=— title: “Kelompok 12_anmul_yuli_devita” author: “yuli and devita” date: “2026-03-03” output: html_document —
LOAD DATASET
# Load dataset
df <- read_csv("/cloud/project/countries.csv")## Rows: 188 Columns: 21
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): Country, Region, GDP per Capita, Data Quality
## dbl (17): Population (millions), HDI, Cropland Footprint, Grazing Footprint,...
##
## 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.# Lihat struktur data
str(df)## spc_tbl_ [188 × 21] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Country : chr [1:188] "Afghanistan" "Albania" "Algeria" "Angola" ...
## $ Region : chr [1:188] "Middle East/Central Asia" "Northern/Eastern Europe" "Africa" "Africa" ...
## $ Population (millions) : num [1:188] 29.82 3.16 38.48 20.82 0.09 ...
## $ HDI : num [1:188] 0.46 0.73 0.73 0.52 0.78 0.83 0.73 NA 0.93 0.88 ...
## $ GDP per Capita : chr [1:188] "$614.66" "$4,534.37" "$5,430.57" "$4,665.91" ...
## $ Cropland Footprint : num [1:188] 0.3 0.78 0.6 0.33 NA 0.78 0.74 NA 2.68 0.82 ...
## $ Grazing Footprint : num [1:188] 0.2 0.22 0.16 0.15 NA 0.79 0.18 NA 0.63 0.27 ...
## $ Forest Footprint : num [1:188] 0.08 0.25 0.17 0.12 NA 0.29 0.34 NA 0.89 0.63 ...
## $ Carbon Footprint : num [1:188] 0.18 0.87 1.14 0.2 NA 1.08 0.89 NA 4.85 4.14 ...
## $ Fish Footprint : num [1:188] 0 0.02 0.01 0.09 NA 0.1 0.01 NA 0.11 0.06 ...
## $ Total Ecological Footprint : num [1:188] 0.79 2.21 2.12 0.93 5.38 ...
## $ Cropland : num [1:188] 0.24 0.55 0.24 0.2 NA 2.64 0.44 NA 5.42 0.71 ...
## $ Grazing Land : num [1:188] 0.2 0.21 0.27 1.42 NA 1.86 0.26 NA 5.81 0.16 ...
## $ Forest Land : num [1:188] 0.02 0.29 0.03 0.64 NA 0.66 0.1 NA 2.01 2.04 ...
## $ Fishing Water : num [1:188] 0 0.07 0.01 0.26 NA 1.67 0.02 NA 3.19 0 ...
## $ Urban Land : num [1:188] 0.04 0.06 0.03 0.04 NA 0.1 0.07 NA 0.14 0.15 ...
## $ Total Biocapacity : num [1:188] 0.5 1.18 0.59 2.55 0.94 ...
## $ Biocapacity Deficit or Reserve: num [1:188] -0.3 -1.03 -1.53 1.61 -4.44 ...
## $ Earths Required : num [1:188] 0.46 1.27 1.22 0.54 3.11 1.82 1.29 6.86 5.37 3.5 ...
## $ Countries Required : num [1:188] 1.6 1.87 3.61 0.37 5.7 ...
## $ Data Quality : chr [1:188] "6" "6" "5" "6" ...
## - attr(*, "spec")=
## .. cols(
## .. Country = col_character(),
## .. Region = col_character(),
## .. `Population (millions)` = col_double(),
## .. HDI = col_double(),
## .. `GDP per Capita` = col_character(),
## .. `Cropland Footprint` = col_double(),
## .. `Grazing Footprint` = col_double(),
## .. `Forest Footprint` = col_double(),
## .. `Carbon Footprint` = col_double(),
## .. `Fish Footprint` = col_double(),
## .. `Total Ecological Footprint` = col_double(),
## .. Cropland = col_double(),
## .. `Grazing Land` = col_double(),
## .. `Forest Land` = col_double(),
## .. `Fishing Water` = col_double(),
## .. `Urban Land` = col_double(),
## .. `Total Biocapacity` = col_double(),
## .. `Biocapacity Deficit or Reserve` = col_double(),
## .. `Earths Required` = col_double(),
## .. `Countries Required` = col_double(),
## .. `Data Quality` = col_character()
## .. )
## - attr(*, "problems")=<externalptr># Lihat 6 data pertama
head(df)## # A tibble: 6 × 21
## Country Region Population (millions…¹ HDI `GDP per Capita`
## <chr> <chr> <dbl> <dbl> <chr>
## 1 Afghanistan Middle East… 29.8 0.46 $614.66
## 2 Albania Northern/Ea… 3.16 0.73 $4,534.37
## 3 Algeria Africa 38.5 0.73 $5,430.57
## 4 Angola Africa 20.8 0.52 $4,665.91
## 5 Antigua and Barbuda Latin Ameri… 0.09 0.78 $13,205.10
## 6 Argentina Latin Ameri… 41.1 0.83 $13,540.00
## # ℹ abbreviated name: ¹`Population (millions)`
## # ℹ 16 more variables: `Cropland Footprint` <dbl>, `Grazing Footprint` <dbl>,
## # `Forest Footprint` <dbl>, `Carbon Footprint` <dbl>, `Fish Footprint` <dbl>,
## # `Total Ecological Footprint` <dbl>, Cropland <dbl>, `Grazing Land` <dbl>,
## # `Forest Land` <dbl>, `Fishing Water` <dbl>, `Urban Land` <dbl>,
## # `Total Biocapacity` <dbl>, `Biocapacity Deficit or Reserve` <dbl>,
## # `Earths Required` <dbl>, `Countries Required` <dbl>, `Data Quality` <chr>MEMASTIKAN NUMERIK dan Pemilihan variavel gunakan 10 sub-indeks
df_selected <- df[, c(
"HDI",
"Cropland Footprint",
"Grazing Footprint",
"Forest Footprint",
"Carbon Footprint",
"Fish Footprint",
"Total Ecological Footprint",
"Total Biocapacity",
"Biocapacity Deficit or Reserve",
"Earths Required"
)]Cek missing:
colSums(is.na(df_selected))## HDI Cropland Footprint
## 16 15
## Grazing Footprint Forest Footprint
## 15 15
## Carbon Footprint Fish Footprint
## 15 15
## Total Ecological Footprint Total Biocapacity
## 0 0
## Biocapacity Deficit or Reserve Earths Required
## 0 0Imputasi median (jika ada NA):
df_selected <- data.frame(
lapply(df_selected, function(x) {
x[is.na(x)] <- median(x, na.rm = TRUE)
return(x)
})
)
colSums(is.na(df_selected))## HDI Cropland.Footprint
## 0 0
## Grazing.Footprint Forest.Footprint
## 0 0
## Carbon.Footprint Fish.Footprint
## 0 0
## Total.Ecological.Footprint Total.Biocapacity
## 0 0
## Biocapacity.Deficit.or.Reserve Earths.Required
## 0 0colSums(is.na(df_selected))## HDI Cropland.Footprint
## 0 0
## Grazing.Footprint Forest.Footprint
## 0 0
## Carbon.Footprint Fish.Footprint
## 0 0
## Total.Ecological.Footprint Total.Biocapacity
## 0 0
## Biocapacity.Deficit.or.Reserve Earths.Required
## 0 0head (df_selected)## HDI Cropland.Footprint Grazing.Footprint Forest.Footprint Carbon.Footprint
## 1 0.46 0.30 0.20 0.08 0.18
## 2 0.73 0.78 0.22 0.25 0.87
## 3 0.73 0.60 0.16 0.17 1.14
## 4 0.52 0.33 0.15 0.12 0.20
## 5 0.78 0.52 0.18 0.26 1.14
## 6 0.83 0.78 0.79 0.29 1.08
## Fish.Footprint Total.Ecological.Footprint Total.Biocapacity
## 1 0.00 0.79 0.50
## 2 0.02 2.21 1.18
## 3 0.01 2.12 0.59
## 4 0.09 0.93 2.55
## 5 0.07 5.38 0.94
## 6 0.10 3.14 6.92
## Biocapacity.Deficit.or.Reserve Earths.Required
## 1 -0.30 0.46
## 2 -1.03 1.27
## 3 -1.53 1.22
## 4 1.61 0.54
## 5 -4.44 3.11
## 6 3.78 1.82KARAKTERISTIK DATA (statistika deskriptif)
describe(df_selected)## vars n mean sd median trimmed mad min
## HDI 1 188 0.69 0.15 0.72 0.70 0.15 0.34
## Cropland.Footprint 2 188 0.57 0.34 0.52 0.53 0.24 0.07
## Grazing.Footprint 3 188 0.26 0.34 0.18 0.20 0.13 0.00
## Forest.Footprint 4 188 0.36 0.35 0.26 0.31 0.17 0.01
## Carbon.Footprint 5 188 1.75 1.83 1.14 1.46 1.37 0.00
## Fish.Footprint 6 188 0.12 0.15 0.07 0.09 0.07 0.00
## Total.Ecological.Footprint 7 188 3.32 2.37 2.74 3.00 2.11 0.42
## Total.Biocapacity 8 188 4.02 11.69 1.31 1.89 1.15 0.05
## Biocapacity.Deficit.or.Reserve 9 188 0.70 11.77 -0.73 -0.81 1.72 -14.14
## Earths.Required 10 188 1.92 1.37 1.58 1.73 1.22 0.24
## max range skew kurtosis se
## HDI 0.94 0.60 -0.43 -0.75 0.01
## Cropland.Footprint 2.68 2.61 2.53 10.52 0.02
## Grazing.Footprint 3.47 3.47 5.39 43.09 0.02
## Forest.Footprint 3.03 3.02 3.57 20.02 0.03
## Carbon.Footprint 12.65 12.65 2.20 7.48 0.13
## Fish.Footprint 0.82 0.82 2.55 7.13 0.01
## Total.Ecological.Footprint 15.82 15.40 1.60 3.97 0.17
## Total.Biocapacity 111.35 111.30 7.06 54.37 0.85
## Biocapacity.Deficit.or.Reserve 109.01 123.15 6.93 53.61 0.86
## Earths.Required 9.14 8.90 1.60 3.97 0.10KORELASI MATRIX
df_selected <- data.frame(lapply(df_selected, function(x) as.numeric(as.character(x))))cor_matrix <- cor(df_selected)
corrplot(cor_matrix,
method = "color", # kotak warna
type = "upper", # segitiga atas
addCoef.col = "black", # angka di dalam kotak
number.cex = 0.7, # ukuran angka
tl.col = "black", # warna nama variabel
tl.srt = 45, # rotasi label
diag = FALSE) # hilangkan diagonal
str(df_selected)## 'data.frame': 188 obs. of 10 variables:
## $ HDI : num 0.46 0.73 0.73 0.52 0.78 0.83 0.73 0.72 0.93 0.88 ...
## $ Cropland.Footprint : num 0.3 0.78 0.6 0.33 0.52 0.78 0.74 0.52 2.68 0.82 ...
## $ Grazing.Footprint : num 0.2 0.22 0.16 0.15 0.18 0.79 0.18 0.18 0.63 0.27 ...
## $ Forest.Footprint : num 0.08 0.25 0.17 0.12 0.26 0.29 0.34 0.26 0.89 0.63 ...
## $ Carbon.Footprint : num 0.18 0.87 1.14 0.2 1.14 1.08 0.89 1.14 4.85 4.14 ...
## $ Fish.Footprint : num 0 0.02 0.01 0.09 0.07 0.1 0.01 0.07 0.11 0.06 ...
## $ Total.Ecological.Footprint : num 0.79 2.21 2.12 0.93 5.38 ...
## $ Total.Biocapacity : num 0.5 1.18 0.59 2.55 0.94 ...
## $ Biocapacity.Deficit.or.Reserve: num -0.3 -1.03 -1.53 1.61 -4.44 ...
## $ Earths.Required : num 0.46 1.27 1.22 0.54 3.11 1.82 1.29 6.86 5.37 3.5 ...colSums(is.na(df_selected))## HDI Cropland.Footprint
## 0 0
## Grazing.Footprint Forest.Footprint
## 0 0
## Carbon.Footprint Fish.Footprint
## 0 0
## Total.Ecological.Footprint Total.Biocapacity
## 0 0
## Biocapacity.Deficit.or.Reserve Earths.Required
## 0 0#cor_matrix <- cor(df_selected)
#corrplot(cor_matrix,
#method = "color",
# = "upper",
#addCoef.col = "black", # tampilkan angka
#tl.col = "black", # warna label
#tl.srt = 45, # rotasi label
#number.cex = 0.7) # ukuran angkaUJI ASUMSI
- KMO
KMO(cor(df_selected))## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cor(df_selected))
## Overall MSA = 0.71
## MSA for each item =
## HDI Cropland.Footprint
## 0.93 0.85
## Grazing.Footprint Forest.Footprint
## 0.76 0.74
## Carbon.Footprint Fish.Footprint
## 0.95 0.61
## Total.Ecological.Footprint Total.Biocapacity
## 0.70 0.39
## Biocapacity.Deficit.or.Reserve Earths.Required
## 0.40 0.85OPSIONAL DI MASUKKAN KE CODE APA ENGGA (saya buat soalnya biar bisa di publish di Rpubs)
# 1. Load Data
df <- read.csv("countries.csv")
# 2. Scaling (Pastikan baris ini ada DI ATAS baris KMO)
df_scaled <- scale(df[, c(
"HDI",
"Cropland.Footprint",
"Grazing.Footprint",
"Forest.Footprint",
"Carbon.Footprint",
"Fish.Footprint",
"Total.Ecological.Footprint",
"Total.Biocapacity",
"Biocapacity.Deficit.or.Reserve",
"Earths.Required"
)])
# 3. Baru panggil KMO
library(psych)
KMO(df_scaled)## Warning in sqrt(S2): NaNs produced## Warning in cov2cor(Q): diag(V) had non-positive or NA entries; the non-finite
## result may be dubious## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = df_scaled)
## Overall MSA = NaN
## MSA for each item =
## HDI Cropland.Footprint
## NaN NaN
## Grazing.Footprint Forest.Footprint
## NaN NaN
## Carbon.Footprint Fish.Footprint
## NaN NaN
## Total.Ecological.Footprint Total.Biocapacity
## NaN NaN
## Biocapacity.Deficit.or.Reserve Earths.Required
## NaN NaNKMO(df_scaled)## Warning in sqrt(S2): NaNs produced## Warning in cov2cor(Q): diag(V) had non-positive or NA entries; the non-finite
## result may be dubious## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = df_scaled)
## Overall MSA = NaN
## MSA for each item =
## HDI Cropland.Footprint
## NaN NaN
## Grazing.Footprint Forest.Footprint
## NaN NaN
## Carbon.Footprint Fish.Footprint
## NaN NaN
## Total.Ecological.Footprint Total.Biocapacity
## NaN NaN
## Biocapacity.Deficit.or.Reserve Earths.Required
## NaN NaNdf_selected2 <- df_selected[, names(df_selected) != "Total.Biocapacity"]
colnames(df_selected2)## [1] "HDI" "Cropland.Footprint"
## [3] "Grazing.Footprint" "Forest.Footprint"
## [5] "Carbon.Footprint" "Fish.Footprint"
## [7] "Total.Ecological.Footprint" "Biocapacity.Deficit.or.Reserve"
## [9] "Earths.Required"df_scaled2 <- scale(df_selected2)
KMO(df_scaled2)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = df_scaled2)
## Overall MSA = 0.8
## MSA for each item =
## HDI Cropland.Footprint
## 0.93 0.85
## Grazing.Footprint Forest.Footprint
## 0.73 0.69
## Carbon.Footprint Fish.Footprint
## 0.95 0.78
## Total.Ecological.Footprint Biocapacity.Deficit.or.Reserve
## 0.73 0.60
## Earths.Required
## 0.73Bartlett Test
cortest.bartlett(cor(df_scaled2), n = nrow(df_scaled2))## $chisq
## [1] 2756.2
##
## $p.value
## [1] 0
##
## $df
## [1] 36STANDARISASI DATA
df_scaled <- scale(df_selected2)df_scaled_matrix <- scale(df_selected2)attr(df_scaled, "scaled:center")## HDI Cropland.Footprint
## 0.6892226 0.5735638
## Grazing.Footprint Forest.Footprint
## 0.2565426 0.3647340
## Carbon.Footprint Fish.Footprint
## 1.7518617 0.1182979
## Total.Ecological.Footprint Biocapacity.Deficit.or.Reserve
## 3.3176064 0.7020745
## Earths.Required
## 1.9157447colMeans(df_scaled)## HDI Cropland.Footprint
## -2.318716e-16 -9.674774e-17
## Grazing.Footprint Forest.Footprint
## -6.352041e-17 5.755037e-17
## Carbon.Footprint Fish.Footprint
## 5.880528e-17 -2.629767e-17
## Total.Ecological.Footprint Biocapacity.Deficit.or.Reserve
## -2.744185e-17 4.775103e-18
## Earths.Required
## -6.874303e-19apply(df_scaled, 2, sd)## HDI Cropland.Footprint
## 1 1
## Grazing.Footprint Forest.Footprint
## 1 1
## Carbon.Footprint Fish.Footprint
## 1 1
## Total.Ecological.Footprint Biocapacity.Deficit.or.Reserve
## 1 1
## Earths.Required
## 1MELIHAT MEAN ASLI PAKE SCALE ()
attr(df_scaled_matrix, "scaled:center")## HDI Cropland.Footprint
## 0.6892226 0.5735638
## Grazing.Footprint Forest.Footprint
## 0.2565426 0.3647340
## Carbon.Footprint Fish.Footprint
## 1.7518617 0.1182979
## Total.Ecological.Footprint Biocapacity.Deficit.or.Reserve
## 3.3176064 0.7020745
## Earths.Required
## 1.9157447df_scaled <- as.data.frame(df_scaled)
head(df_scaled)## HDI Cropland.Footprint Grazing.Footprint Forest.Footprint
## 1 -1.5331435 -0.80108097 -0.1670847 -0.8228831
## 2 0.2727377 0.60451006 -0.1079842 -0.3315821
## 3 0.2727377 0.07741342 -0.2852857 -0.5627825
## 4 -1.1318366 -0.71323153 -0.3148360 -0.7072828
## 5 0.6071601 -0.15685175 -0.2261852 -0.3026820
## 6 0.9415825 0.60451006 1.5763803 -0.2159818
## Carbon.Footprint Fish.Footprint Total.Ecological.Footprint
## 1 -0.8591763 -0.7751770 -1.06608162
## 2 -0.4820238 -0.6441219 -0.46716088
## 3 -0.3344423 -0.7096495 -0.50512064
## 4 -0.8482444 -0.1854290 -1.00703310
## 5 -0.3344423 -0.3164841 0.86986643
## 6 -0.3672382 -0.1199015 -0.07490996
## Biocapacity.Deficit.or.Reserve Earths.Required
## 1 -0.08512833 -1.06287918
## 2 -0.14714337 -0.47147593
## 3 -0.18961942 -0.50798230
## 4 0.07713018 -1.00446899
## 5 -0.43683005 0.87195862
## 6 0.26147625 -0.06990582PRINCIPAL COMPONENT ANALYSIS
pca <- prcomp(df_scaled2, center = TRUE, scale. = TRUE)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.0089 1.0837 1.0148 0.9923 0.8679 0.73770 0.57982
## Proportion of Variance 0.4484 0.1305 0.1144 0.1094 0.0837 0.06047 0.03735
## Cumulative Proportion 0.4484 0.5789 0.6933 0.8027 0.8864 0.94690 0.98425
## PC8 PC9
## Standard deviation 0.37646 0.001763
## Proportion of Variance 0.01575 0.000000
## Cumulative Proportion 1.00000 1.000000Tentukan jumlah komponen
eigen_value <- pca$sdev^2
eigen_value## [1] 4.035797e+00 1.174348e+00 1.029837e+00 9.846036e-01 7.532913e-01
## [6] 5.442080e-01 3.361878e-01 1.417235e-01 3.107763e-06eigen_value[eigen_value > 1]## [1] 4.035797 1.174348 1.029837data.frame(
Komponen = paste0("PC", 1:length(pca$sdev)),
Eigenvalue = pca$sdev^2,
Proporsi_Varian = (pca$sdev^2) / sum(pca$sdev^2),
Kumulatif = cumsum((pca$sdev^2) / sum(pca$sdev^2))
)## Komponen Eigenvalue Proporsi_Varian Kumulatif
## 1 PC1 4.035797e+00 4.484219e-01 0.4484219
## 2 PC2 1.174348e+00 1.304831e-01 0.5789051
## 3 PC3 1.029837e+00 1.144263e-01 0.6933314
## 4 PC4 9.846036e-01 1.094004e-01 0.8027318
## 5 PC5 7.532913e-01 8.369903e-02 0.8864308
## 6 PC6 5.442080e-01 6.046756e-02 0.9468984
## 7 PC7 3.361878e-01 3.735420e-02 0.9842526
## 8 PC8 1.417235e-01 1.574706e-02 0.9999997
## 9 PC9 3.107763e-06 3.453070e-07 1.0000000Scree Plot
fviz_eig(pca, addlabels = TRUE)## Warning in geom_bar(stat = "identity", fill = barfill, color = barcolor, :
## Ignoring empty aesthetic: `width`.
prop_var <- eigen_value / sum(eigen_value)
cum_var <- cumsum(prop_var)
data.frame(
PC = paste0("PC", 1:length(eigen_value)),
Eigenvalue = eigen_value,
Proporsi = prop_var,
Kumulatif = cum_var
)## PC Eigenvalue Proporsi Kumulatif
## 1 PC1 4.035797e+00 4.484219e-01 0.4484219
## 2 PC2 1.174348e+00 1.304831e-01 0.5789051
## 3 PC3 1.029837e+00 1.144263e-01 0.6933314
## 4 PC4 9.846036e-01 1.094004e-01 0.8027318
## 5 PC5 7.532913e-01 8.369903e-02 0.8864308
## 6 PC6 5.442080e-01 6.046756e-02 0.9468984
## 7 PC7 3.361878e-01 3.735420e-02 0.9842526
## 8 PC8 1.417235e-01 1.574706e-02 0.9999997
## 9 PC9 3.107763e-06 3.453070e-07 1.0000000LOADINGS (INTERPRETASI)
loading <- pca$rotation
loading## PC1 PC2 PC3 PC4
## HDI 0.39962722 -0.11229071 -0.09806487 -0.03464002
## Cropland.Footprint 0.33813409 0.20592000 -0.22439714 0.26731629
## Grazing.Footprint 0.11793849 0.29904237 0.69433812 -0.44228385
## Forest.Footprint 0.21729301 0.58116165 -0.31467874 0.25513385
## Carbon.Footprint 0.43583516 -0.16854262 0.08556846 -0.05713497
## Fish.Footprint 0.10544646 -0.44297920 -0.47288446 -0.54142659
## Total.Ecological.Footprint 0.47859700 -0.02678479 0.09310399 -0.04532560
## Biocapacity.Deficit.or.Reserve -0.07514487 0.54013932 -0.33259280 -0.60509031
## Earths.Required 0.47860694 -0.02659784 0.09312930 -0.04514343
## PC5 PC6 PC7 PC8
## HDI -0.2136665 0.41554952 -0.77364141 0.004052255
## Cropland.Footprint 0.2872232 0.66253349 0.43730384 -0.093636086
## Grazing.Footprint 0.4246501 0.12689615 -0.10039717 -0.111507093
## Forest.Footprint 0.3502886 -0.47483509 -0.29608269 -0.122814494
## Carbon.Footprint -0.2901083 -0.22952148 0.19410073 -0.772357840
## Fish.Footprint 0.5166516 -0.09183116 0.01082753 -0.020220622
## Total.Ecological.Footprint -0.1036426 -0.19206130 0.16911231 0.428361924
## Biocapacity.Deficit.or.Reserve -0.4429702 0.10852156 0.13274722 0.015138940
## Earths.Required -0.1037479 -0.19240433 0.16877985 0.427820055
## PC9
## HDI -7.716656e-05
## Cropland.Footprint 1.889865e-04
## Grazing.Footprint 2.286860e-07
## Forest.Footprint -3.113628e-04
## Carbon.Footprint -3.025181e-04
## Fish.Footprint 1.469850e-04
## Total.Ecological.Footprint -7.069529e-01
## Biocapacity.Deficit.or.Reserve 4.339122e-05
## Earths.Required 7.072604e-01MENGAMBIL SAMPAI PC3 KARENA EIGENVALUE > 1
loading <- pca$rotation[,1:3]
round(loading,2)## PC1 PC2 PC3
## HDI 0.40 -0.11 -0.10
## Cropland.Footprint 0.34 0.21 -0.22
## Grazing.Footprint 0.12 0.30 0.69
## Forest.Footprint 0.22 0.58 -0.31
## Carbon.Footprint 0.44 -0.17 0.09
## Fish.Footprint 0.11 -0.44 -0.47
## Total.Ecological.Footprint 0.48 -0.03 0.09
## Biocapacity.Deficit.or.Reserve -0.08 0.54 -0.33
## Earths.Required 0.48 -0.03 0.09INTERPRETASI KOMPONEN
library(psych)
print.psych(loading, cut = 0.5)METODE FAKTOR AALYSIS (FA)
varcov = cov(df_scaled)
pc = eigen(varcov)
cat("eigen value:")## eigen value:pc$values## [1] 4.035797e+00 1.174348e+00 1.029837e+00 9.846036e-01 7.532913e-01
## [6] 5.442080e-01 3.361878e-01 1.417235e-01 3.107763e-06cat("eigen vector:")## eigen vector:pc$vectors## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.39962722 -0.11229071 -0.09806487 0.03464002 -0.2136665 0.41554952
## [2,] -0.33813409 0.20592000 -0.22439714 -0.26731629 0.2872232 0.66253349
## [3,] -0.11793849 0.29904237 0.69433812 0.44228385 0.4246501 0.12689615
## [4,] -0.21729301 0.58116165 -0.31467874 -0.25513385 0.3502886 -0.47483509
## [5,] -0.43583516 -0.16854262 0.08556846 0.05713497 -0.2901083 -0.22952148
## [6,] -0.10544646 -0.44297920 -0.47288446 0.54142659 0.5166516 -0.09183116
## [7,] -0.47859700 -0.02678479 0.09310399 0.04532560 -0.1036426 -0.19206130
## [8,] 0.07514487 0.54013932 -0.33259280 0.60509031 -0.4429702 0.10852156
## [9,] -0.47860694 -0.02659784 0.09312930 0.04514343 -0.1037479 -0.19240433
## [,7] [,8] [,9]
## [1,] 0.77364141 -0.004052255 -7.716656e-05
## [2,] -0.43730384 0.093636086 1.889865e-04
## [3,] 0.10039717 0.111507093 2.286860e-07
## [4,] 0.29608269 0.122814494 -3.113628e-04
## [5,] -0.19410073 0.772357840 -3.025181e-04
## [6,] -0.01082753 0.020220622 1.469850e-04
## [7,] -0.16911231 -0.428361924 -7.069529e-01
## [8,] -0.13274722 -0.015138940 4.339122e-05
## [9,] -0.16877985 -0.427820055 7.072604e-01sp = sum(pc$values[1:3])
L1 = sqrt(pc$values[1])*pc$vectors[,1]
L2 = sqrt(pc$values[2])*pc$vectors[,2]
L3 = sqrt(pc$values[3])*pc$vectors[,3]
L = cbind(L1,L2,L3)
cat("factor loading:")## factor loading:L## L1 L2 L3
## [1,] -0.8028229 -0.12168646 -0.09951709
## [2,] -0.6792875 0.22315005 -0.22772019
## [3,] -0.2369301 0.32406429 0.70462044
## [4,] -0.4365263 0.62978948 -0.31933875
## [5,] -0.8755621 -0.18264517 0.08683563
## [6,] -0.2118345 -0.48004481 -0.47988731
## [7,] -0.9614676 -0.02902597 0.09448275
## [8,] 0.1509607 0.58533466 -0.33751810
## [9,] -0.9614876 -0.02882337 0.09450844FA with function Principal
fa <- principal(df_scaled, nfactors = 3, rotate = "none")
fa## Principal Components Analysis
## Call: principal(r = df_scaled, nfactors = 3, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 h2 u2 com
## HDI 0.80 -0.12 0.10 0.67 0.331 1.1
## Cropland.Footprint 0.68 0.22 0.23 0.56 0.437 1.5
## Grazing.Footprint 0.24 0.32 -0.70 0.66 0.342 1.7
## Forest.Footprint 0.44 0.63 0.32 0.69 0.311 2.3
## Carbon.Footprint 0.88 -0.18 -0.09 0.81 0.192 1.1
## Fish.Footprint 0.21 -0.48 0.48 0.51 0.494 2.4
## Total.Ecological.Footprint 0.96 -0.03 -0.09 0.93 0.066 1.0
## Biocapacity.Deficit.or.Reserve -0.15 0.59 0.34 0.48 0.521 1.8
## Earths.Required 0.96 -0.03 -0.09 0.93 0.066 1.0
##
## PC1 PC2 PC3
## SS loadings 4.04 1.17 1.03
## Proportion Var 0.45 0.13 0.11
## Cumulative Var 0.45 0.58 0.69
## Proportion Explained 0.65 0.19 0.17
## Cumulative Proportion 0.65 0.83 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.08
## with the empirical chi square 83.74 with prob < 8e-13
##
## Fit based upon off diagonal values = 0.96df_scaled <- as.matrix(scale(df_selected2))
str(df_scaled)## num [1:188, 1:9] -1.533 0.273 0.273 -1.132 0.607 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:9] "HDI" "Cropland.Footprint" "Grazing.Footprint" "Forest.Footprint" ...
## - attr(*, "scaled:center")= Named num [1:9] 0.689 0.574 0.257 0.365 1.752 ...
## ..- attr(*, "names")= chr [1:9] "HDI" "Cropland.Footprint" "Grazing.Footprint" "Forest.Footprint" ...
## - attr(*, "scaled:scale")= Named num [1:9] 0.15 0.341 0.338 0.346 1.829 ...
## ..- attr(*, "names")= chr [1:9] "HDI" "Cropland.Footprint" "Grazing.Footprint" "Forest.Footprint" ...cor_matrix <- cor(df_scaled)
det(cor_matrix)## [1] 2.91713e-07round(cor(df_scaled), 2)## HDI Cropland.Footprint Grazing.Footprint
## HDI 1.00 0.52 0.08
## Cropland.Footprint 0.52 1.00 0.08
## Grazing.Footprint 0.08 0.08 1.00
## Forest.Footprint 0.21 0.44 0.06
## Carbon.Footprint 0.66 0.41 0.13
## Fish.Footprint 0.19 0.08 -0.05
## Total.Ecological.Footprint 0.70 0.54 0.25
## Biocapacity.Deficit.or.Reserve -0.08 -0.09 0.04
## Earths.Required 0.70 0.54 0.25
## Forest.Footprint Carbon.Footprint Fish.Footprint
## HDI 0.21 0.66 0.19
## Cropland.Footprint 0.44 0.41 0.08
## Grazing.Footprint 0.06 0.13 -0.05
## Forest.Footprint 1.00 0.20 -0.03
## Carbon.Footprint 0.20 1.00 0.16
## Fish.Footprint -0.03 0.16 1.00
## Total.Ecological.Footprint 0.36 0.87 0.17
## Biocapacity.Deficit.or.Reserve 0.10 -0.14 -0.01
## Earths.Required 0.36 0.87 0.16
## Total.Ecological.Footprint
## HDI 0.70
## Cropland.Footprint 0.54
## Grazing.Footprint 0.25
## Forest.Footprint 0.36
## Carbon.Footprint 0.87
## Fish.Footprint 0.17
## Total.Ecological.Footprint 1.00
## Biocapacity.Deficit.or.Reserve -0.14
## Earths.Required 1.00
## Biocapacity.Deficit.or.Reserve Earths.Required
## HDI -0.08 0.70
## Cropland.Footprint -0.09 0.54
## Grazing.Footprint 0.04 0.25
## Forest.Footprint 0.10 0.36
## Carbon.Footprint -0.14 0.87
## Fish.Footprint -0.01 0.16
## Total.Ecological.Footprint -0.14 1.00
## Biocapacity.Deficit.or.Reserve 1.00 -0.14
## Earths.Required -0.14 1.00df_reduced <- df_selected2[,
!(names(df_selected2) %in% c("Earths.Required"))
]
df_scaled <- scale(df_reduced)
det(cor(df_scaled))## [1] 0.0469538colnames(df_scaled)## [1] "HDI" "Cropland.Footprint"
## [3] "Grazing.Footprint" "Forest.Footprint"
## [5] "Carbon.Footprint" "Fish.Footprint"
## [7] "Total.Ecological.Footprint" "Biocapacity.Deficit.or.Reserve"Factor Analysis with rotation varimax
fa_1 <- principal(df_scaled, nfactors = 3, rotate = "varimax")
fa_1## Principal Components Analysis
## Call: principal(r = df_scaled, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 h2 u2 com
## HDI 0.83 -0.01 -0.11 0.70 0.30 1.0
## Cropland.Footprint 0.70 0.31 0.01 0.58 0.42 1.4
## Grazing.Footprint 0.21 -0.07 0.74 0.59 0.41 1.2
## Forest.Footprint 0.40 0.70 0.12 0.67 0.33 1.7
## Carbon.Footprint 0.87 -0.14 0.00 0.78 0.22 1.1
## Fish.Footprint 0.25 -0.10 -0.70 0.56 0.44 1.3
## Total.Ecological.Footprint 0.93 -0.01 0.09 0.88 0.12 1.0
## Biocapacity.Deficit.or.Reserve -0.21 0.72 -0.05 0.57 0.43 1.2
##
## RC1 RC2 RC3
## SS loadings 3.12 1.14 1.07
## Proportion Var 0.39 0.14 0.13
## Cumulative Var 0.39 0.53 0.67
## Proportion Explained 0.59 0.21 0.20
## Cumulative Proportion 0.59 0.80 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.09
## with the empirical chi square 86.22 with prob < 7.4e-16
##
## Fit based upon off diagonal values = 0.93scores <- factor.scores(df_scaled, fa_1, method = "regression")
head(scores$scores)## RC1 RC2 RC3
## [1,] -1.3043640 -0.4059612527 0.44008295
## [2,] -0.1618322 0.0001942359 0.25738952
## [3,] -0.2783624 -0.2909968041 0.17155656
## [4,] -1.1170970 -0.2500024208 -0.09504026
## [5,] 0.2653933 -0.4798952378 0.07169314
## [6,] 0.2980877 0.0451555327 1.01545927