Modul anmul
Shakyla Andhara Chandraningtyas (24031554199) Desnanty Ratna Aulia (24031554163)
2026-03-05
Analisis pada modul ini bertujuan untuk mengeksplorasi data, menguji asumsi, serta menerapkan metode Principal Component Analysis (PCA) dan Factor Analysis (FA) untuk melihat hubungan antar variabel dan mereduksi dimensi data. Dataset yang digunakan berisi data kualitas udara dan indikator kesehatan yang kemudian dianalisis melalui tahap karakteristik data, standarisasi variabel, serta pembentukan komponen dan faktor utama.
Dataset dapat diakses melalui link berikut: https://www.kaggle.com/datasets/tfisthis/global-air-quality-and-respiratory-health-outcomes
1. Karakteristik Data
1.1 Import Library
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, unionlibrary(ggplot2)
library(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(corrplot)## corrplot 0.95 loadedlibrary(tidyr)
library(reshape2)##
## Attaching package: 'reshape2'## The following object is masked from 'package:tidyr':
##
## smithslibrary(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa1.2 Import Dataset
getwd()## [1] "C:/Users/lenovo loq/OneDrive/Dokumen/Modul 1 Analisis Multivariat"1.3 Membaca Dataet
df <- read.csv("air_quality_health_dataset.csv")
head(df)## city date aqi pm2_5 pm10 no2 o3 temperature humidity
## 1 Los Angeles 2020-01-01 65 34.0 52.7 2.2 38.5 33.5 33
## 2 Beijing 2020-01-02 137 33.7 31.5 36.7 27.5 -1.6 32
## 3 London 2020-01-03 266 43.0 59.6 30.4 57.3 36.4 25
## 4 Mexico City 2020-01-04 293 33.7 37.9 12.3 42.7 -1.0 67
## 5 Delhi 2020-01-05 493 50.3 34.8 31.2 35.6 33.5 72
## 6 Cairo 2020-01-06 28 67.2 44.9 41.9 47.8 7.9 89
## hospital_admissions population_density hospital_capacity
## 1 5 Rural 1337
## 2 4 Urban 1545
## 3 10 Suburban 1539
## 4 10 Urban 552
## 5 9 Suburban 1631
## 6 11 Urban 12911.4 Struktur Data
print(paste("Jumlah baris dan kolom:", dim(df)[1], "baris", dim(df)[2], "kolom"))## [1] "Jumlah baris dan kolom: 88489 baris 12 kolom"str(df)## 'data.frame': 88489 obs. of 12 variables:
## $ city : chr "Los Angeles" "Beijing" "London" "Mexico City" ...
## $ date : chr "2020-01-01" "2020-01-02" "2020-01-03" "2020-01-04" ...
## $ aqi : int 65 137 266 293 493 28 217 449 342 279 ...
## $ pm2_5 : num 34 33.7 43 33.7 50.3 67.2 29 60.8 44.9 27.1 ...
## $ pm10 : num 52.7 31.5 59.6 37.9 34.8 44.9 63.7 56.2 63.4 101 ...
## $ no2 : num 2.2 36.7 30.4 12.3 31.2 41.9 22.3 40 31 47.8 ...
## $ o3 : num 38.5 27.5 57.3 42.7 35.6 47.8 56 18.1 34.9 42.2 ...
## $ temperature : num 33.5 -1.6 36.4 -1 33.5 7.9 27.7 26.3 28 -2.1 ...
## $ humidity : int 33 32 25 67 72 89 22 46 34 24 ...
## $ hospital_admissions: int 5 4 10 10 9 11 8 14 7 8 ...
## $ population_density : chr "Rural" "Urban" "Suburban" "Urban" ...
## $ hospital_capacity : int 1337 1545 1539 552 1631 1291 1852 350 878 179 ...1.5 Mengecek Missing Value
colSums(is.na(df))## city date aqi pm2_5
## 0 0 0 0
## pm10 no2 o3 temperature
## 0 0 0 0
## humidity hospital_admissions population_density hospital_capacity
## 0 0 0 01.6 Mengambil Variabel Numerik
data_numerik <- df %>%
select(where(is.numeric))
head(data_numerik)## aqi pm2_5 pm10 no2 o3 temperature humidity hospital_admissions
## 1 65 34.0 52.7 2.2 38.5 33.5 33 5
## 2 137 33.7 31.5 36.7 27.5 -1.6 32 4
## 3 266 43.0 59.6 30.4 57.3 36.4 25 10
## 4 293 33.7 37.9 12.3 42.7 -1.0 67 10
## 5 493 50.3 34.8 31.2 35.6 33.5 72 9
## 6 28 67.2 44.9 41.9 47.8 7.9 89 11
## hospital_capacity
## 1 1337
## 2 1545
## 3 1539
## 4 552
## 5 1631
## 6 12911.7 Statistik Deskriptif
statistik <- data.frame(
Mean = sapply(data_numerik, mean),
Median = sapply(data_numerik, median),
Std_Deviasi = sapply(data_numerik, sd),
Minimum = sapply(data_numerik, min),
Maksimum = sapply(data_numerik, max)
)
statistik## Mean Median Std_Deviasi Minimum Maksimum
## aqi 249.370182 249.0 144.479132 0 499.0
## pm2_5 35.144951 35.1 14.767994 0 109.9
## pm10 50.118654 50.0 19.796392 0 143.5
## no2 30.006211 30.0 9.963139 0 71.4
## o3 39.978895 40.0 12.007258 0 93.5
## temperature 17.522962 17.5 12.961024 -5 40.0
## humidity 56.950966 57.0 21.629675 20 94.0
## hospital_admissions 8.049385 8.0 3.715458 0 25.0
## hospital_capacity 1024.463165 1026.0 561.978071 50 1999.01.8 Histogram Distribusi Data
data_numerik %>%
pivot_longer(cols = everything()) %>%
ggplot(aes(value)) +
geom_histogram(bins = 20, fill="skyblue") +
facet_wrap(~name, scales="free") +
theme_minimal()
1.9 Boxplot ( Deteksi Outlier)
data_numerik %>%
pivot_longer(cols = everything()) %>%
ggplot(aes(x=name, y=value)) +
geom_boxplot(fill="sky blue") +
theme_minimal() +
theme(axis.text.x = element_text(angle=45, hjust=1))
1.10 Korelasi Antar Variabel (Heatmap)
cor_matrix <- cor(data_numerik)
cor_long <- melt(cor_matrix)
ggplot(cor_long, aes(x = Var2, y = Var1, fill = value)) +
geom_tile(color = "white") +
geom_text(aes(label = round(value,4)), color = "black", size = 3) +
scale_fill_gradient2(
low = "blue",
mid = "white",
high = "red",
midpoint = mean(cor_long$value)
) +
labs(
title = "Heatmap Korelasi",
x = "",
y = ""
) +
theme_minimal() +
theme(
axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1),
panel.grid = element_blank()
)
2. Uji Asumsi PCA dan FA
2.1 Import library
library(psych)
library(GPArotation)##
## Attaching package: 'GPArotation'## The following objects are masked from 'package:psych':
##
## equamax, varimin2.2 Data yang Digunakan untuk Analisis
X <- data_numerik
head(X)## aqi pm2_5 pm10 no2 o3 temperature humidity hospital_admissions
## 1 65 34.0 52.7 2.2 38.5 33.5 33 5
## 2 137 33.7 31.5 36.7 27.5 -1.6 32 4
## 3 266 43.0 59.6 30.4 57.3 36.4 25 10
## 4 293 33.7 37.9 12.3 42.7 -1.0 67 10
## 5 493 50.3 34.8 31.2 35.6 33.5 72 9
## 6 28 67.2 44.9 41.9 47.8 7.9 89 11
## hospital_capacity
## 1 1337
## 2 1545
## 3 1539
## 4 552
## 5 1631
## 6 12912.3 Uji KMO
kmo_result <- KMO(X)
print("Nilai KMO tiap variabel:")## [1] "Nilai KMO tiap variabel:"kmo_result$MSAi## aqi pm2_5 pm10 no2
## 0.4802833 0.5000364 0.5011362 0.5092699
## o3 temperature humidity hospital_admissions
## 0.5061713 0.5413704 0.4961910 0.5000348
## hospital_capacity
## 0.5076825print("Nilai KMO keseluruhan:")## [1] "Nilai KMO keseluruhan:"kmo_result$MSA## [1] 0.50005592.4 Uji Bartlett
bartlett <- cortest.bartlett(cor(X), n = nrow(X))
print("Chi-Square:")## [1] "Chi-Square:"bartlett$chisq## [1] 14826.19print("P-Value:")## [1] "P-Value:"bartlett$p.value## [1] 03. PCA (Principal Component Analysis)
3.1 Standarisasi Data
X_scaled <- scale(X)
head(X_scaled)## aqi pm2_5 pm10 no2 o3 temperature
## [1,] -1.2761025 -0.07752924 0.1303948 -2.7909088 -0.1231667 1.2326987
## [2,] -0.7777606 -0.09784344 -0.9405075 0.6718555 -1.0392793 -1.4754206
## [3,] 0.1151019 0.53189681 0.4789431 0.0395246 1.4425529 1.4564465
## [4,] 0.3019801 -0.09784344 -0.6172162 -1.7771720 0.2266217 -1.4291280
## [5,] 1.6862630 1.02620904 -0.7738104 0.1198206 -0.3646873 1.2326987
## [6,] -1.5321949 2.17057573 -0.2636164 1.1937793 0.6513648 -0.7424538
## humidity hospital_admissions hospital_capacity
## [1,] -1.1073197 -0.8207291 0.5561371
## [2,] -1.1535525 -1.0898749 0.9262583
## [3,] -1.4771820 0.5249999 0.9155817
## [4,] 0.4645948 0.5249999 -0.8407146
## [5,] 0.6957587 0.2558541 1.0792892
## [6,] 1.4817160 0.7941457 0.47428333.2 Menjalankan PCA
pca <- prcomp(X_scaled)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## Standard deviation 1.1801 1.0081 1.0036 1.0016 1.0008 0.9971 0.9965 0.9921
## Proportion of Variance 0.1547 0.1129 0.1119 0.1115 0.1113 0.1105 0.1103 0.1094
## Cumulative Proportion 0.1547 0.2676 0.3796 0.4910 0.6023 0.7128 0.8231 0.9325
## PC9
## Standard deviation 0.77951
## Proportion of Variance 0.06752
## Cumulative Proportion 1.000003.3 Eigenvalue
eigenvalues <- pca$sdev^2
eigenvalues## [1] 1.3925464 1.0162024 1.0073050 1.0032155 1.0016148 0.9942710 0.9929363
## [8] 0.9842733 0.60763523.4 Cumulative Variance
variance <- eigenvalues / sum(eigenvalues)
cumulative_variance <- cumsum(variance)
tabel_pca <- data.frame(
Komponen = 1:length(cumulative_variance),
Cumulative_Variance = cumulative_variance
)
tabel_pca## Komponen Cumulative_Variance
## 1 1 0.1547274
## 2 2 0.2676388
## 3 3 0.3795615
## 4 4 0.4910299
## 5 5 0.6023205
## 6 6 0.7127950
## 7 7 0.8231213
## 8 8 0.9324850
## 9 9 1.00000003.5 Scree Plot PCA
plot(
1:length(cumulative_variance),
cumulative_variance,
type = "b",
pch = 19,
xlab = "Komponen",
ylab = "Cumulative Variance",
main = "Scree Plot PCA"
)
3.6 Menentukan Jumlah Komponen
jumlah_komponen <- which(cumulative_variance >= 0.80)[1]
print(paste("Jumlah komponen yang dipilih:", jumlah_komponen))## [1] "Jumlah komponen yang dipilih: 7"3.7 PCA Akhir
pca_final <- prcomp(X_scaled)
principal_components <- pca_final$x[,1:jumlah_komponen]
head(principal_components)## PC1 PC2 PC3 PC4 PC5 PC6
## [1,] -0.6954021 -1.61665706 1.3370414 0.75521907 0.8261413 -2.291876754
## [2,] -0.8022406 -0.01489562 0.2195584 -0.62384272 1.0909681 1.046552147
## [3,] 0.7113288 -0.31169351 1.7017844 -0.08430627 -1.8870353 -0.714702802
## [4,] 0.3027201 -1.44883858 -1.5020883 -0.40152444 0.9635191 -0.014527909
## [5,] 0.9077235 1.27058292 1.1816741 -1.24535265 0.2320035 -0.001604094
## [6,] 2.1220266 0.91583922 -0.4972262 1.74561880 0.0658516 1.601789856
## PC7
## [1,] -1.1016165
## [2,] 0.3685704
## [3,] -0.5211250
## [4,] -1.0115142
## [5,] -0.6716781
## [6,] -0.49043873.8 Component Loading
loading <- pca_final$rotation[,1:jumlah_komponen]
loading## PC1 PC2 PC3 PC4
## aqi 0.004865307 0.183172917 -0.126481948 -0.840540645
## pm2_5 0.706959264 -0.005775048 0.005819455 0.003058129
## pm10 0.001096697 0.317508817 -0.402155085 0.196548748
## no2 0.011262232 0.485380750 0.100873320 0.030199038
## o3 -0.007064914 -0.286569269 -0.033428957 0.195277022
## temperature -0.017886512 0.101601670 0.742660763 0.222581578
## humidity 0.005506994 0.491605409 -0.361722057 0.382004086
## hospital_admissions 0.706821888 -0.013770877 0.011432129 0.008103238
## hospital_capacity 0.007716071 0.543780884 0.358368899 -0.142373528
## PC5 PC6 PC7
## aqi -0.2178026767 -0.072776063 -0.060630832
## pm2_5 -0.0058801857 -0.001781499 -0.002467229
## pm10 -0.4402926131 -0.661481505 0.190695037
## no2 -0.3476120079 0.592858656 0.516077636
## o3 -0.7370966792 0.260088498 -0.509013987
## temperature -0.1569462203 -0.325557696 0.129484527
## humidity 0.2603002910 0.164440051 -0.300787834
## hospital_admissions -0.0002692731 -0.012298052 0.001143806
## hospital_capacity 0.0462144960 -0.069539132 -0.5720847674. Factor Analysis (FA)
4.1 Menentukan Jumlah Faktor
jumlah_faktor <- 3
print(paste("Jumlah faktor yang digunakan:", jumlah_faktor))## [1] "Jumlah faktor yang digunakan: 3"4.2 Menjalankan Factor Analysis
fa <- factanal(X, factors = jumlah_faktor)
fa##
## Call:
## factanal(x = X, factors = jumlah_faktor)
##
## Uniquenesses:
## aqi pm2_5 pm10 no2
## 0.999 0.606 0.998 0.995
## o3 temperature humidity hospital_admissions
## 0.999 0.886 0.993 0.608
## hospital_capacity
## 0.993
##
## Loadings:
## Factor1 Factor2 Factor3
## aqi
## pm2_5 0.627
## pm10
## no2
## o3
## temperature 0.338
## humidity
## hospital_admissions 0.626
## hospital_capacity
##
## Factor1 Factor2 Factor3
## SS loadings 0.784 0.115 0.022
## Proportion Var 0.087 0.013 0.002
## Cumulative Var 0.087 0.100 0.102
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 7.71 on 12 degrees of freedom.
## The p-value is 0.8074.3 Eigenvalue Factor Analysis
ev <- eigen(cor(X))$values
ev## [1] 1.3925464 1.0162024 1.0073050 1.0032155 1.0016148 0.9942710 0.9929363
## [8] 0.9842733 0.60763524.5 Scree Plot FA
plot(
ev,
type = "b",
pch = 19,
xlab = "Faktor",
ylab = "Eigenvalue",
main = "Scree Plot Factor Analysis"
)
4.5 Menjalankan Factor Analysis
X <- scale(data_numerik)
jumlah_faktor <- 7
fa_model <- fa(X, nfactors = jumlah_faktor, rotate = "varimax")4.6 Membuat tabel Factor Loading
loading_faktor <- data.frame(
fa_model$loadings[1:ncol(X),]
)
rownames(loading_faktor) <- colnames(X)
colnames(loading_faktor) <- paste("Faktor", 1:jumlah_faktor)
loading_faktor <- round(loading_faktor, 6)
loading_faktor## Faktor 1 Faktor 2 Faktor 3 Faktor 4 Faktor 5 Faktor 6
## aqi 0.000566 -0.018028 0.122903 0.016474 0.013256 0.008368
## pm2_5 0.626753 -0.029285 0.012379 0.003917 0.046726 -0.013920
## pm10 -0.000216 -0.009251 0.005748 0.001795 0.021763 0.099041
## no2 0.003648 0.012170 0.011320 0.025300 0.066041 0.023008
## o3 -0.001752 0.003020 -0.005651 -0.014374 -0.003760 0.006458
## temperature -0.005940 0.113326 -0.024523 0.029701 0.019639 -0.007672
## humidity -0.001257 -0.074864 -0.056563 0.056688 0.060468 0.047604
## hospital_admissions 0.628372 0.001427 -0.006847 0.005767 -0.022338 0.013852
## hospital_capacity 0.002082 0.029092 0.021075 0.107536 0.038501 0.001412
## Faktor 7
## aqi -0.009239
## pm2_5 0.008398
## pm10 0.007737
## no2 -0.002597
## o3 0.093781
## temperature 0.000296
## humidity -0.040142
## hospital_admissions -0.022014
## hospital_capacity -0.0249104.7 Variance Tiap Faktor
variance_matrix <- fa_model$Vaccounted
variance_faktor <- data.frame(variance_matrix)
colnames(variance_faktor) <- paste("Faktor", 1:ncol(variance_faktor))
variance_faktor <- round(variance_faktor, 6)
variance_faktor## Faktor 1 Faktor 2 Faktor 3 Faktor 4 Faktor 5 Faktor 6
## SS loadings 0.787729 0.020721 0.019743 0.016830 0.013232 0.013163
## Proportion Var 0.087525 0.002302 0.002194 0.001870 0.001470 0.001463
## Cumulative Var 0.087525 0.089828 0.092022 0.093891 0.095362 0.096824
## Proportion Explained 0.891953 0.023463 0.022355 0.019056 0.014982 0.014904
## Cumulative Proportion 0.891953 0.915415 0.937771 0.956827 0.971809 0.986714
## Faktor 7
## SS loadings 0.011734
## Proportion Var 0.001304
## Cumulative Var 0.098128
## Proportion Explained 0.013286
## Cumulative Proportion 1.000000