Load Dataset

library(tidyverse)

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library(dlookr)

## Registered S3 methods overwritten by 'dlookr':
##   method          from  
##   plot.transform  scales
##   print.transform scales
## 
## Attaching package: 'dlookr'
## 
## The following object is masked from 'package:tidyr':
## 
##     extract
## 
## The following object is masked from 'package:base':
## 
##     transform

folderData <- "C:/Users/LUCKY SURYA/Documents/kuliah/semester 4/analisis multivariat/pertemuan 3 anmul"


data_udara <- read_delim(
  paste0(folderData, "/AirQualityUCI.csv"),
  delim = ";"
)

## Rows: 9357 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ";"
## chr (4): CO(GT), C6H6(GT), T, AH
## dbl (8): PT08.S1(CO), NMHC(GT), PT08.S2(NMHC), NOx(GT), PT08.S3(NOx), NO2(GT...
## num (1): RH
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Mengubah koma menjadi titik

data_udara[] <- lapply(data_udara, function(x) as.numeric(gsub(",", ".", x)))
print((data_udara))

## # A tibble: 9,357 × 13
##    `CO(GT)` `PT08.S1(CO)` `NMHC(GT)` `C6H6(GT)` `PT08.S2(NMHC)` `NOx(GT)`
##       <dbl>         <dbl>      <dbl>      <dbl>           <dbl>     <dbl>
##  1      2.6          1360        150       11.9            1046       166
##  2      2            1292        112        9.4             955       103
##  3      2.2          1402         88        9               939       131
##  4      2.2          1376         80        9.2             948       172
##  5      1.6          1272         51        6.5             836       131
##  6      1.2          1197         38        4.7             750        89
##  7      1.2          1185         31        3.6             690        62
##  8      1            1136         31        3.3             672        62
##  9      0.9          1094         24        2.3             609        45
## 10      0.6          1010         19        1.7             561      -200
## # ℹ 9,347 more rows
## # ℹ 7 more variables: `PT08.S3(NOx)` <dbl>, `NO2(GT)` <dbl>,
## #   `PT08.S4(NO2)` <dbl>, `PT08.S5(O3)` <dbl>, T <dbl>, RH <dbl>, AH <dbl>

glimpse(data_udara)

## Rows: 9,357
## Columns: 13
## $ `CO(GT)`        <dbl> 2.6, 2.0, 2.2, 2.2, 1.6, 1.2, 1.2, 1.0, 0.9, 0.6, -200…
## $ `PT08.S1(CO)`   <dbl> 1360, 1292, 1402, 1376, 1272, 1197, 1185, 1136, 1094, …
## $ `NMHC(GT)`      <dbl> 150, 112, 88, 80, 51, 38, 31, 31, 24, 19, 14, 8, 16, 2…
## $ `C6H6(GT)`      <dbl> 11.9, 9.4, 9.0, 9.2, 6.5, 4.7, 3.6, 3.3, 2.3, 1.7, 1.3…
## $ `PT08.S2(NMHC)` <dbl> 1046, 955, 939, 948, 836, 750, 690, 672, 609, 561, 527…
## $ `NOx(GT)`       <dbl> 166, 103, 131, 172, 131, 89, 62, 62, 45, -200, 21, 16,…
## $ `PT08.S3(NOx)`  <dbl> 1056, 1174, 1140, 1092, 1205, 1337, 1462, 1453, 1579, …
## $ `NO2(GT)`       <dbl> 113, 92, 114, 122, 116, 96, 77, 76, 60, -200, 34, 28, …
## $ `PT08.S4(NO2)`  <dbl> 1692, 1559, 1555, 1584, 1490, 1393, 1333, 1333, 1276, …
## $ `PT08.S5(O3)`   <dbl> 1268, 972, 1074, 1203, 1110, 949, 733, 730, 620, 501, …
## $ T               <dbl> 13.6, 13.3, 11.9, 11.0, 11.2, 11.2, 11.3, 10.7, 10.7, …
## $ RH              <dbl> 489, 477, 54, 60, 596, 592, 568, 60, 597, 602, 605, 56…
## $ AH              <dbl> 0.7578, 0.7255, 0.7502, 0.7867, 0.7888, 0.7848, 0.7603…

karena bahasa r menerima data float menggunakan titik

sum(is.na(data_udara))

## [1] 0

Boxplot (deteksi outlier)

data_udara %>%
  pivot_longer(cols = everything(),
               names_to = "Variabel",
               values_to = "Nilai") %>%
  ggplot(aes(x = Variabel, y = Nilai)) +
  geom_boxplot(fill = "orange") +
  coord_flip() +
  theme_minimal() +
  labs(title = "Boxplot Setiap Variabel",
       x = NULL,
       y = "Nilai")

berdasarkan hasil plot terdapat banyak outlier yang tersebar pada setiap fitur

Interpolasi

data_udara[data_udara == -200] <- NA

library(zoo)

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

data_udara <- data_udara %>%
  mutate(across(where(is.numeric), ~ na.approx(., na.rm = FALSE))) %>%
  mutate(across(where(is.numeric), ~ na.locf(., na.rm = FALSE))) %>%
  mutate(across(where(is.numeric), ~ na.locf(., fromLast = TRUE)))

pada dataset air quality sebagai data time series nilai dari -200 dianggap sebagai missing value sehingga cara penangannya yaitu di interpolasikan. JIka langsung di drop satu baris hal itu akan sangat mengurangi data yang berpengaruh ke dalam model.

Statistika Deskriptif

stat_deskriptif <- data.frame(
  Variabel = colnames(data_udara),
  Minimum = apply(data_udara, 2, min, na.rm = TRUE),
  Maksimum = apply(data_udara, 2, max, na.rm = TRUE),
  Mean = round(apply(data_udara, 2, mean, na.rm = TRUE), 3),
  Std_Dev = round(apply(data_udara, 2, sd, na.rm = TRUE), 3)
)

knitr::kable(
  stat_deskriptif,
  #caption = "Tabel 1. Statistika Deskriptif Variabel Penelitian"
)

	Variabel	Minimum	Maksimum	Mean	Std_Dev
CO(GT)	CO(GT)	0.1000	11.900	2.131	1.432
PT08.S1(CO)	PT08.S1(CO)	647.0000	2040.000	1103.060	218.196
NMHC(GT)	NMHC(GT)	7.0000	1189.000	269.834	74.252
C6H6(GT)	C6H6(GT)	0.1000	63.700	10.179	7.504
PT08.S2(NMHC)	PT08.S2(NMHC)	383.0000	2214.000	942.143	267.867
NOx(GT)	NOx(GT)	2.0000	1479.000	241.922	204.315
PT08.S3(NOx)	PT08.S3(NOx)	322.0000	2683.000	832.759	255.710
NO2(GT)	NO2(GT)	2.0000	340.000	109.632	46.462
PT08.S4(NO2)	PT08.S4(NO2)	551.0000	2775.000	1453.299	343.206
PT08.S5(O3)	PT08.S5(O3)	221.0000	2523.000	1032.544	404.448
T	T	-1.9000	44.600	18.233	8.782
RH	RH	10.0000	887.000	445.885	209.655
AH	AH	0.1847	2.231	1.020	0.402

corr <-cor(data_udara)
corr

##                    CO(GT) PT08.S1(CO)    NMHC(GT)    C6H6(GT) PT08.S2(NMHC)
## CO(GT)         1.00000000  0.79405446  0.26750239  0.81651815    0.80709429
## PT08.S1(CO)    0.79405446  1.00000000  0.23450242  0.88050678    0.89204527
## NMHC(GT)       0.26750239  0.23450242  1.00000000  0.23338212    0.23382543
## C6H6(GT)       0.81651815  0.88050678  0.23338212  1.00000000    0.98227741
## PT08.S2(NMHC)  0.80709429  0.89204527  0.23382543  0.98227741    1.00000000
## NOx(GT)        0.79127203  0.66709860  0.14174699  0.65500884    0.64692509
## PT08.S3(NOx)  -0.64771255 -0.77708257 -0.25888994 -0.73100040   -0.79318030
## NO2(GT)        0.67580351  0.61771356  0.18671130  0.57026898    0.60164989
## PT08.S4(NO2)   0.55656356  0.66736052  0.17317355  0.75226916    0.76528987
## PT08.S5(O3)    0.77481719  0.90173053  0.20310747  0.85848251    0.87513007
## T              0.01889891  0.03123799  0.07944770  0.19059773    0.23056903
## RH             0.04092761  0.07299005 -0.03701566 -0.05778683   -0.07591059
## AH             0.06026414  0.11224074  0.06037334  0.15176418    0.17034403
##                  NOx(GT) PT08.S3(NOx)     NO2(GT) PT08.S4(NO2) PT08.S5(O3)
## CO(GT)         0.7912720  -0.64771255  0.67580351    0.5565636  0.77481719
## PT08.S1(CO)    0.6670986  -0.77708257  0.61771356    0.6673605  0.90173053
## NMHC(GT)       0.1417470  -0.25888994  0.18671130    0.1731736  0.20310747
## C6H6(GT)       0.6550088  -0.73100040  0.57026898    0.7522692  0.85848251
## PT08.S2(NMHC)  0.6469251  -0.79318030  0.60164989    0.7652899  0.87513007
## NOx(GT)        1.0000000  -0.62681354  0.76303802    0.2146550  0.73598198
## PT08.S3(NOx)  -0.6268135   1.00000000 -0.62214221   -0.5286039 -0.79837530
## NO2(GT)        0.7630380  -0.62214221  1.00000000    0.1342030  0.67975367
## PT08.S4(NO2)   0.2146550  -0.52860393  0.13420299    1.0000000  0.56954459
## PT08.S5(O3)    0.7359820  -0.79837530  0.67975367    0.5695446  1.00000000
## T             -0.2462799  -0.12659189 -0.19441838    0.5608469 -0.04750581
## RH             0.1437271  -0.04271305 -0.07058327   -0.0169087  0.08586366
## AH            -0.1226303  -0.21247527 -0.32224271    0.6294811  0.04461077
##                         T          RH          AH
## CO(GT)         0.01889891  0.04092761  0.06026414
## PT08.S1(CO)    0.03123799  0.07299005  0.11224074
## NMHC(GT)       0.07944770 -0.03701566  0.06037334
## C6H6(GT)       0.19059773 -0.05778683  0.15176418
## PT08.S2(NMHC)  0.23056903 -0.07591059  0.17034403
## NOx(GT)       -0.24627989  0.14372709 -0.12263028
## PT08.S3(NOx)  -0.12659189 -0.04271305 -0.21247527
## NO2(GT)       -0.19441838 -0.07058327 -0.32224271
## PT08.S4(NO2)   0.56084692 -0.01690870  0.62948113
## PT08.S5(O3)   -0.04750581  0.08586366  0.04461077
## T              1.00000000 -0.41659281  0.65876052
## RH            -0.41659281  1.00000000  0.13809711
## AH             0.65876052  0.13809711  1.00000000

library(corrr)

## 
## Attaching package: 'corrr'

## The following object is masked from 'package:dlookr':
## 
##     correlate

library(ggcorrplot)

ggcorrplot(corr, lab = TRUE, lab_size = 3, type = "full")

## 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 ggcorrplot package.
##   Please report the issue at <https://github.com/kassambara/ggcorrplot/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

##Cek MSA menggunakan Uji KMO dan Barlets

library(psych)

## 
## Attaching package: 'psych'

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

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

corr<- cor(data_udara)
KMO(corr)

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = corr)
## Overall MSA =  0.82
## MSA for each item = 
##        CO(GT)   PT08.S1(CO)      NMHC(GT)      C6H6(GT) PT08.S2(NMHC) 
##          0.91          0.94          0.81          0.84          0.79 
##       NOx(GT)  PT08.S3(NOx)       NO2(GT)  PT08.S4(NO2)   PT08.S5(O3) 
##          0.81          0.82          0.89          0.75          0.95 
##             T            RH            AH 
##          0.58          0.36          0.44

data_udara =  data_udara[ ,-12]

corr<- cor(data_udara)
KMO(corr)

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = corr)
## Overall MSA =  0.82
## MSA for each item = 
##        CO(GT)   PT08.S1(CO)      NMHC(GT)      C6H6(GT) PT08.S2(NMHC) 
##          0.91          0.94          0.80          0.84          0.78 
##       NOx(GT)  PT08.S3(NOx)       NO2(GT)  PT08.S4(NO2)   PT08.S5(O3) 
##          0.79          0.81          0.88          0.74          0.94 
##             T            AH 
##          0.62          0.43

data_udara =  data_udara[ ,-12]

corr<- cor(data_udara)
KMO(corr)

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = corr)
## Overall MSA =  0.86
## MSA for each item = 
##        CO(GT)   PT08.S1(CO)      NMHC(GT)      C6H6(GT) PT08.S2(NMHC) 
##          0.89          0.93          0.78          0.82          0.81 
##       NOx(GT)  PT08.S3(NOx)       NO2(GT)  PT08.S4(NO2)   PT08.S5(O3) 
##          0.87          0.88          0.86          0.79          0.94 
##             T 
##          0.51

KMO_result<-KMO(corr)

kmo_table <- data.frame(
  Variabel = names(KMO_result$MSAi),
  MSA = round(KMO_result$MSAi,3)
)
kmo_table

##                    Variabel   MSA
## CO(GT)               CO(GT) 0.894
## PT08.S1(CO)     PT08.S1(CO) 0.933
## NMHC(GT)           NMHC(GT) 0.781
## C6H6(GT)           C6H6(GT) 0.822
## PT08.S2(NMHC) PT08.S2(NMHC) 0.814
## NOx(GT)             NOx(GT) 0.866
## PT08.S3(NOx)   PT08.S3(NOx) 0.880
## NO2(GT)             NO2(GT) 0.865
## PT08.S4(NO2)   PT08.S4(NO2) 0.794
## PT08.S5(O3)     PT08.S5(O3) 0.938
## T                         T 0.507

#Bartlett Test
library(psych)
uji_barlets<-cortest.bartlett(corr, n = nrow(data_udara))
print(uji_barlets)

## $chisq
## [1] 133895.9
## 
## $p.value
## [1] 0
## 
## $df
## [1] 55

Scaling (standardisasi data)

scale_data = scale(data_udara)
r = cov(scale_data)
r

##                    CO(GT) PT08.S1(CO)   NMHC(GT)   C6H6(GT) PT08.S2(NMHC)
## CO(GT)         1.00000000  0.79405446  0.2675024  0.8165181     0.8070943
## PT08.S1(CO)    0.79405446  1.00000000  0.2345024  0.8805068     0.8920453
## NMHC(GT)       0.26750239  0.23450242  1.0000000  0.2333821     0.2338254
## C6H6(GT)       0.81651815  0.88050678  0.2333821  1.0000000     0.9822774
## PT08.S2(NMHC)  0.80709429  0.89204527  0.2338254  0.9822774     1.0000000
## NOx(GT)        0.79127203  0.66709860  0.1417470  0.6550088     0.6469251
## PT08.S3(NOx)  -0.64771255 -0.77708257 -0.2588899 -0.7310004    -0.7931803
## NO2(GT)        0.67580351  0.61771356  0.1867113  0.5702690     0.6016499
## PT08.S4(NO2)   0.55656356  0.66736052  0.1731736  0.7522692     0.7652899
## PT08.S5(O3)    0.77481719  0.90173053  0.2031075  0.8584825     0.8751301
## T              0.01889891  0.03123799  0.0794477  0.1905977     0.2305690
##                  NOx(GT) PT08.S3(NOx)    NO2(GT) PT08.S4(NO2) PT08.S5(O3)
## CO(GT)         0.7912720   -0.6477126  0.6758035    0.5565636  0.77481719
## PT08.S1(CO)    0.6670986   -0.7770826  0.6177136    0.6673605  0.90173053
## NMHC(GT)       0.1417470   -0.2588899  0.1867113    0.1731736  0.20310747
## C6H6(GT)       0.6550088   -0.7310004  0.5702690    0.7522692  0.85848251
## PT08.S2(NMHC)  0.6469251   -0.7931803  0.6016499    0.7652899  0.87513007
## NOx(GT)        1.0000000   -0.6268135  0.7630380    0.2146550  0.73598198
## PT08.S3(NOx)  -0.6268135    1.0000000 -0.6221422   -0.5286039 -0.79837530
## NO2(GT)        0.7630380   -0.6221422  1.0000000    0.1342030  0.67975367
## PT08.S4(NO2)   0.2146550   -0.5286039  0.1342030    1.0000000  0.56954459
## PT08.S5(O3)    0.7359820   -0.7983753  0.6797537    0.5695446  1.00000000
## T             -0.2462799   -0.1265919 -0.1944184    0.5608469 -0.04750581
##                         T
## CO(GT)         0.01889891
## PT08.S1(CO)    0.03123799
## NMHC(GT)       0.07944770
## C6H6(GT)       0.19059773
## PT08.S2(NMHC)  0.23056903
## NOx(GT)       -0.24627989
## PT08.S3(NOx)  -0.12659189
## NO2(GT)       -0.19441838
## PT08.S4(NO2)   0.56084692
## PT08.S5(O3)   -0.04750581
## T              1.00000000

library(corrr)
library(ggcorrplot)

ggcorrplot(r, lab = TRUE, lab_size = 3, type = "full")

PCA

library('FactoMineR')
library('factoextra')

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

pca_result <- PCA(data_udara,
                  scale.unit = TRUE,
                  graph = FALSE,
                  ncp=ncol(data_udara))     


pca_result$eig

##         eigenvalue percentage of variance cumulative percentage of variance
## comp 1  6.75985600            61.45323633                          61.45324
## comp 2  1.75131088            15.92100798                          77.37424
## comp 3  0.93525473             8.50231571                          85.87656
## comp 4  0.48703526             4.42759326                          90.30415
## comp 5  0.39875966             3.62508780                          93.92924
## comp 6  0.22605614             2.05505582                          95.98430
## comp 7  0.14775058             1.34318706                          97.32748
## comp 8  0.11656466             1.05967874                          98.38716
## comp 9  0.08534334             0.77584852                          99.16301
## comp 10 0.08170581             0.74278009                          99.90579
## comp 11 0.01036296             0.09420869                         100.00000

#pca_result$svd$V        
#pca_result$ind['coord']

#pca_result$var

pca_table <- data.frame(
  Komponen = paste0("PC", 1:nrow(pca_result$eig)),
  Eigenvalue = pca_result$eig[,1],
  Variance_Percent = pca_result$eig[,2],
  Cumulative_Variance = pca_result$eig[,3]
)

knitr::kable(pca_table, digits = 3)

	Komponen	Eigenvalue	Variance_Percent	Cumulative_Variance
comp 1	PC1	6.760	61.453	61.453
comp 2	PC2	1.751	15.921	77.374
comp 3	PC3	0.935	8.502	85.877
comp 4	PC4	0.487	4.428	90.304
comp 5	PC5	0.399	3.625	93.929
comp 6	PC6	0.226	2.055	95.984
comp 7	PC7	0.148	1.343	97.327
comp 8	PC8	0.117	1.060	98.387
comp 9	PC9	0.085	0.776	99.163
comp 10	PC10	0.082	0.743	99.906
comp 11	PC11	0.010	0.094	100.000

loading <- pca_result$var$coord[,1:2]

colnames(loading) <- c("PC1", "PC2")

knitr::kable(round(loading,3))

	PC1	PC2
CO(GT)	0.890	-0.104
PT08.S1(CO)	0.935	0.012
NMHC(GT)	0.292	0.085
C6H6(GT)	0.944	0.161
PT08.S2(NMHC)	0.959	0.180
NOx(GT)	0.781	-0.470
PT08.S3(NOx)	-0.848	-0.010
NO2(GT)	0.725	-0.475
PT08.S4(NO2)	0.680	0.661
PT08.S5(O3)	0.932	-0.110
T	0.101	0.882

# membuat scree plot
eigenvalues <- pca_result$eig[,1]

plot(eigenvalues,
     type="b",
     xlab="Komponen",
     ylab="Eigenvalue",
     main="Scree Plot")
abline(h=1, col="red")

#Biplot
fviz_pca_biplot(pca_result,
                geom.ind = "point",
                #col.ind = status.ipm,
                #palette = c("#FC4E07","#E7B800", "#00AFBB"),
                addEllipses = TRUE,
                #legend.title = "Kategori"
                )

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## ℹ The deprecated feature was likely used in the ggpubr package.
##   Please report the issue at <https://github.com/kassambara/ggpubr/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# correlation circle
contrib_circle <- fviz_pca_var(pca_result, col.var = "contrib",
                               gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
                               repel = TRUE) +
  ggtitle("Kontribusi Variabel")
plot(contrib_circle)

#contribution
contrib_v_PC1 <- fviz_contrib(pca_result, choice = "var", axes = 1, top = 5) + ggtitle("PC1")
plot(contrib_v_PC1)

contrib_v_PC2 <- fviz_contrib(pca_result, choice = "var", axes = 2, top = 5) + ggtitle("PC2")
plot(contrib_v_PC2)

Faktor Analisis

fa.parallel(scale_data)

## Parallel analysis suggests that the number of factors =  4  and the number of components =  2

FA <- fa(scale_data,
         covar = TRUE,
         nfactors = 2,
         rotate = "varimax", fm="pm")

## factor method not specified correctly, minimum residual (unweighted least squares  used

load <- FA$loadings
load

## 
## Loadings:
##               MR1    MR2   
## CO(GT)         0.869  0.119
## PT08.S1(CO)    0.894  0.250
## NMHC(GT)       0.237  0.100
## C6H6(GT)       0.871  0.399
## PT08.S2(NMHC)  0.886  0.426
## NOx(GT)        0.864 -0.255
## PT08.S3(NOx)  -0.791 -0.202
## NO2(GT)        0.792 -0.251
## PT08.S4(NO2)   0.480  0.865
## PT08.S5(O3)    0.924  0.128
## T                     0.677
## 
##                  MR1   MR2
## SS loadings    6.245 1.819
## Proportion Var 0.568 0.165
## Cumulative Var 0.568 0.733

load_table <- as.data.frame(unclass(FA$loadings))

load_table$Variabel <- rownames(load_table)

colnames(load_table)[1:2] <- c("Faktor Polutan", "Faktor Lingkungan")

load_table <- load_table[, c("Faktor Polutan", 
                             "Faktor Lingkungan")]

load_table <- load_table[order(-abs(load_table$`Faktor Polutan`)), ]

knitr::kable(load_table, digits = 3, caption = "Tabel Factor Loadings")

Tabel Factor Loadings
	Faktor Polutan	Faktor Lingkungan
PT08.S5(O3)	0.924	0.128
PT08.S1(CO)	0.894	0.250
PT08.S2(NMHC)	0.886	0.426
C6H6(GT)	0.871	0.399
CO(GT)	0.869	0.119
NOx(GT)	0.864	-0.255
NO2(GT)	0.792	-0.251
PT08.S3(NOx)	-0.791	-0.202
PT08.S4(NO2)	0.480	0.865
NMHC(GT)	0.237	0.100
T	-0.084	0.677

#FA$scores

colnames(FA$loadings) <- c("faktor Polusi", "Faktor lingkungan")

fa.diagram(FA)

TUGAS 2 : Analisis Dataset AirQuality menggunakan PCA dan FA

Lucky Surya Revansyah (24031554090), Nasliyatul Intani (24031554097)

2026-02-21