0.015
##
## Fit based upon off diagonal values = 0.99fa.diagram(pc,
cut = 0.40,
digits = 2,
sort = TRUE,
cex = 0.7) 
7 Factor Analysis
7.1 Manual FA
fa_eigen <- eigen(r)
fa_eigen$values## [1] 8.543020116 5.909418055 1.767097501 1.548861969 1.312008248 1.082754767
## [7] 1.004615498 0.918128477 0.862861127 0.743264160 0.613419767 0.558760336
## [13] 0.396786097 0.354203219 0.267787216 0.236783770 0.213971445 0.197460719
## [19] 0.127368589 0.118080201 0.074695297 0.056775299 0.041017532 0.023099247
## [25] 0.018565507 0.005410330 0.003785511sp <- sum(fa_eigen$values[1:7])
sp## [1] 21.16778L1 = sqrt(fa_eigen$values[1])*fa_eigen$vectors[,1]
L2 = sqrt(fa_eigen$values[2])*fa_eigen$vectors[,2]
L3 = sqrt(fa_eigen$values[3])*fa_eigen$vectors[,3]
L4 = sqrt(fa_eigen$values[4])*fa_eigen$vectors[,4]
L5 = sqrt(fa_eigen$values[5])*fa_eigen$vectors[,5]
L6 = sqrt(fa_eigen$values[6])*fa_eigen$vectors[,6]
L7 = sqrt(fa_eigen$values[7])*fa_eigen$vectors[,7]
L = cbind(L1,L2,L3,L4,L5,L6,L7)
L## L1 L2 L3 L4 L5
## [1,] -0.688195548 0.52846370 -0.0049291360 0.198251104 -5.457138e-02
## [2,] -0.866423161 -0.45382013 -0.0026340642 0.123881457 4.008050e-03
## [3,] -0.462911693 -0.83684257 -0.0008200313 0.001246451 3.480860e-02
## [4,] -0.935805588 0.12460613 -0.0121605231 0.109676253 3.567558e-02
## [5,] -0.921751200 -0.01413401 0.0040237951 0.110179137 8.145805e-02
## [6,] -0.878498147 0.23104802 0.0150606208 0.143041043 -2.147641e-02
## [7,] 0.084688471 -0.96596412 0.0245799371 -0.017114010 -3.737297e-03
## [8,] -0.089625313 0.96613252 -0.0235528322 0.025377590 1.029807e-02
## [9,] -0.030247572 0.73924455 -0.1409104905 -0.109968751 1.392580e-03
## [10,] -0.674129965 -0.50976286 -0.1385180254 -0.171380763 1.744637e-01
## [11,] -0.863370717 0.14560733 -0.0437601241 0.136444601 1.434911e-02
## [12,] -0.944672910 0.16491265 -0.0105681289 0.126094877 5.388223e-03
## [13,] -0.026073586 -0.20753662 0.0313034317 -0.155554059 -1.752006e-01
## [14,] -0.322263446 -0.90935746 0.0188558759 0.051620548 4.806938e-05
## [15,] -0.627390734 -0.72244086 -0.0183280799 0.064220487 3.939560e-02
## [16,] -0.874960509 0.15472469 -0.0142019196 0.091536597 -1.346121e-02
## [17,] -0.192156842 -0.08553131 -0.2860166315 -0.478849767 -4.470673e-01
## [18,] 0.424105520 -0.18117683 0.0721130447 0.071117162 3.410607e-01
## [19,] -0.422644365 0.01180695 -0.1326409057 -0.348657479 -4.782052e-01
## [20,] -0.280888638 0.13309084 0.7995307639 -0.369970981 1.734874e-01
## [21,] -0.382914688 0.12749030 0.7595412896 -0.398702698 1.512292e-01
## [22,] -0.057960998 -0.15308386 0.0523515749 -0.470080662 -2.012156e-01
## [23,] -0.480530052 0.43837069 -0.3520809005 -0.342807401 3.073764e-01
## [24,] 0.075225168 0.08179817 0.4992414982 0.568319323 -5.109037e-01
## [25,] 0.049321239 -0.19847370 -0.1378436076 -0.060874623 2.204388e-01
## [26,] -0.609840925 0.39621200 -0.0165170549 -0.116275003 -8.596003e-02
## [27,] 0.003577503 0.15735008 -0.0812641734 0.053230384 4.317375e-01
## L6 L7
## [1,] -0.141536556 0.0214249789
## [2,] -0.057790550 0.0065254969
## [3,] 0.012701973 -0.0151183303
## [4,] -0.006339024 0.0003089088
## [5,] 0.110390944 -0.0395482101
## [6,] -0.069668333 0.0308442443
## [7,] -0.001026549 -0.0160786923
## [8,] 0.006589191 0.0233023886
## [9,] -0.186494100 0.0777154995
## [10,] 0.126521286 -0.0102588393
## [11,] 0.033509044 0.0153354557
## [12,] -0.062997899 0.0304819645
## [13,] 0.245712671 0.7568736325
## [14,] -0.030692673 -0.0075417388
## [15,] -0.009784611 -0.0021924343
## [16,] -0.104934026 0.0188135267
## [17,] 0.215039018 -0.0589193075
## [18,] -0.011345685 0.2169075143
## [19,] 0.036861014 -0.1045419589
## [20,] 0.039422641 0.0172558204
## [21,] -0.037975461 0.0170864555
## [22,] -0.275735343 -0.3775972063
## [23,] 0.010499252 0.1162876063
## [24,] 0.040883343 -0.1185853469
## [25,] -0.674663675 0.0003959960
## [26,] 0.136359956 0.0229938411
## [27,] 0.558114125 -0.43272713457.2 With Function Principal for Rotate
fa_norotate <- principal(scale_data, nfactors = 7, rotate = "none")
fa_norotate## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 7, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 h2 u2 com
## Height 0.69 -0.53 0.00 -0.20 -0.05 0.14 0.02 0.82 0.184 2.2
## Weight 0.87 0.45 0.00 -0.12 0.00 0.06 0.01 0.98 0.025 1.6
## BMI 0.46 0.84 0.00 0.00 0.03 -0.01 -0.02 0.92 0.084 1.6
## TBW 0.94 -0.12 -0.01 -0.11 0.04 0.01 0.00 0.90 0.095 1.1
## ECW 0.92 0.01 0.00 -0.11 0.08 -0.11 -0.04 0.88 0.118 1.1
## ICW 0.88 -0.23 0.02 -0.14 -0.02 0.07 0.03 0.85 0.148 1.2
## TBFR -0.08 0.97 0.02 0.02 0.00 0.00 -0.02 0.94 0.059 1.0
## LeanMass 0.09 -0.97 -0.02 -0.03 0.01 -0.01 0.02 0.94 0.057 1.0
## Protein 0.03 -0.74 -0.14 0.11 0.00 0.19 0.08 0.62 0.380 1.3
## VFR 0.67 0.51 -0.14 0.17 0.17 -0.13 -0.01 0.81 0.191 2.4
## BoneMass 0.86 -0.15 -0.04 -0.14 0.01 -0.03 0.02 0.79 0.211 1.1
## MuscleMass 0.94 -0.16 -0.01 -0.13 0.01 0.06 0.03 0.94 0.059 1.1
## Obesity 0.03 0.21 0.03 0.16 -0.18 -0.25 0.76 0.73 0.267 1.6
## TFC 0.32 0.91 0.02 -0.05 0.00 0.03 -0.01 0.93 0.065 1.3
## VFA 0.63 0.72 -0.02 -0.06 0.04 0.01 0.00 0.92 0.078 2.0
## VMA 0.87 -0.15 -0.01 -0.09 -0.01 0.10 0.02 0.81 0.190 1.1
## Glucose 0.19 0.09 -0.29 0.48 -0.45 -0.22 -0.06 0.60 0.395 3.6
## HDL -0.42 0.18 0.07 -0.07 0.34 0.01 0.22 0.39 0.614 3.0
## Triglyceride 0.42 -0.01 -0.13 0.35 -0.48 -0.04 -0.10 0.56 0.441 3.1
## AST 0.28 -0.13 0.80 0.37 0.17 -0.04 0.02 0.90 0.095 1.9
## ALT 0.38 -0.13 0.76 0.40 0.15 0.04 0.02 0.92 0.077 2.2
## ALP 0.06 0.15 0.05 0.47 -0.20 0.28 -0.38 0.51 0.490 3.4
## Creatinine 0.48 -0.44 -0.35 0.34 0.31 -0.01 0.12 0.77 0.227 4.6
## GFR -0.08 -0.08 0.50 -0.57 -0.51 -0.04 -0.12 0.86 0.139 3.2
## CRP -0.05 0.20 -0.14 0.06 0.22 0.67 0.00 0.57 0.432 1.5
## HGB 0.61 -0.40 -0.02 0.12 -0.09 -0.14 0.02 0.57 0.431 2.0
## VitaminD 0.00 -0.16 -0.08 -0.05 0.43 -0.56 -0.43 0.72 0.281 3.1
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## SS loadings 8.54 5.91 1.77 1.55 1.31 1.08 1.00
## Proportion Var 0.32 0.22 0.07 0.06 0.05 0.04 0.04
## Cumulative Var 0.32 0.54 0.60 0.66 0.71 0.75 0.78
## Proportion Explained 0.40 0.28 0.08 0.07 0.06 0.05 0.05
## Cumulative Proportion 0.40 0.68 0.77 0.84 0.90 0.95 1.00
##
## Mean item complexity = 2
## Test of the hypothesis that 7 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.03
## with the empirical chi square 226.72 with prob < 0.015
##
## Fit based upon off diagonal values = 0.99fa_norotate$loadings##
## Loadings:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Height 0.688 -0.528 -0.198 0.142
## Weight 0.866 0.454 -0.124
## BMI 0.463 0.837
## TBW 0.936 -0.125 -0.110
## ECW 0.922 -0.110 -0.110
## ICW 0.878 -0.231 -0.143
## TBFR 0.966
## LeanMass -0.966
## Protein -0.739 -0.141 0.110 0.186
## VFR 0.674 0.510 -0.139 0.171 0.174 -0.127
## BoneMass 0.863 -0.146 -0.136
## MuscleMass 0.945 -0.165 -0.126
## Obesity 0.208 0.156 -0.175 -0.246 0.757
## TFC 0.322 0.909
## VFA 0.627 0.722
## VMA 0.875 -0.155 0.105
## Glucose 0.192 -0.286 0.479 -0.447 -0.215
## HDL -0.424 0.181 0.341 0.217
## Triglyceride 0.423 -0.133 0.349 -0.478 -0.105
## AST 0.281 -0.133 0.800 0.370 0.173
## ALT 0.383 -0.127 0.760 0.399 0.151
## ALP 0.153 0.470 -0.201 0.276 -0.378
## Creatinine 0.481 -0.438 -0.352 0.343 0.307 0.116
## GFR 0.499 -0.568 -0.511 -0.119
## CRP 0.198 -0.138 0.220 0.675
## HGB 0.610 -0.396 0.116 -0.136
## VitaminD -0.157 0.432 -0.558 -0.433
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## SS loadings 8.543 5.909 1.767 1.549 1.312 1.083 1.005
## Proportion Var 0.316 0.219 0.065 0.057 0.049 0.040 0.037
## Cumulative Var 0.316 0.535 0.601 0.658 0.707 0.747 0.784fa.diagram(fa_norotate$loadings,
cut = 0.40,
digits = 2,
sort = TRUE,
cex = 0.7) 
fa_varimax <- principal(scale_data,nfactors = 7 ,rotate = "varimax")
fa_varimax## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 7, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 RC5 RC4 RC6 RC7 h2 u2 com
## Height 0.82 -0.36 0.04 0.02 -0.06 0.06 -0.05 0.82 0.184 1.4
## Weight 0.75 0.63 0.05 0.08 0.02 0.08 0.01 0.98 0.025 2.0
## BMI 0.25 0.92 0.02 0.08 0.06 0.06 0.04 0.92 0.084 1.2
## TBW 0.93 0.10 0.10 0.08 0.06 -0.04 -0.01 0.90 0.095 1.1
## ECW 0.88 0.24 0.11 0.06 0.07 -0.15 -0.01 0.88 0.118 1.3
## ICW 0.91 -0.03 0.10 0.07 0.00 0.03 0.00 0.85 0.148 1.0
## TBFR -0.30 0.91 -0.05 0.01 -0.02 0.10 0.04 0.94 0.059 1.3
## LeanMass 0.31 -0.91 0.05 -0.02 0.02 -0.11 -0.03 0.94 0.057 1.3
## Protein 0.19 -0.74 -0.01 0.05 0.16 0.12 -0.03 0.62 0.380 1.3
## VFR 0.48 0.65 0.07 0.16 0.34 -0.09 0.04 0.81 0.191 2.6
## BoneMass 0.88 0.06 0.05 0.07 0.04 -0.07 0.02 0.79 0.211 1.0
## MuscleMass 0.96 0.05 0.09 0.08 0.04 0.02 0.00 0.94 0.059 1.0
## Obesity -0.05 0.15 0.05 0.05 0.06 0.07 0.83 0.73 0.267 1.1
## TFC 0.11 0.95 -0.02 0.03 -0.01 0.12 0.03 0.93 0.065 1.1
## VFA 0.45 0.84 0.01 0.06 0.06 0.06 0.03 0.92 0.078 1.6
## VMA 0.88 0.04 0.09 0.10 0.04 0.07 -0.02 0.81 0.190 1.1
## Glucose 0.04 0.08 -0.08 0.73 0.14 -0.09 0.15 0.60 0.395 1.3
## HDL -0.41 0.09 0.01 -0.43 0.12 0.03 0.12 0.39 0.614 2.4
## Triglyceride 0.31 0.04 0.03 0.68 0.00 0.04 0.05 0.56 0.441 1.4
## AST 0.15 -0.03 0.94 -0.02 -0.04 -0.06 0.03 0.90 0.095 1.1
## ALT 0.25 -0.01 0.93 0.03 0.00 0.02 0.01 0.92 0.077 1.1
## ALP -0.10 0.14 0.23 0.49 0.09 0.23 -0.36 0.51 0.490 3.3
## Creatinine 0.49 -0.33 0.03 0.12 0.63 -0.06 0.04 0.77 0.227 2.6
## GFR 0.05 -0.07 0.05 -0.07 -0.92 -0.03 -0.02 0.86 0.139 1.0
## CRP -0.06 0.14 -0.06 -0.17 0.26 0.61 -0.27 0.57 0.432 2.2
## HGB 0.62 -0.25 0.15 0.25 0.09 -0.15 0.08 0.57 0.431 2.0
## VitaminD 0.01 -0.06 -0.01 -0.15 0.20 -0.75 -0.30 0.72 0.281 1.6
##
## RC1 RC2 RC3 RC5 RC4 RC6 RC7
## SS loadings 7.92 5.96 1.89 1.63 1.58 1.14 1.05
## Proportion Var 0.29 0.22 0.07 0.06 0.06 0.04 0.04
## Cumulative Var 0.29 0.51 0.58 0.64 0.70 0.75 0.78
## Proportion Explained 0.37 0.28 0.09 0.08 0.07 0.05 0.05
## Cumulative Proportion 0.37 0.66 0.74 0.82 0.90 0.95 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 7 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.03
## with the empirical chi square 226.72 with prob < 0.015
##
## Fit based upon off diagonal values = 0.99fa.diagram(fa_varimax$loadings,
cut = 0.40,
digits = 2,
sort = TRUE,
cex = 0.7) 