Modul 1 PCA & FA - Identifikasi Faktor Risiko Kesehatan Ibu Hamil

1. Persiapan Data

# Load Library
library(psych)
library(corrplot)

## corrplot 0.95 loaded

library(FactoMineR)
library(factoextra)

## Loading required package: ggplot2

## 
## Attaching package: 'ggplot2'

## The following objects are masked from 'package:psych':
## 
##     %+%, alpha

## Welcome to factoextra!

## Want to learn more? See two factoextra-related books at https://www.datanovia.com/en/product/practical-guide-to-principal-component-methods-in-r/

library(GPArotation)

## 
## Attaching package: 'GPArotation'

## The following objects are masked from 'package:psych':
## 
##     equamax, varimin

library(ggplot2)
library(tidyr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(Hmisc)

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:dplyr':
## 
##     src, summarize

## The following object is masked from 'package:psych':
## 
##     describe

## The following objects are masked from 'package:base':
## 
##     format.pval, units

library(sjPlot)

## 
## Attaching package: 'sjPlot'

## The following object is masked from 'package:ggplot2':
## 
##     set_theme

library(openxlsx)

# Import Dataset
data <- read.csv('D:/KULIYEAH/Semester 4/Analisis Multivariat/Dataset_Updated.csv')

cat("Dimensi data:", dim(data), "\n")

## Dimensi data: 1205 12

# Ambil variabel numerik
data_num <- data[, sapply(data, is.numeric)]

# Cek Struktur
str(data_num)

## 'data.frame':    1205 obs. of  11 variables:
##  $ Age                   : int  22 22 27 20 20 22 20 23 22 26 ...
##  $ Systolic.BP           : int  90 110 110 100 90 120 110 110 90 110 ...
##  $ Diastolic             : int  60 70 70 70 60 70 70 80 60 70 ...
##  $ BS                    : num  9 7.1 7.5 7.2 7.5 7.01 9 7 6.4 12 ...
##  $ Body.Temp             : int  100 98 98 98 98 98 102 98 98 100 ...
##  $ BMI                   : num  18 20.4 23 21.2 19.7 24 17.6 21.3 22 30.2 ...
##  $ Previous.Complications: int  1 0 1 0 0 0 0 0 0 1 ...
##  $ Preexisting.Diabetes  : int  1 0 0 0 0 0 1 0 0 1 ...
##  $ Gestational.Diabetes  : int  0 0 0 0 0 0 0 0 0 1 ...
##  $ Mental.Health         : int  1 0 0 0 0 0 0 0 0 1 ...
##  $ Heart.Rate            : int  80 74 72 74 74 76 78 74 72 80 ...

# Statistik Deskriptif 
summary(data_num)

##       Age          Systolic.BP      Diastolic            BS        
##  Min.   : 10.00   Min.   : 70.0   Min.   : 40.00   Min.   : 3.000  
##  1st Qu.: 21.00   1st Qu.:100.0   1st Qu.: 65.00   1st Qu.: 6.000  
##  Median : 25.00   Median :120.0   Median : 80.00   Median : 6.900  
##  Mean   : 27.73   Mean   :116.8   Mean   : 77.17   Mean   : 7.501  
##  3rd Qu.: 32.00   3rd Qu.:130.0   3rd Qu.: 90.00   3rd Qu.: 7.900  
##  Max.   :325.00   Max.   :200.0   Max.   :140.00   Max.   :19.000  
##                   NA's   :5       NA's   :4        NA's   :2       
##    Body.Temp          BMI        Previous.Complications Preexisting.Diabetes
##  Min.   : 97.0   Min.   : 0.00   Min.   :0.0000         Min.   :0.0000      
##  1st Qu.: 98.0   1st Qu.:20.45   1st Qu.:0.0000         1st Qu.:0.0000      
##  Median : 98.0   Median :23.00   Median :0.0000         Median :0.0000      
##  Mean   : 98.4   Mean   :23.32   Mean   :0.1754         Mean   :0.2884      
##  3rd Qu.: 98.0   3rd Qu.:25.00   3rd Qu.:0.0000         3rd Qu.:1.0000      
##  Max.   :103.0   Max.   :37.00   Max.   :1.0000         Max.   :1.0000      
##                  NA's   :18      NA's   :2              NA's   :2           
##  Gestational.Diabetes Mental.Health      Heart.Rate   
##  Min.   :0.0000       Min.   :0.0000   Min.   :58.00  
##  1st Qu.:0.0000       1st Qu.:0.0000   1st Qu.:70.00  
##  Median :0.0000       Median :0.0000   Median :76.00  
##  Mean   :0.1178       Mean   :0.3344   Mean   :75.82  
##  3rd Qu.:0.0000       3rd Qu.:1.0000   3rd Qu.:80.00  
##  Max.   :1.0000       Max.   :1.0000   Max.   :92.00  
##                                        NA's   :2

describe(data_num)

## data_num 
## 
##  11  Variables      1205  Observations
## --------------------------------------------------------------------------------
## Age 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       43    0.998    27.73     26.5    10.19       17 
##      .10      .25      .50      .75      .90      .95 
##       18       21       25       32       39       48 
## 
## lowest :  10  12  13  15  16, highest:  55  60  63  65 325
## --------------------------------------------------------------------------------
## Systolic.BP 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1200        5       24    0.964    116.8      115    20.67       90 
##      .10      .25      .50      .75      .90      .95 
##       90      100      120      130      140      140 
## 
## lowest :  70  75  76  78  80, highest: 150 160 170 180 200
## --------------------------------------------------------------------------------
## Diastolic 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1201        4       21    0.975    77.17     76.5    16.07       60 
##      .10      .25      .50      .75      .90      .95 
##       60       65       80       90      100      100 
## 
## lowest :  40  45  49  50  55, highest: 100 110 120 130 140
## --------------------------------------------------------------------------------
## BS 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1203        2       84    0.998    7.501     6.95    3.061      3.9 
##      .10      .25      .50      .75      .90      .95 
##      4.1      6.0      6.9      7.9     11.0     15.0 
## 
## lowest : 3    3.01 3.3  3.4  3.5 , highest: 15   16   17   18   19  
## --------------------------------------------------------------------------------
## Body.Temp 
##        n  missing distinct     Info     Mean  pMedian      Gmd 
##     1205        0        7    0.375     98.4       98   0.7403 
##                                                     
## Value         97    98    99   100   101   102   103
## Frequency     12  1030     7    41    66    43     6
## Proportion 0.010 0.855 0.006 0.034 0.055 0.036 0.005
## --------------------------------------------------------------------------------
## BMI 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1187       18      157    0.998    23.32       23    4.282    18.00 
##      .10      .25      .50      .75      .90      .95 
##    18.90    20.45    23.00    25.00    29.00    30.27 
## 
## lowest : 0    15   15.5 15.6 15.9, highest: 34.5 35   35.1 36   37  
## --------------------------------------------------------------------------------
## Previous.Complications 
##        n  missing distinct     Info      Sum     Mean 
##     1203        2        2    0.434      211   0.1754 
## 
## --------------------------------------------------------------------------------
## Preexisting.Diabetes 
##        n  missing distinct     Info      Sum     Mean 
##     1203        2        2    0.616      347   0.2884 
## 
## --------------------------------------------------------------------------------
## Gestational.Diabetes 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.312      142   0.1178 
## 
## --------------------------------------------------------------------------------
## Mental.Health 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.668      403   0.3344 
## 
## --------------------------------------------------------------------------------
## Heart.Rate 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1203        2       31     0.99    75.82       75    8.032       66 
##      .10      .25      .50      .75      .90      .95 
##       70       70       76       80       88       90 
## 
## lowest : 58 60 62 64 65, highest: 87 88 89 90 92
## --------------------------------------------------------------------------------

# Cek Missing Value
colSums(is.na(data_num))

##                    Age            Systolic.BP              Diastolic 
##                      0                      5                      4 
##                     BS              Body.Temp                    BMI 
##                      2                      0                     18 
## Previous.Complications   Preexisting.Diabetes   Gestational.Diabetes 
##                      2                      2                      0 
##          Mental.Health             Heart.Rate 
##                      0                      2

# Handling Missing Value
data_num1 <- data.frame(lapply(data_num, function(x) {
  x[is.na(x)] <- median(x, na.rm = TRUE)
  return(x)
}))

# Cek Missing Value Setelah Handling
colSums(is.na(data_num1))

##                    Age            Systolic.BP              Diastolic 
##                      0                      0                      0 
##                     BS              Body.Temp                    BMI 
##                      0                      0                      0 
## Previous.Complications   Preexisting.Diabetes   Gestational.Diabetes 
##                      0                      0                      0 
##          Mental.Health             Heart.Rate 
##                      0                      0

summary(data_num1)

##       Age          Systolic.BP      Diastolic            BS      
##  Min.   : 10.00   Min.   : 70.0   Min.   : 40.00   Min.   : 3.0  
##  1st Qu.: 21.00   1st Qu.:100.0   1st Qu.: 65.00   1st Qu.: 6.0  
##  Median : 25.00   Median :120.0   Median : 80.00   Median : 6.9  
##  Mean   : 27.73   Mean   :116.8   Mean   : 77.18   Mean   : 7.5  
##  3rd Qu.: 32.00   3rd Qu.:130.0   3rd Qu.: 90.00   3rd Qu.: 7.9  
##  Max.   :325.00   Max.   :200.0   Max.   :140.00   Max.   :19.0  
##    Body.Temp          BMI        Previous.Complications Preexisting.Diabetes
##  Min.   : 97.0   Min.   : 0.00   Min.   :0.0000         Min.   :0.000       
##  1st Qu.: 98.0   1st Qu.:21.00   1st Qu.:0.0000         1st Qu.:0.000       
##  Median : 98.0   Median :23.00   Median :0.0000         Median :0.000       
##  Mean   : 98.4   Mean   :23.31   Mean   :0.1751         Mean   :0.288       
##  3rd Qu.: 98.0   3rd Qu.:25.00   3rd Qu.:0.0000         3rd Qu.:1.000       
##  Max.   :103.0   Max.   :37.00   Max.   :1.0000         Max.   :1.000       
##  Gestational.Diabetes Mental.Health      Heart.Rate   
##  Min.   :0.0000       Min.   :0.0000   Min.   :58.00  
##  1st Qu.:0.0000       1st Qu.:0.0000   1st Qu.:70.00  
##  Median :0.0000       Median :0.0000   Median :76.00  
##  Mean   :0.1178       Mean   :0.3344   Mean   :75.82  
##  3rd Qu.:0.0000       3rd Qu.:1.0000   3rd Qu.:80.00  
##  Max.   :1.0000       Max.   :1.0000   Max.   :92.00

describe(data_num1)

## data_num1 
## 
##  11  Variables      1205  Observations
## --------------------------------------------------------------------------------
## Age 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       43    0.998    27.73     26.5    10.19       17 
##      .10      .25      .50      .75      .90      .95 
##       18       21       25       32       39       48 
## 
## lowest :  10  12  13  15  16, highest:  55  60  63  65 325
## --------------------------------------------------------------------------------
## Systolic.BP 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       24    0.964    116.8      115    20.62       90 
##      .10      .25      .50      .75      .90      .95 
##       90      100      120      130      140      140 
## 
## lowest :  70  75  76  78  80, highest: 150 160 170 180 200
## --------------------------------------------------------------------------------
## Diastolic 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       21    0.975    77.18     76.5    16.04       60 
##      .10      .25      .50      .75      .90      .95 
##       60       65       80       90      100      100 
## 
## lowest :  40  45  49  50  55, highest: 100 110 120 130 140
## --------------------------------------------------------------------------------
## BS 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       84    0.998      7.5     6.95    3.057      3.9 
##      .10      .25      .50      .75      .90      .95 
##      4.1      6.0      6.9      7.9     11.0     15.0 
## 
## lowest : 3    3.01 3.3  3.4  3.5 , highest: 15   16   17   18   19  
## --------------------------------------------------------------------------------
## Body.Temp 
##        n  missing distinct     Info     Mean  pMedian      Gmd 
##     1205        0        7    0.375     98.4       98   0.7403 
##                                                     
## Value         97    98    99   100   101   102   103
## Frequency     12  1030     7    41    66    43     6
## Proportion 0.010 0.855 0.006 0.034 0.055 0.036 0.005
## --------------------------------------------------------------------------------
## BMI 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0      157    0.997    23.31       23    4.243    18.00 
##      .10      .25      .50      .75      .90      .95 
##    18.90    21.00    23.00    25.00    28.96    30.20 
## 
## lowest : 0    15   15.5 15.6 15.9, highest: 34.5 35   35.1 36   37  
## --------------------------------------------------------------------------------
## Previous.Complications 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.433      211   0.1751 
## 
## --------------------------------------------------------------------------------
## Preexisting.Diabetes 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.615      347    0.288 
## 
## --------------------------------------------------------------------------------
## Gestational.Diabetes 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.312      142   0.1178 
## 
## --------------------------------------------------------------------------------
## Mental.Health 
##        n  missing distinct     Info      Sum     Mean 
##     1205        0        2    0.668      403   0.3344 
## 
## --------------------------------------------------------------------------------
## Heart.Rate 
##        n  missing distinct     Info     Mean  pMedian      Gmd      .05 
##     1205        0       31     0.99    75.82       75    8.025       66 
##      .10      .25      .50      .75      .90      .95 
##       70       70       76       80       88       90 
## 
## lowest : 58 60 62 64 65, highest: 87 88 89 90 92
## --------------------------------------------------------------------------------

desc <- describe(data_num1)

# Simpan dalam Bentuk Tabel
desc_table <- data.frame(
  Variable = rownames(desc),
  Mean = round(as.numeric(desc$mean), 3),
  Median = round(as.numeric(desc$median), 3),
  SD = round(as.numeric(desc$sd), 3),
  Min = as.numeric(desc$min),
  Max = as.numeric(desc$max)
)

write.xlsx(desc_table, "tabel_deskriptif.xlsx", rowNames = FALSE)

# Plot Distribusi Tiap Variabel
data_long <- stack(data_num1)

ggplot(data_long, aes(x = values)) +
  geom_histogram(bins = 30, fill = "skyblue", color = "black") +
  facet_wrap(~ ind, scales = "free") +
  theme_minimal()

data_long <- data_num1 %>%
  pivot_longer(cols = everything(),
               names_to = "Variable",
               values_to = "Value")

ggplot(data_long, aes(x = Variable, y = Value)) +
  geom_boxplot(fill = "#69b3a2", alpha = 0.7) +
  theme_minimal(base_size = 12) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  labs(title = "Boxplot Seluruh Variabel Numerik",
       x = "Variabel",
       y = "Nilai")

# Standarisasi Skala
data_scaled <- scale(data_num1)

data_scaled_long <- as.data.frame(data_scaled) %>%
  pivot_longer(cols = everything(),
               names_to = "Variable",
               values_to = "Value")

ggplot(data_scaled_long, aes(x = Variable, y = Value)) +
  geom_boxplot(fill = "#E69F00", alpha = 0.7) +
  theme_minimal(base_size = 12) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  labs(title = "Boxplot Setelah Standarisasi",
       y = "Z-Score")

2. Uji Asumsi

2a. Uji Korelasi

cor_matrix <- cor(data_num1, method = "pearson")
cor_matrix

##                                Age Systolic.BP  Diastolic        BS   Body.Temp
## Age                     1.00000000   0.1598061  0.1558714 0.4306982 -0.08900263
## Systolic.BP             0.15980605   1.0000000  0.7931054 0.3420373 -0.17810105
## Diastolic               0.15587136   0.7931054  1.0000000 0.3613747 -0.11861485
## BS                      0.43069816   0.3420373  0.3613747 1.0000000  0.08005480
## Body.Temp              -0.08900263  -0.1781011 -0.1186149 0.0800548  1.00000000
## BMI                     0.23519153   0.2850881  0.2707933 0.4913860  0.02153467
## Previous.Complications  0.14276178   0.1331392  0.1822971 0.4221103  0.11335281
## Preexisting.Diabetes    0.17749855   0.1649305  0.1929384 0.5487575  0.06846207
## Gestational.Diabetes   -0.04996601   0.1378353  0.1570357 0.1129843  0.15565044
## Mental.Health           0.07657281   0.1844298  0.1954217 0.3812072  0.13496110
## Heart.Rate              0.06289193   0.1562080  0.1667512 0.2981745  0.09797216
##                               BMI Previous.Complications Preexisting.Diabetes
## Age                    0.23519153              0.1427618           0.17749855
## Systolic.BP            0.28508814              0.1331392           0.16493053
## Diastolic              0.27079328              0.1822971           0.19293842
## BS                     0.49138603              0.4221103           0.54875755
## Body.Temp              0.02153467              0.1133528           0.06846207
## BMI                    1.00000000              0.3696315           0.29121565
## Previous.Complications 0.36963145              1.0000000           0.36763890
## Preexisting.Diabetes   0.29121565              0.3676389           1.00000000
## Gestational.Diabetes   0.31234936              0.2108601          -0.04485550
## Mental.Health          0.32081732              0.4509411           0.43098666
## Heart.Rate             0.21483602              0.2769475           0.37382313
##                        Gestational.Diabetes Mental.Health Heart.Rate
## Age                             -0.04996601    0.07657281 0.06289193
## Systolic.BP                      0.13783532    0.18442979 0.15620798
## Diastolic                        0.15703567    0.19542169 0.16675118
## BS                               0.11298426    0.38120718 0.29817446
## Body.Temp                        0.15565044    0.13496110 0.09797216
## BMI                              0.31234936    0.32081732 0.21483602
## Previous.Complications           0.21086012    0.45094115 0.27694750
## Preexisting.Diabetes            -0.04485550    0.43098666 0.37382313
## Gestational.Diabetes             1.00000000    0.24282292 0.18717567
## Mental.Health                    0.24282292    1.00000000 0.32594303
## Heart.Rate                       0.18717567    0.32594303 1.00000000

cor_test <- rcorr(as.matrix(data_num1))

cor_test$r

##                                Age Systolic.BP  Diastolic        BS   Body.Temp
## Age                     1.00000000   0.1598061  0.1558714 0.4306982 -0.08900263
## Systolic.BP             0.15980605   1.0000000  0.7931054 0.3420373 -0.17810105
## Diastolic               0.15587136   0.7931054  1.0000000 0.3613747 -0.11861485
## BS                      0.43069816   0.3420373  0.3613747 1.0000000  0.08005480
## Body.Temp              -0.08900263  -0.1781011 -0.1186149 0.0800548  1.00000000
## BMI                     0.23519153   0.2850881  0.2707933 0.4913860  0.02153467
## Previous.Complications  0.14276178   0.1331392  0.1822971 0.4221103  0.11335281
## Preexisting.Diabetes    0.17749855   0.1649305  0.1929384 0.5487575  0.06846207
## Gestational.Diabetes   -0.04996601   0.1378353  0.1570357 0.1129843  0.15565044
## Mental.Health           0.07657281   0.1844298  0.1954217 0.3812072  0.13496110
## Heart.Rate              0.06289193   0.1562080  0.1667512 0.2981745  0.09797216
##                               BMI Previous.Complications Preexisting.Diabetes
## Age                    0.23519153              0.1427618           0.17749855
## Systolic.BP            0.28508814              0.1331392           0.16493053
## Diastolic              0.27079328              0.1822971           0.19293842
## BS                     0.49138603              0.4221103           0.54875755
## Body.Temp              0.02153467              0.1133528           0.06846207
## BMI                    1.00000000              0.3696315           0.29121565
## Previous.Complications 0.36963145              1.0000000           0.36763890
## Preexisting.Diabetes   0.29121565              0.3676389           1.00000000
## Gestational.Diabetes   0.31234936              0.2108601          -0.04485550
## Mental.Health          0.32081732              0.4509411           0.43098666
## Heart.Rate             0.21483602              0.2769475           0.37382313
##                        Gestational.Diabetes Mental.Health Heart.Rate
## Age                             -0.04996601    0.07657281 0.06289193
## Systolic.BP                      0.13783532    0.18442979 0.15620798
## Diastolic                        0.15703567    0.19542169 0.16675118
## BS                               0.11298426    0.38120718 0.29817446
## Body.Temp                        0.15565044    0.13496110 0.09797216
## BMI                              0.31234936    0.32081732 0.21483602
## Previous.Complications           0.21086012    0.45094115 0.27694750
## Preexisting.Diabetes            -0.04485550    0.43098666 0.37382313
## Gestational.Diabetes             1.00000000    0.24282292 0.18717567
## Mental.Health                    0.24282292    1.00000000 0.32594303
## Heart.Rate                       0.18717567    0.32594303 1.00000000

cor_test$P

##                                 Age  Systolic.BP    Diastolic           BS
## Age                              NA 2.440158e-08 5.375017e-08 0.0000000000
## Systolic.BP            2.440158e-08           NA 0.000000e+00 0.0000000000
## Diastolic              5.375017e-08 0.000000e+00           NA 0.0000000000
## BS                     0.000000e+00 0.000000e+00 0.000000e+00           NA
## Body.Temp              1.984847e-03 4.789085e-10 3.662551e-05 0.0054270170
## BMI                    0.000000e+00 0.000000e+00 0.000000e+00 0.0000000000
## Previous.Complications 6.488799e-07 3.525848e-06 1.829386e-10 0.0000000000
## Preexisting.Diabetes   5.488454e-10 8.471870e-09 1.437250e-11 0.0000000000
## Gestational.Diabetes   8.296097e-02 1.565660e-06 4.263626e-08 0.0000847495
## Mental.Health          7.832021e-03 1.111871e-10 7.769785e-12 0.0000000000
## Heart.Rate             2.903066e-02 5.027717e-08 5.771037e-09 0.0000000000
##                           Body.Temp          BMI Previous.Complications
## Age                    1.984847e-03 0.000000e+00           6.488799e-07
## Systolic.BP            4.789085e-10 0.000000e+00           3.525848e-06
## Diastolic              3.662551e-05 0.000000e+00           1.829386e-10
## BS                     5.427017e-03 0.000000e+00           0.000000e+00
## Body.Temp                        NA 4.551563e-01           8.031419e-05
## BMI                    4.551563e-01           NA           0.000000e+00
## Previous.Complications 8.031419e-05 0.000000e+00                     NA
## Preexisting.Diabetes   1.746100e-02 0.000000e+00           0.000000e+00
## Gestational.Diabetes   5.615451e-08 0.000000e+00           1.412204e-13
## Mental.Health          2.581523e-06 0.000000e+00           0.000000e+00
## Heart.Rate             6.602262e-04 4.773959e-14           0.000000e+00
##                        Preexisting.Diabetes Gestational.Diabetes Mental.Health
## Age                            5.488454e-10         8.296097e-02  7.832021e-03
## Systolic.BP                    8.471870e-09         1.565660e-06  1.111871e-10
## Diastolic                      1.437250e-11         4.263626e-08  7.769785e-12
## BS                             0.000000e+00         8.474950e-05  0.000000e+00
## Body.Temp                      1.746100e-02         5.615451e-08  2.581523e-06
## BMI                            0.000000e+00         0.000000e+00  0.000000e+00
## Previous.Complications         0.000000e+00         1.412204e-13  0.000000e+00
## Preexisting.Diabetes                     NA         1.196508e-01  0.000000e+00
## Gestational.Diabetes           1.196508e-01                   NA  0.000000e+00
## Mental.Health                  0.000000e+00         0.000000e+00            NA
## Heart.Rate                     0.000000e+00         5.805356e-11  0.000000e+00
##                          Heart.Rate
## Age                    2.903066e-02
## Systolic.BP            5.027717e-08
## Diastolic              5.771037e-09
## BS                     0.000000e+00
## Body.Temp              6.602262e-04
## BMI                    4.773959e-14
## Previous.Complications 0.000000e+00
## Preexisting.Diabetes   0.000000e+00
## Gestational.Diabetes   5.805356e-11
## Mental.Health          0.000000e+00
## Heart.Rate                       NA

corrplot(cor_test$r,
         method = "square", 
         type = "full",
         addCoef.col = "black", 
         number.cex = 0.3,
         tl.col = "black",
         tl.cex = 0.6, 
         tl.srt = 45)

tab_corr(data_num1, digits = 3, file = "tabel_korelasi.doc")

	Age	Systolic.BP	Diastolic	BS	Body.Temp	BMI	Previous.Complications	Preexisting.Diabetes	Gestational.Diabetes	Mental.Health	Heart.Rate
Age		0.160***	0.156***	0.431***	-0.089**	0.235***	0.143***	0.177***	-0.050	0.077**	0.063*
Systolic.BP	0.160***		0.793***	0.342***	-0.178***	0.285***	0.133***	0.165***	0.138***	0.184***	0.156***
Diastolic	0.156***	0.793***		0.361***	-0.119***	0.271***	0.182***	0.193***	0.157***	0.195***	0.167***
BS	0.431***	0.342***	0.361***		0.080**	0.491***	0.422***	0.549***	0.113***	0.381***	0.298***
Body.Temp	-0.089**	-0.178***	-0.119***	0.080**		0.022	0.113***	0.068*	0.156***	0.135***	0.098***
BMI	0.235***	0.285***	0.271***	0.491***	0.022		0.370***	0.291***	0.312***	0.321***	0.215***
Previous.Complications	0.143***	0.133***	0.182***	0.422***	0.113***	0.370***		0.368***	0.211***	0.451***	0.277***
Preexisting.Diabetes	0.177***	0.165***	0.193***	0.549***	0.068*	0.291***	0.368***		-0.045	0.431***	0.374***
Gestational.Diabetes	-0.050	0.138***	0.157***	0.113***	0.156***	0.312***	0.211***	-0.045		0.243***	0.187***
Mental.Health	0.077**	0.184***	0.195***	0.381***	0.135***	0.321***	0.451***	0.431***	0.243***		0.326***
Heart.Rate	0.063*	0.156***	0.167***	0.298***	0.098***	0.215***	0.277***	0.374***	0.187***	0.326***
Computed correlation used pearson-method with listwise-deletion.

2b. Uji Bartlett

cor_matrix <- cor(data_num1)

bartlett_test <- cortest.bartlett(cor_matrix, n = nrow(data_num1))

bartlett_test

## $chisq
## [1] 3861.738
## 
## $p.value
## [1] 0
## 
## $df
## [1] 55

2c. Uji MSA

cor_matrix <- cor(data_num1)

kmo_result <- KMO(cor_matrix)

kmo_result

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cor_matrix)
## Overall MSA =  0.74
## MSA for each item = 
##                    Age            Systolic.BP              Diastolic 
##                   0.68                   0.62                   0.64 
##                     BS              Body.Temp                    BMI 
##                   0.78                   0.62                   0.84 
## Previous.Complications   Preexisting.Diabetes   Gestational.Diabetes 
##                   0.87                   0.75                   0.61 
##          Mental.Health             Heart.Rate 
##                   0.84                   0.86

3. Principal Component Analysis (PCA)

3a. Total Variance Explained

# 1. PCA tanpa rotasi
pca_result <- prcomp(data_num1, scale. = TRUE)

# Eigenvalue
eigenvalues <- pca_result$sdev^2

# Proporsi Varians
prop_var <- eigenvalues / sum(eigenvalues)

# Kumulatif Varians
cum_var <- cumsum(prop_var)

# Buat tabel Total Variance Explained
total_variance <- data.frame(
  Component = 1:length(eigenvalues),
  Eigenvalue = eigenvalues,
  Proportion_Variance = prop_var,
  Cumulative_Variance = cum_var
)

round(total_variance, 4)

##    Component Eigenvalue Proportion_Variance Cumulative_Variance
## 1          1     3.4778              0.3162              0.3162
## 2          2     1.6141              0.1467              0.4629
## 3          3     1.2551              0.1141              0.5770
## 4          4     0.9735              0.0885              0.6655
## 5          5     0.8201              0.0746              0.7401
## 6          6     0.7345              0.0668              0.8068
## 7          7     0.6005              0.0546              0.8614
## 8          8     0.5484              0.0499              0.9113
## 9          9     0.4517              0.0411              0.9523
## 10        10     0.3227              0.0293              0.9817
## 11        11     0.2016              0.0183              1.0000

total_variance$Proportion_Variance <- total_variance$Proportion_Variance * 100
total_variance$Cumulative_Variance <- total_variance$Cumulative_Variance * 100

round(total_variance, 2)

##    Component Eigenvalue Proportion_Variance Cumulative_Variance
## 1          1       3.48               31.62               31.62
## 2          2       1.61               14.67               46.29
## 3          3       1.26               11.41               57.70
## 4          4       0.97                8.85               66.55
## 5          5       0.82                7.46               74.01
## 6          6       0.73                6.68               80.68
## 7          7       0.60                5.46               86.14
## 8          8       0.55                4.99               91.13
## 9          9       0.45                4.11               95.23
## 10        10       0.32                2.93               98.17
## 11        11       0.20                1.83              100.00

# 2. PCA
pca_result <- prcomp(data_num1, scale. = TRUE)

# Hitung eigenvalue
eigenvalues <- pca_result$sdev^2

# Hitung persen varians
percent_var <- eigenvalues / sum(eigenvalues) * 100

# Hitung kumulatif
cumulative_var <- cumsum(percent_var)

# Buat tabel seperti SPSS
total_variance <- data.frame(
  Komponen = 1:length(eigenvalues),
  Total = round(eigenvalues, 2),
  `Persen Varians` = round(percent_var, 2),
  `Kumulatif %` = round(cumulative_var, 2)
)

total_variance

##    Komponen Total Persen.Varians Kumulatif..
## 1         1  3.48          31.62       31.62
## 2         2  1.61          14.67       46.29
## 3         3  1.26          11.41       57.70
## 4         4  0.97           8.85       66.55
## 5         5  0.82           7.46       74.01
## 6         6  0.73           6.68       80.68
## 7         7  0.60           5.46       86.14
## 8         8  0.55           4.99       91.13
## 9         9  0.45           4.11       95.23
## 10       10  0.32           2.93       98.17
## 11       11  0.20           1.83      100.00

3b. Scree Plot

# Hitung eigenvalue
eigenvalues <- pca_result$sdev^2

plot(eigenvalues,
     type = "b",
     pch = 19,
     xlab = "Komponen",
     ylab = "Eigenvalue",
     main = "Scree Plot PCA",
     ylim = c(0, max(eigenvalues)))

abline(h = 1, col = "red", lty = 2, lwd = 2)

3c. Communalities

# Tentukan jumlah komponen (eigenvalue > 1)
eigenvalues <- pca_result$sdev^2
k <- sum(eigenvalues > 1)

# Jalankan PCA lagi dengan k komponen
pca_k <- prcomp(data_num1, scale. = TRUE)

# Ambil loading
loadings <- pca_k$rotation[, 1:k]

# Hitung communalities (jumlah kuadrat loading)
communalities <- rowSums(loadings^2)

# Buat tabel
communalities_table <- data.frame(
  Variabel = rownames(loadings),
  Initial = 1,
  Extraction = round(communalities, 3)
)

communalities_table

##                                      Variabel Initial Extraction
## Age                                       Age       1      0.312
## Systolic.BP                       Systolic.BP       1      0.423
## Diastolic                           Diastolic       1      0.397
## BS                                         BS       1      0.251
## Body.Temp                           Body.Temp       1      0.259
## BMI                                       BMI       1      0.132
## Previous.Complications Previous.Complications       1      0.178
## Preexisting.Diabetes     Preexisting.Diabetes       1      0.272
## Gestational.Diabetes     Gestational.Diabetes       1      0.457
## Mental.Health                   Mental.Health       1      0.194
## Heart.Rate                         Heart.Rate       1      0.124

# Tentukan jumlah komponen
eigenvalues <- pca_result$sdev^2
k <- sum(eigenvalues > 1)

# Jalankan PCA dengan psych agar lebih mudah
library(psych)

pca_psych <- principal(data_num1, nfactors = k, rotate = "none")

# Ambil communalities (Extraction)
communalities <- pca_psych$communality

# Buat tabel seperti di gambar
comm_table <- data.frame(
  Variabel = names(communalities),
  Extraction = round(communalities, 6)
)

comm_table

##                                      Variabel Extraction
## Age                                       Age   0.493461
## Systolic.BP                       Systolic.BP   0.838861
## Diastolic                           Diastolic   0.809065
## BS                                         BS   0.713695
## Body.Temp                           Body.Temp   0.406529
## BMI                                       BMI   0.446322
## Previous.Complications Previous.Complications   0.500155
## Preexisting.Diabetes     Preexisting.Diabetes   0.616487
## Gestational.Diabetes     Gestational.Diabetes   0.650558
## Mental.Health                   Mental.Health   0.529467
## Heart.Rate                         Heart.Rate   0.342479

3d. Pengelompokan faktor-faktor utama

# Tentukan jumlah komponen (misal eigenvalue > 1)
ev <- eigen(cor(data_num1))$values
k <- sum(ev > 1)

# Jalankan PCA dengan rotasi varimax
pca_rot <- principal(data_num1,
                     nfactors = k,
                     rotate = "varimax",
                     scores = TRUE)

# Lihat hasil loading
print(pca_rot$loadings)

## 
## Loadings:
##                        RC1    RC2    RC3   
## Age                     0.301  0.179 -0.609
## Systolic.BP             0.149  0.904       
## Diastolic               0.191  0.879       
## BS                      0.731  0.280 -0.318
## Body.Temp               0.317 -0.384  0.398
## BMI                     0.580  0.326       
## Previous.Complications  0.702              
## Preexisting.Diabetes    0.716        -0.321
## Gestational.Diabetes    0.287  0.236  0.716
## Mental.Health           0.705         0.168
## Heart.Rate              0.569         0.124
## 
##                  RC1   RC2   RC3
## SS loadings    3.029 2.018 1.300
## Proportion Var 0.275 0.183 0.118
## Cumulative Var 0.275 0.459 0.577

loadings_matrix <- as.data.frame(unclass(pca_rot$loadings))

round(loadings_matrix, 3)

##                          RC1    RC2    RC3
## Age                    0.301  0.179 -0.609
## Systolic.BP            0.149  0.904 -0.017
## Diastolic              0.191  0.879  0.009
## BS                     0.731  0.280 -0.318
## Body.Temp              0.317 -0.384  0.398
## BMI                    0.580  0.326  0.058
## Previous.Complications 0.702  0.043  0.075
## Preexisting.Diabetes   0.716  0.002 -0.321
## Gestational.Diabetes   0.287  0.236  0.716
## Mental.Health          0.705  0.065  0.168
## Heart.Rate             0.569  0.053  0.124

# Ambil loading absolut terbesar tiap variabel
grouping <- apply(abs(loadings_matrix), 1, which.max)

# Buat tabel pengelompokan
hasil_kelompok <- data.frame(
  Variabel = rownames(loadings_matrix),
  Komponen_Dominan = paste0("Komponen ", grouping)
)

hasil_kelompok

##                  Variabel Komponen_Dominan
## 1                     Age       Komponen 3
## 2             Systolic.BP       Komponen 2
## 3               Diastolic       Komponen 2
## 4                      BS       Komponen 1
## 5               Body.Temp       Komponen 3
## 6                     BMI       Komponen 1
## 7  Previous.Complications       Komponen 1
## 8    Preexisting.Diabetes       Komponen 1
## 9    Gestational.Diabetes       Komponen 3
## 10          Mental.Health       Komponen 1
## 11             Heart.Rate       Komponen 1

# Ambil rotated loadings
loadings_matrix <- as.data.frame(unclass(pca_rot$loadings))

# Bulatkan
loadings_matrix <- round(loadings_matrix, 3)

# Ganti nama kolom sesuai jumlah komponen
colnames(loadings_matrix) <- paste0("Komponen ", 1:ncol(loadings_matrix))

# Tambahkan nama variabel sebagai kolom
loadings_matrix$Variabel <- rownames(loadings_matrix)

# Pindahkan kolom Variabel ke depan
loadings_matrix <- loadings_matrix[, c("Variabel", paste0("Komponen ", 1:ncol(pca_rot$loadings)))]

loadings_matrix

##                                      Variabel Komponen 1 Komponen 2 Komponen 3
## Age                                       Age      0.301      0.179     -0.609
## Systolic.BP                       Systolic.BP      0.149      0.904     -0.017
## Diastolic                           Diastolic      0.191      0.879      0.009
## BS                                         BS      0.731      0.280     -0.318
## Body.Temp                           Body.Temp      0.317     -0.384      0.398
## BMI                                       BMI      0.580      0.326      0.058
## Previous.Complications Previous.Complications      0.702      0.043      0.075
## Preexisting.Diabetes     Preexisting.Diabetes      0.716      0.002     -0.321
## Gestational.Diabetes     Gestational.Diabetes      0.287      0.236      0.716
## Mental.Health                   Mental.Health      0.705      0.065      0.168
## Heart.Rate                         Heart.Rate      0.569      0.053      0.124

dominant <- apply(abs(loadings_matrix[, -1]), 1, which.max)

loadings_matrix$Dominan <- paste0("Komponen ", dominant)

loadings_matrix

##                                      Variabel Komponen 1 Komponen 2 Komponen 3
## Age                                       Age      0.301      0.179     -0.609
## Systolic.BP                       Systolic.BP      0.149      0.904     -0.017
## Diastolic                           Diastolic      0.191      0.879      0.009
## BS                                         BS      0.731      0.280     -0.318
## Body.Temp                           Body.Temp      0.317     -0.384      0.398
## BMI                                       BMI      0.580      0.326      0.058
## Previous.Complications Previous.Complications      0.702      0.043      0.075
## Preexisting.Diabetes     Preexisting.Diabetes      0.716      0.002     -0.321
## Gestational.Diabetes     Gestational.Diabetes      0.287      0.236      0.716
## Mental.Health                   Mental.Health      0.705      0.065      0.168
## Heart.Rate                         Heart.Rate      0.569      0.053      0.124
##                           Dominan
## Age                    Komponen 3
## Systolic.BP            Komponen 2
## Diastolic              Komponen 2
## BS                     Komponen 1
## Body.Temp              Komponen 3
## BMI                    Komponen 1
## Previous.Complications Komponen 1
## Preexisting.Diabetes   Komponen 1
## Gestational.Diabetes   Komponen 3
## Mental.Health          Komponen 1
## Heart.Rate             Komponen 1

3e. Komponen transformasi matriks

pca_result <- principal(data_num1,
                        nfactors = 3,
                        rotate = "varimax")
# Menampilkan matriks transformasi komponen
pca_result$rot.mat

##            [,1]       [,2]        [,3]
## [1,]  0.8728880 -0.4853979 -0.04955209
## [2,]  0.4728276  0.8164489  0.33142911
## [3,] -0.1204182 -0.3127301  0.94217797

round(pca_result$rot.mat, 3)

##        [,1]   [,2]   [,3]
## [1,]  0.873 -0.485 -0.050
## [2,]  0.473  0.816  0.331
## [3,] -0.120 -0.313  0.942

round(t(pca_result$rot.mat) %*% pca_result$rot.mat, 3)

##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

4. Factor Analysis (FA)

4a. Estimasi Faktor Matriks

# 1. Hitung Eigen Value
df2 <- data_scaled
cor_matrix <- cor(df2)
eigen_result <- eigen(cor_matrix)
eigenvalues  <- eigen_result$values
print(eigenvalues)

##  [1] 3.4778297 1.6141165 1.2551309 0.9734905 0.8200721 0.7344577 0.6005218
##  [8] 0.5484470 0.4516542 0.3226874 0.2015922

eigen <- data.frame(
  Eigenvalue   = round(eigenvalues, 3),
  Proporsi_Var = round(eigenvalues / sum(eigenvalues) * 100, 2),
  Kumulatif    = round(cumsum(eigenvalues / sum(eigenvalues)) * 100, 2)
)
print(eigen)

##    Eigenvalue Proporsi_Var Kumulatif
## 1       3.478        31.62     31.62
## 2       1.614        14.67     46.29
## 3       1.255        11.41     57.70
## 4       0.973         8.85     66.55
## 5       0.820         7.46     74.01
## 6       0.734         6.68     80.68
## 7       0.601         5.46     86.14
## 8       0.548         4.99     91.13
## 9       0.452         4.11     95.23
## 10      0.323         2.93     98.17
## 11      0.202         1.83    100.00

# 2. FA tanpa rotasi
n_factors <- sum(eigenvalues > 1)
fa_unrotated <- fa(df2, 
                   nfactors = n_factors, 
                   rotate   = "none", 
                   fm       = "pa",   
                   use      = "complete.obs")
print(fa_unrotated$loadings, cutoff = 0.1)

## 
## Loadings:
##                        PA1    PA2    PA3   
## Age                     0.320        -0.318
## Systolic.BP             0.628 -0.699       
## Diastolic               0.611 -0.561       
## BS                      0.775  0.161 -0.294
## Body.Temp                      0.301  0.184
## BMI                     0.575              
## Previous.Complications  0.546  0.296       
## Preexisting.Diabetes    0.578  0.285 -0.255
## Gestational.Diabetes    0.285         0.558
## Mental.Health           0.560  0.289  0.161
## Heart.Rate              0.424  0.192       
## 
##                  PA1   PA2   PA3
## SS loadings    3.009 1.225 0.656
## Proportion Var 0.274 0.111 0.060
## Cumulative Var 0.274 0.385 0.445

cat("\n>> Jumlah faktor dengan eigenvalue > 1:", n_factors, "\n")

## 
## >> Jumlah faktor dengan eigenvalue > 1: 3

4b. Communality

commun <- data.frame(Communality = round(fa_unrotated$communality, 3))
print(commun)

##                        Communality
## Age                          0.203
## Systolic.BP                  0.887
## Diastolic                    0.692
## BS                           0.713
## Body.Temp                    0.126
## BMI                          0.347
## Previous.Complications       0.395
## Preexisting.Diabetes         0.480
## Gestational.Diabetes         0.399
## Mental.Health                0.423
## Heart.Rate                   0.225

4c. Factor Rotation

varimax <- fa(df2, 
                 nfactors = n_factors, 
                 rotate   = "varimax", 
                 fm       = "pa",
                 use      = "complete.obs")

4d. Interpretasi & Respecifikasi

# 1. Communality
print(varimax$loadings, cutoff = 0.4)

## 
## Loadings:
##                        PA1    PA2    PA3   
## Age                     0.404              
## Systolic.BP                    0.923       
## Diastolic                      0.796       
## BS                      0.807              
## Body.Temp                                  
## BMI                     0.434              
## Previous.Complications  0.485              
## Preexisting.Diabetes    0.684              
## Gestational.Diabetes                  0.615
## Mental.Health           0.459         0.457
## Heart.Rate                                 
## 
##                  PA1   PA2   PA3
## SS loadings    2.128 1.674 1.089
## Proportion Var 0.193 0.152 0.099
## Cumulative Var 0.193 0.346 0.445

commun_varimax <- data.frame(
  Variabel    = names(varimax$communality),
  Communality = round(varimax$communality, 3)
)
print(commun_varimax)

##                                      Variabel Communality
## Age                                       Age       0.203
## Systolic.BP                       Systolic.BP       0.887
## Diastolic                           Diastolic       0.692
## BS                                         BS       0.713
## Body.Temp                           Body.Temp       0.126
## BMI                                       BMI       0.347
## Previous.Complications Previous.Complications       0.395
## Preexisting.Diabetes     Preexisting.Diabetes       0.480
## Gestational.Diabetes     Gestational.Diabetes       0.399
## Mental.Health                   Mental.Health       0.423
## Heart.Rate                         Heart.Rate       0.225

# 2. Variance
load_varimax <- as.matrix(varimax$loadings)
var_varimax <- data.frame(
  Faktor       = colnames(load_varimax),
  SS_Loadings  = round(colSums(load_varimax^2), 3),
  Proporsi_Var = round(colSums(load_varimax^2) / ncol(df2) * 100, 2),
  Kumulatif    = round(cumsum(colSums(load_varimax^2) / ncol(df2)) * 100, 2)
)
print(var_varimax)

##     Faktor SS_Loadings Proporsi_Var Kumulatif
## PA1    PA1       2.128        19.34     19.34
## PA2    PA2       1.674        15.22     34.56
## PA3    PA3       1.089         9.90     44.46

# 3. Cross loading
for (i in 1:nrow(load_varimax)) {
  sig_idx <- which(abs(load_varimax[i, ]) >= 0.40)
  if (length(sig_idx) > 1) {
    vals <- sort(abs(load_varimax[i, sig_idx]), decreasing = TRUE)
    ratio <- vals[1]^2 / vals[2]^2
    if (ratio <= 1.5) {
      status <- "kuat"
    } else if (ratio <= 2.0) {
      status <- "sedang"
    } else {
      status <- "lemah"
    }
    cat(sprintf("%-25s | %.3f vs %.3f | Ratio: %.2f | %s\n",
                rownames(load_varimax)[i],
                vals[1], vals[2], ratio, status))
  }
}

## Mental.Health             | 0.459 vs 0.457 | Ratio: 1.01 | kuat

# 4. Variabel per Faktor
for (j in 1:ncol(load_varimax)) {
  vars_in_factor <- rownames(load_varimax)[abs(load_varimax[, j]) >= 0.40]
  cat("Faktor", j, ":", paste(vars_in_factor, collapse = ", "), "\n")
}

## Faktor 1 : Age, BS, BMI, Previous.Complications, Preexisting.Diabetes, Mental.Health 
## Faktor 2 : Systolic.BP, Diastolic 
## Faktor 3 : Gestational.Diabetes, Mental.Health

Modul 1 PCA & FA - Identifikasi Faktor Risiko Kesehatan Ibu Hamil

Cantika Latifatul Nur Ella (24031554023) & Sofia Dwi Kinasih (24031554079)

2026-03-02

1. Persiapan Data

2. Uji Asumsi

2a. Uji Korelasi

2b. Uji Bartlett

2c. Uji MSA

3. Principal Component Analysis (PCA)

3a. Total Variance Explained

3b. Scree Plot

3c. Communalities

3d. Pengelompokan faktor-faktor utama

3e. Komponen transformasi matriks

4. Factor Analysis (FA)

4a. Estimasi Faktor Matriks

4b. Communality

4c. Factor Rotation

4d. Interpretasi & Respecifikasi