Import Data
data <- read.csv2("WEO_Data.csv", stringsAsFactors = FALSE)
str(data)
## 'data.frame': 1775 obs. of 7 variables:
## $ Country : chr "Albania" "Albania" "Albania" "Albania" ...
## $ Subject.Descriptor : chr "Gross domestic product, constant prices" "Gross domestic product per capita, current prices" "Total investment" "Gross national savings" ...
## $ Units : chr "Percent change" "U.S. dollars" "Percent of GDP" "Percent of GDP" ...
## $ Scale : chr "" "Units" "" "" ...
## $ Country.Series.specific.Notes: chr "See notes for: Gross domestic product, constant prices (National currency)." "See notes for: Gross domestic product, current prices (National currency) Population (Persons)." "Source: IMF Staff Estimates. Official national accounts, including real GDP growth, rates available from 1996 o"| __truncated__ "Source: IMF Staff Estimates. Official national accounts, including real GDP growth, rates available from 1996 o"| __truncated__ ...
## $ X2022 : chr "4.000" "6,369.009" "28.492" "14.597" ...
## $ Estimates.Start.After : int 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 ...
head(data)
## Country Subject.Descriptor
## 1 Albania Gross domestic product, constant prices
## 2 Albania Gross domestic product per capita, current prices
## 3 Albania Total investment
## 4 Albania Gross national savings
## 5 Albania Inflation, average consumer prices
## 6 Albania Unemployment rate
## Units Scale
## 1 Percent change
## 2 U.S. dollars Units
## 3 Percent of GDP
## 4 Percent of GDP
## 5 Percent change
## 6 Percent of total labor force
## Country.Series.specific.Notes
## 1 See notes for: Gross domestic product, constant prices (National currency).
## 2 See notes for: Gross domestic product, current prices (National currency) Population (Persons).
## 3 Source: IMF Staff Estimates. Official national accounts, including real GDP growth, rates available from 1996 onwards. Latest actual data: 2020 National accounts manual used: European System of Accounts (ESA) 2010 GDP valuation: Market prices Reporting in calendar year: Yes Start/end months of reporting year: January/December Base year: 1996 Chain-weighted: Yes, from 1996 Primary domestic currency: Albanian lek Data last updated: 09/2022
## 4 Source: IMF Staff Estimates. Official national accounts, including real GDP growth, rates available from 1996 onwards. Latest actual data: 2020 National accounts manual used: European System of Accounts (ESA) 2010 GDP valuation: Market prices Reporting in calendar year: Yes Start/end months of reporting year: January/December Base year: 1996 Chain-weighted: Yes, from 1996 Primary domestic currency: Albanian lek Data last updated: 09/2022
## 5 See notes for: Inflation, average consumer prices (Index).
## 6 Source: National Statistics Office Latest actual data: 2020 Employment type: National definition Primary domestic currency: Albanian lek Data last updated: 09/2022
## X2022 Estimates.Start.After
## 1 4.000 2020
## 2 6,369.009 2020
## 3 28.492 2020
## 4 14.597 2020
## 5 6.243 2020
## 6 10.300 2020
colnames(data)
## [1] "Country" "Subject.Descriptor"
## [3] "Units" "Scale"
## [5] "Country.Series.specific.Notes" "X2022"
## [7] "Estimates.Start.After"
Memilih Variabel Penelitian
target_vars <- c(
"Gross domestic product, constant prices",
"Gross domestic product per capita, current prices",
"Total investment",
"Gross national savings",
"Inflation, average consumer prices",
"Unemployment rate",
"General government revenue",
"General government net lending/borrowing",
"General government gross debt",
"Current account balance"
)
data_subset <- data[data$Subject.Descriptor %in% target_vars, ]
Mengubah Data Long menjadi Wide
data_wide <- pivot_wider(
data_subset,
id_cols = Country,
names_from = Subject.Descriptor,
values_from = X2022
)
Menyiapkan Data Numerik
data_numeric <- data_wide[,-1]
data_numeric <- as.data.frame(
lapply(data_numeric, function(x)
as.numeric(gsub(",", "", x))
)
)
df_raw <- data_numeric
Cek Missing Value
colSums(is.na(df_raw))
## Gross.domestic.product..constant.prices
## 0
## Gross.domestic.product.per.capita..current.prices
## 1
## Total.investment
## 23
## Gross.national.savings
## 26
## Inflation..average.consumer.prices
## 0
## Unemployment.rate
## 92
## General.government.revenue
## 3
## General.government.net.lending.borrowing
## 3
## General.government.gross.debt
## 7
## Current.account.balance
## 2
Analisis Skewness
apply(df_raw,2,e1071::skewness,na.rm=TRUE)
## Gross.domestic.product..constant.prices
## 1.6883843
## Gross.domestic.product.per.capita..current.prices
## 2.1253248
## Total.investment
## 1.7190098
## Gross.national.savings
## 0.7808055
## Inflation..average.consumer.prices
## 7.1693992
## Unemployment.rate
## 2.7088947
## General.government.revenue
## 3.4275177
## General.government.net.lending.borrowing
## -0.8492560
## General.government.gross.debt
## 1.5805015
## Current.account.balance
## 0.1369176
Imputasi Missing Value
df_imputed <- df_raw
for(i in 1:ncol(df_imputed)){
df_imputed[is.na(df_imputed[,i]),i] <- median(df_imputed[,i],na.rm=TRUE)
}
sum(is.na(df_imputed))
## [1] 0
Analisis Outlier
boxplot(df_imputed,
main="Boxplot Sebelum Penanganan Outlier",
col="orange",
las=2)
Penanganan Outlier (Winsorizing)
handle_outliers <- function(x){
qnt <- quantile(x,probs=c(.25,.75))
caps <- quantile(x,probs=c(.05,.95))
H <- 1.5*IQR(x)
x[x < (qnt[1]-H)] <- caps[1]
x[x > (qnt[2]+H)] <- caps[2]
return(x)
}
df_clean <- as.data.frame(lapply(df_imputed,handle_outliers))
boxplot(df_clean,
main="Boxplot Setelah Penanganan Outlier",
col="lightgreen",
las=2)
Statistik Deskriptif
cat("Jumlah Observasi:",nrow(df_clean))
## Jumlah Observasi: 193
cat("Jumlah Variabel:",ncol(df_clean))
## Jumlah Variabel: 10
stats_desc <- describe(df_clean)
kable(stats_desc,digits=2,
caption="Statistik Deskriptif") %>%
kable_styling(full_width=FALSE)
Statistik Deskriptif
|
|
vars
|
n
|
mean
|
sd
|
median
|
trimmed
|
mad
|
min
|
max
|
range
|
skew
|
kurtosis
|
se
|
|
Gross.domestic.product..constant.prices
|
1
|
193
|
3.70
|
2.42
|
3.60
|
3.70
|
2.14
|
-1.50
|
9.27
|
10.77
|
0.04
|
0.06
|
0.17
|
|
Gross.domestic.product.per.capita..current.prices
|
2
|
193
|
15565.25
|
18535.94
|
6717.39
|
11980.18
|
8199.73
|
292.62
|
60361.78
|
60069.16
|
1.39
|
0.68
|
1334.25
|
|
Total.investment
|
3
|
193
|
24.62
|
6.78
|
24.11
|
24.15
|
5.32
|
10.46
|
40.16
|
29.70
|
0.62
|
0.21
|
0.49
|
|
Gross.national.savings
|
4
|
193
|
21.76
|
9.27
|
21.14
|
21.37
|
8.21
|
1.79
|
43.02
|
41.23
|
0.34
|
-0.11
|
0.67
|
|
Inflation..average.consumer.prices
|
5
|
193
|
9.95
|
7.24
|
7.90
|
8.50
|
4.02
|
1.90
|
30.54
|
28.64
|
1.81
|
2.66
|
0.52
|
|
Unemployment.rate
|
6
|
193
|
6.91
|
3.35
|
6.11
|
6.70
|
0.32
|
3.00
|
12.54
|
9.54
|
0.74
|
-0.72
|
0.24
|
|
General.government.revenue
|
7
|
193
|
28.90
|
12.04
|
27.14
|
28.35
|
13.21
|
7.02
|
61.56
|
54.54
|
0.37
|
-0.68
|
0.87
|
|
General.government.net.lending.borrowing
|
8
|
193
|
-3.29
|
3.66
|
-3.83
|
-3.55
|
2.73
|
-9.98
|
5.49
|
15.48
|
0.71
|
0.39
|
0.26
|
|
General.government.gross.debt
|
9
|
193
|
60.45
|
30.20
|
56.27
|
58.54
|
27.83
|
0.00
|
133.95
|
133.95
|
0.51
|
-0.11
|
2.17
|
|
Current.account.balance
|
10
|
193
|
-2.70
|
8.43
|
-3.45
|
-3.18
|
6.78
|
-20.31
|
16.11
|
36.42
|
0.46
|
0.00
|
0.61
|
Standarisasi Data
df_scaled <- as.data.frame(scale(df_clean))
Matriks Korelasi
cor_matrix <- cor(df_clean)
corrplot(cor_matrix,
method = "color",
type = "upper",
addCoef.col = "black",
tl.col = "black",
tl.srt = 45,
number.cex = 0.7,
tl.cex = 0.7,
diag = FALSE,
mar = c(0,0,2,0),
title = "Matriks Korelasi Indikator Makroekonomi")
Uji Kelayakan (KMO dan Bartlett)
res_kmo <- KMO(df_clean)
res_kmo
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = df_clean)
## Overall MSA = 0.5
## MSA for each item =
## Gross.domestic.product..constant.prices
## 0.39
## Gross.domestic.product.per.capita..current.prices
## 0.72
## Total.investment
## 0.21
## Gross.national.savings
## 0.44
## Inflation..average.consumer.prices
## 0.56
## Unemployment.rate
## 0.63
## General.government.revenue
## 0.61
## General.government.net.lending.borrowing
## 0.77
## General.government.gross.debt
## 0.62
## Current.account.balance
## 0.49
cortest.bartlett(cor(df_clean),n=nrow(df_clean))
## $chisq
## [1] 520.582
##
## $p.value
## [1] 3.545043e-82
##
## $df
## [1] 45
PCA
pca_obj <- principal(df_clean,
nfactors=ncol(df_clean),
rotate="none")
pca_obj
## Principal Components Analysis
## Call: principal(r = df_clean, nfactors = ncol(df_clean), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5
## Gross.domestic.product..constant.prices -0.01 0.46 0.36 -0.67 0.16
## Gross.domestic.product.per.capita..current.prices 0.65 0.08 0.42 0.30 -0.07
## Total.investment 0.03 0.79 -0.49 0.23 0.06
## Gross.national.savings 0.72 0.41 -0.43 0.00 0.13
## Inflation..average.consumer.prices -0.31 -0.38 -0.48 0.28 0.26
## Unemployment.rate -0.34 -0.01 0.08 -0.02 0.86
## General.government.revenue 0.48 0.03 0.39 0.54 0.19
## General.government.net.lending.borrowing 0.69 -0.29 -0.04 -0.18 0.34
## General.government.gross.debt -0.40 0.34 0.43 0.30 0.13
## Current.account.balance 0.81 -0.21 -0.07 -0.17 0.06
## PC6 PC7 PC8 PC9 PC10
## Gross.domestic.product..constant.prices 0.16 0.39 -0.09 -0.07 0.01
## Gross.domestic.product.per.capita..current.prices 0.23 0.00 -0.38 0.33 0.00
## Total.investment -0.17 0.06 0.01 0.13 0.16
## Gross.national.savings 0.20 -0.11 0.00 -0.12 -0.22
## Inflation..average.consumer.prices 0.46 0.41 -0.11 -0.01 0.01
## Unemployment.rate -0.14 -0.27 -0.20 0.00 0.00
## General.government.revenue -0.34 0.29 0.06 -0.31 0.00
## General.government.net.lending.borrowing -0.13 0.14 0.37 0.34 0.00
## General.government.gross.debt 0.53 -0.12 0.36 0.02 0.00
## Current.account.balance 0.34 -0.21 0.00 -0.25 0.19
## h2 u2 com
## Gross.domestic.product..constant.prices 1 4.4e-16 3.5
## Gross.domestic.product.per.capita..current.prices 1 3.3e-16 4.0
## Total.investment 1 -1.8e-15 2.2
## Gross.national.savings 1 7.8e-16 3.0
## Inflation..average.consumer.prices 1 1.2e-15 6.1
## Unemployment.rate 1 0.0e+00 1.7
## General.government.revenue 1 7.8e-16 5.3
## General.government.net.lending.borrowing 1 4.4e-16 3.6
## General.government.gross.debt 1 -2.2e-16 5.6
## Current.account.balance 1 1.1e-16 2.2
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## SS loadings 2.68 1.40 1.30 1.11 1.04 0.90 0.57 0.48 0.42 0.11
## Proportion Var 0.27 0.14 0.13 0.11 0.10 0.09 0.06 0.05 0.04 0.01
## Cumulative Var 0.27 0.41 0.54 0.65 0.75 0.84 0.90 0.95 0.99 1.00
## Proportion Explained 0.27 0.14 0.13 0.11 0.10 0.09 0.06 0.05 0.04 0.01
## Cumulative Proportion 0.27 0.41 0.54 0.65 0.75 0.84 0.90 0.95 0.99 1.00
##
## Mean item complexity = 3.7
## Test of the hypothesis that 10 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1
Variance PCA
eigenvalues <- pca_obj$values
prop_variance <- eigenvalues/sum(eigenvalues)
cum_variance <- cumsum(prop_variance)
data.frame(
Eigenvalue=eigenvalues,
Proporsi=prop_variance,
Kumulatif=cum_variance
)
## Eigenvalue Proporsi Kumulatif
## 1 2.6799173 0.26799173 0.2679917
## 2 1.3967176 0.13967176 0.4076635
## 3 1.3048313 0.13048313 0.5381466
## 4 1.1117006 0.11117006 0.6493167
## 5 1.0359905 0.10359905 0.7529157
## 6 0.9048374 0.09048374 0.8433995
## 7 0.5652881 0.05652881 0.8999283
## 8 0.4751623 0.04751623 0.9474445
## 9 0.4153766 0.04153766 0.9889822
## 10 0.1101783 0.01101783 1.0000000
Scree Plot
plot(eigenvalues,
type="b",
pch=19,
main="Scree Plot PCA",
xlab="Komponen",
ylab="Eigenvalue")
abline(h=1,col="red",lty=2)
Loading PCA
loadings_matrix <- as.data.frame(unclass(pca_obj$loadings))
kable(round(loadings_matrix[,1:4],3),
caption="Component Loading PCA") %>%
kable_styling(full_width=FALSE)
Component Loading PCA
|
|
PC1
|
PC2
|
PC3
|
PC4
|
|
Gross.domestic.product..constant.prices
|
-0.005
|
0.455
|
0.357
|
-0.671
|
|
Gross.domestic.product.per.capita..current.prices
|
0.647
|
0.082
|
0.421
|
0.301
|
|
Total.investment
|
0.027
|
0.793
|
-0.490
|
0.225
|
|
Gross.national.savings
|
0.722
|
0.409
|
-0.426
|
-0.001
|
|
Inflation..average.consumer.prices
|
-0.308
|
-0.380
|
-0.480
|
0.277
|
|
Unemployment.rate
|
-0.341
|
-0.013
|
0.080
|
-0.025
|
|
General.government.revenue
|
0.482
|
0.031
|
0.386
|
0.537
|
|
General.government.net.lending.borrowing
|
0.689
|
-0.291
|
-0.044
|
-0.180
|
|
General.government.gross.debt
|
-0.401
|
0.337
|
0.432
|
0.305
|
|
Current.account.balance
|
0.813
|
-0.207
|
-0.066
|
-0.172
|
Parallel Analysis
fa.parallel(df_clean,
fa="fa",
main="Parallel Analysis")
## Parallel analysis suggests that the number of factors = 6 and the number of components = NA
Menentukan Jumlah Faktor
n_factors_final <- sum(eigenvalues>1)
n_factors_final
## [1] 5
Factor Analysis
fa_res <- fa(df_clean,
nfactors=n_factors_final,
rotate="varimax",
fm="minres")
fa_res
## Factor Analysis using method = minres
## Call: fa(r = df_clean, nfactors = n_factors_final, rotate = "varimax",
## fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 MR5
## Gross.domestic.product..constant.prices -0.01 0.01 0.99 0.08 -0.03
## Gross.domestic.product.per.capita..current.prices 0.36 -0.04 0.03 0.09 0.62
## Total.investment -0.06 1.00 0.02 0.02 0.01
## Gross.national.savings 0.75 0.51 0.05 -0.05 0.11
## Inflation..average.consumer.prices -0.04 -0.04 -0.26 0.07 -0.34
## Unemployment.rate -0.19 -0.03 0.03 0.09 -0.13
## General.government.revenue 0.11 0.02 -0.08 -0.02 0.63
## General.government.net.lending.borrowing 0.47 -0.09 0.02 -0.25 0.25
## General.government.gross.debt -0.22 0.00 0.05 0.97 0.02
## Current.account.balance 0.93 -0.17 0.02 -0.08 0.15
## h2 u2 com
## Gross.domestic.product..constant.prices 0.998 0.0024 1.0
## Gross.domestic.product.per.capita..current.prices 0.525 0.4751 1.7
## Total.investment 0.995 0.0047 1.0
## Gross.national.savings 0.842 0.1582 1.9
## Inflation..average.consumer.prices 0.189 0.8106 2.1
## Unemployment.rate 0.062 0.9383 2.5
## General.government.revenue 0.421 0.5788 1.1
## General.government.net.lending.borrowing 0.351 0.6493 2.2
## General.government.gross.debt 0.999 0.0014 1.1
## Current.account.balance 0.912 0.0876 1.1
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 1.86 1.30 1.07 1.05 1.02
## Proportion Var 0.19 0.13 0.11 0.11 0.10
## Cumulative Var 0.19 0.32 0.42 0.53 0.63
## Proportion Explained 0.30 0.21 0.17 0.17 0.16
## Cumulative Proportion 0.30 0.50 0.67 0.84 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 45 with the objective function = 2.77 with Chi Square = 520.58
## df of the model are 5 and the objective function was 0.09
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.09
##
## The harmonic n.obs is 193 with the empirical chi square 8.18 with prob < 0.15
## The total n.obs was 193 with Likelihood Chi Square = 17.34 with prob < 0.0039
##
## Tucker Lewis Index of factoring reliability = 0.762
## RMSEA index = 0.113 and the 90 % confidence intervals are 0.058 0.174
## BIC = -8.98
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4 MR5
## Correlation of (regression) scores with factors 0.96 1.00 1.00 1.00 0.78
## Multiple R square of scores with factors 0.92 0.99 1.00 0.99 0.61
## Minimum correlation of possible factor scores 0.83 0.99 0.99 0.99 0.21
Factor Loading
print(fa_res$loadings,cutoff=0.4)
##
## Loadings:
## MR1 MR2 MR3 MR4
## Gross.domestic.product..constant.prices 0.995
## Gross.domestic.product.per.capita..current.prices
## Total.investment 0.995
## Gross.national.savings 0.747 0.515
## Inflation..average.consumer.prices
## Unemployment.rate
## General.government.revenue
## General.government.net.lending.borrowing 0.466
## General.government.gross.debt 0.974
## Current.account.balance 0.926
## MR5
## Gross.domestic.product..constant.prices
## Gross.domestic.product.per.capita..current.prices 0.622
## Total.investment
## Gross.national.savings
## Inflation..average.consumer.prices
## Unemployment.rate
## General.government.revenue 0.634
## General.government.net.lending.borrowing
## General.government.gross.debt
## Current.account.balance
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 1.858 1.297 1.073 1.050 1.015
## Proportion Var 0.186 0.130 0.107 0.105 0.102
## Cumulative Var 0.186 0.316 0.423 0.528 0.629
Communality
fa_res$communality
## Gross.domestic.product..constant.prices
## 0.99755261
## Gross.domestic.product.per.capita..current.prices
## 0.52485040
## Total.investment
## 0.99529272
## Gross.national.savings
## 0.84177533
## Inflation..average.consumer.prices
## 0.18944675
## Unemployment.rate
## 0.06172196
## General.government.revenue
## 0.42115909
## General.government.net.lending.borrowing
## 0.35065181
## General.government.gross.debt
## 0.99861231
## Current.account.balance
## 0.91239570
Factor Scores
factor_scores <- factor.scores(df_clean,fa_res)
head(factor_scores$scores)
## MR1 MR2 MR3 MR4 MR5
## [1,] -0.8290228 0.4916485 0.06019258 0.1009657 -0.0744428
## [2,] 1.6226893 1.8466496 0.36666480 0.3757603 -0.9354594
## [3,] 1.3980180 -0.0621761 1.32310813 -0.3486771 1.0525576
## [4,] 2.0118563 -0.1592663 -0.40036791 0.3790579 -1.5460635
## [5,] -1.7059551 2.1968849 0.87319467 0.6715522 0.3121221
## [6,] 0.3817650 -0.5495017 0.06015940 0.5622553 -0.6799843
Diagram Struktur Faktor
fa.diagram(fa_res,
main="Diagram Struktur Faktor")
