Tugas1_Multivariat
Santi Laelatul M
2026-02-09
Implementasi PCA dan FA pada Fat Food Nutrition
library(readr) # import csv
library(psych) # MSA, PCA, FA
library(dplyr) # wrangling##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionIMPORT DATA
data <- read_csv("FastFoodNutritionMenuV3.csv")## Rows: 1147 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (14): Company, Item, Calories, Calories from
## Fat, Total Fat
## (g), Saturat...
##
## 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.head(data)## # A tibble: 6 × 14
## Company Item Calories `Calories from\nFat` `Total Fat\n(g)`
## <chr> <chr> <chr> <chr> <chr>
## 1 McDonald’s Hamburger 250 80 9
## 2 McDonald’s Cheeseburger 300 110 12
## 3 McDonald’s Double Cheeseburger 440 210 23
## 4 McDonald’s McDouble 390 170 19
## 5 McDonald’s Quarter Pounder® wi… 510 230 26
## 6 McDonald’s Double Quarter Poun… 740 380 42
## # ℹ 9 more variables: `Saturated Fat\n(g)` <chr>, `Trans Fat\n(g)` <chr>,
## # `Cholesterol\n(mg)` <chr>, `Sodium \n(mg)` <chr>, `Carbs\n(g)` <chr>,
## # `Fiber\n(g)` <chr>, `Sugars\n(g)` <chr>, `Protein\n(g)` <chr>,
## # `Weight Watchers\nPnts` <chr>dim(data)## [1] 1147 14data_nutrisi <- data[, -c(1, 2)]kode diatas untuk membuang variabel identitas (company dan item)
str(data_nutrisi)## tibble [1,147 × 12] (S3: tbl_df/tbl/data.frame)
## $ Calories : chr [1:1147] "250" "300" "440" "390" ...
## $ Calories from
## Fat : chr [1:1147] "80" "110" "210" "170" ...
## $ Total Fat
## (g) : chr [1:1147] "9" "12" "23" "19" ...
## $ Saturated Fat
## (g) : chr [1:1147] "3.5" "6" "11" "8" ...
## $ Trans Fat
## (g) : chr [1:1147] "0.5" "0.5" "1.5" "1" ...
## $ Cholesterol
## (mg) : chr [1:1147] "25" "40" "80" "65" ...
## $ Sodium
## (mg) : chr [1:1147] "520" "750" "1150" "920" ...
## $ Carbs
## (g) : chr [1:1147] "31" "33" "34" "33" ...
## $ Fiber
## (g) : chr [1:1147] "2" "2" "2" "2" ...
## $ Sugars
## (g) : chr [1:1147] "6" "6" "7" "7" ...
## $ Protein
## (g) : chr [1:1147] "12" "15" "25" "22" ...
## $ Weight Watchers
## Pnts: chr [1:1147] "247.5" "297" "433" "383" ...dim(data_nutrisi)## [1] 1147 12data_nutrisi_num <- data.frame(
lapply(data_nutrisi, function(x) {
x <- gsub(",", ".", x)
x <- gsub("[^0-9.]", "", x)
as.numeric(x)
})
)str(data_nutrisi_num)## 'data.frame': 1147 obs. of 12 variables:
## $ Calories : num 250 300 440 390 510 740 540 460 510 790 ...
## $ Calories.from.Fat : num 80 110 210 170 230 380 260 220 250 350 ...
## $ Total.Fat..g. : num 9 12 23 19 26 42 29 24 28 39 ...
## $ Saturated.Fat..g. : num 3.5 6 11 8 12 19 10 8 11 17 ...
## $ Trans.Fat..g. : num 0.5 0.5 1.5 1 1.5 2.5 1.5 1.5 1.5 2 ...
## $ Cholesterol..mg. : num 25 40 80 65 90 155 75 70 85 145 ...
## $ Sodium...mg. : num 520 750 1150 920 1190 1380 1040 720 960 2070 ...
## $ Carbs..g. : num 31 33 34 33 40 40 45 37 38 63 ...
## $ Fiber..g. : num 2 2 2 2 3 3 3 3 3 4 ...
## $ Sugars..g. : num 6 6 7 7 9 9 9 8 8 13 ...
## $ Protein..g. : num 12 15 25 22 29 48 25 24 27 45 ...
## $ Weight.Watchers.Pnts: num 248 297 433 383 502 ...colSums(is.na(data_nutrisi_num))## Calories Calories.from.Fat Total.Fat..g.
## 14 517 68
## Saturated.Fat..g. Trans.Fat..g. Cholesterol..mg.
## 68 68 14
## Sodium...mg. Carbs..g. Fiber..g.
## 14 68 68
## Sugars..g. Protein..g. Weight.Watchers.Pnts
## 14 68 271membersihkan dan konversi data ke numerik. kemudian kita cek dan bersihkan NA
data_nutrisi_num <- na.omit(data_nutrisi_num)Proses konversi dilakukan untuk memastikan seluruh variabel bertipe numerik. Observasi dengan missing valuekemudian dihapus agar tidak memengaruhi hasil analisis.
dim(data_nutrisi_num)## [1] 504 12Setelah proses ini, jumlah data menjadi 504 observasi
Assumptions
- Data Correlation
cor(data_nutrisi_num)## Calories Calories.from.Fat Total.Fat..g.
## Calories 1.0000000 0.8564877 0.8560343
## Calories.from.Fat 0.8564877 1.0000000 0.9997348
## Total.Fat..g. 0.8560343 0.9997348 1.0000000
## Saturated.Fat..g. 0.8538338 0.9018924 0.9024010
## Trans.Fat..g. 0.6584781 0.6407983 0.6405507
## Cholesterol..mg. 0.6672815 0.7406299 0.7398754
## Sodium...mg. 0.7211498 0.8680613 0.8682218
## Carbs..g. 0.6885597 0.2344647 0.2337730
## Fiber..g. 0.4848605 0.5532789 0.5528773
## Sugars..g. 0.3151264 -0.1750588 -0.1753243
## Protein..g. 0.7945189 0.8586232 0.8579541
## Weight.Watchers.Pnts 0.9905870 0.7869997 0.7865693
## Saturated.Fat..g. Trans.Fat..g. Cholesterol..mg.
## Calories 0.85383382 0.6584781 0.6672815
## Calories.from.Fat 0.90189237 0.6407983 0.7406299
## Total.Fat..g. 0.90240096 0.6405507 0.7398754
## Saturated.Fat..g. 1.00000000 0.7454114 0.7300517
## Trans.Fat..g. 0.74541135 1.0000000 0.3836053
## Cholesterol..mg. 0.73005166 0.3836053 1.0000000
## Sodium...mg. 0.71148884 0.4180755 0.7478659
## Carbs..g. 0.34536392 0.2968973 0.2143612
## Fiber..g. 0.37191957 0.1600745 0.4134973
## Sugars..g. 0.02329736 0.1080291 -0.1244729
## Protein..g. 0.81211217 0.7201252 0.6880122
## Weight.Watchers.Pnts 0.81419174 0.6343659 0.6143252
## Sodium...mg. Carbs..g. Fiber..g. Sugars..g. Protein..g.
## Calories 0.7211498 0.6885597 0.4848605 0.31512637 0.7945189
## Calories.from.Fat 0.8680613 0.2344647 0.5532789 -0.17505878 0.8586232
## Total.Fat..g. 0.8682218 0.2337730 0.5528773 -0.17532434 0.8579541
## Saturated.Fat..g. 0.7114888 0.3453639 0.3719196 0.02329736 0.8121122
## Trans.Fat..g. 0.4180755 0.2968973 0.1600745 0.10802907 0.7201252
## Cholesterol..mg. 0.7478659 0.2143612 0.4134973 -0.12447291 0.6880122
## Sodium...mg. 1.0000000 0.1342515 0.6311587 -0.29938854 0.8222226
## Carbs..g. 0.1342515 1.0000000 0.1439478 0.86564332 0.2145493
## Fiber..g. 0.6311587 0.1439478 1.0000000 -0.25537903 0.4727289
## Sugars..g. -0.2993885 0.8656433 -0.2553790 1.00000000 -0.1434103
## Protein..g. 0.8222226 0.2145493 0.4727289 -0.14341027 1.0000000
## Weight.Watchers.Pnts 0.6374389 0.7751406 0.4230806 0.44033505 0.7224764
## Weight.Watchers.Pnts
## Calories 0.9905870
## Calories.from.Fat 0.7869997
## Total.Fat..g. 0.7865693
## Saturated.Fat..g. 0.8141917
## Trans.Fat..g. 0.6343659
## Cholesterol..mg. 0.6143252
## Sodium...mg. 0.6374389
## Carbs..g. 0.7751406
## Fiber..g. 0.4230806
## Sugars..g. 0.4403351
## Protein..g. 0.7224764
## Weight.Watchers.Pnts 1.0000000The Measure of Sampling Adequacy (MSA)
#Check MSA
r <- cor(data_nutrisi_num)
KMO(r)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = r)
## Overall MSA = 0.73
## MSA for each item =
## Calories Calories.from.Fat Total.Fat..g.
## 0.63 0.86 0.86
## Saturated.Fat..g. Trans.Fat..g. Cholesterol..mg.
## 0.69 0.91 0.94
## Sodium...mg. Carbs..g. Fiber..g.
## 0.95 0.89 0.95
## Sugars..g. Protein..g. Weight.Watchers.Pnts
## 0.28 0.63 0.62Variabel Sugars <0.5, sehingga perlu dihapus terlebih dahulu
#Hapus Variabel Sugars
data_nutrisi_fix <- data_nutrisi_num[, !names(data_nutrisi_num) %in% "Sugars..g."]names(data_nutrisi_fix)## [1] "Calories" "Calories.from.Fat" "Total.Fat..g."
## [4] "Saturated.Fat..g." "Trans.Fat..g." "Cholesterol..mg."
## [7] "Sodium...mg." "Carbs..g." "Fiber..g."
## [10] "Protein..g." "Weight.Watchers.Pnts"dim(data_nutrisi_fix)## [1] 504 11#Cek Ulang
KMO (data_nutrisi_fix)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_nutrisi_fix)
## Overall MSA = 0.83
## MSA for each item =
## Calories Calories.from.Fat Total.Fat..g.
## 0.79 0.86 0.85
## Saturated.Fat..g. Trans.Fat..g. Cholesterol..mg.
## 0.89 0.86 0.91
## Sodium...mg. Carbs..g. Fiber..g.
## 0.92 0.65 0.75
## Protein..g. Weight.Watchers.Pnts
## 0.86 0.75Setelah penghapusan variabel Sugars, nilai KMO meningkat menjadi 0,83 yang termasuk kategori sangat baik
Bartlett Test
#Bartlett Test
cortest.bartlett(data_nutrisi_fix)## R was not square, finding R from data## $chisq
## [1] 14047.22
##
## $p.value
## [1] 0
##
## $df
## [1] 55p-value < 0,05 maka data layak untuk dilakukan PCA dan FA. PCA
manual
# scale data
scale_data = scale(data_nutrisi_fix)
r = cov(scale_data)
# eigen value and vector
pc <- eigen(r)
print(pc$values)## [1] 7.5599150202 1.3858015747 0.9136701166 0.5212132940 0.2449772090
## [6] 0.2203330632 0.0862490454 0.0633738728 0.0038089610 0.0004001546
## [11] 0.0002576885print(pc$vectors)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.3446145 0.24896683 0.10113517 -0.001578267 0.11969342 -0.04963096
## [2,] -0.3478539 -0.15912536 -0.05723691 0.011385538 0.35634942 0.19061187
## [3,] -0.3477525 -0.15948298 -0.05774151 0.011588059 0.35971559 0.19262259
## [4,] -0.3363975 0.01897338 -0.24021540 -0.087328074 0.07811748 0.45666647
## [5,] -0.2570856 0.16465013 -0.56811701 0.453543750 -0.41890997 0.05074449
## [6,] -0.2846761 -0.18197847 0.06163207 -0.685869996 -0.58942724 0.14898871
## [7,] -0.3111684 -0.31487366 0.16401115 -0.099067404 0.19746030 -0.49167184
## [8,] -0.1599026 0.71048843 0.32785888 -0.067368722 -0.07393845 -0.10842922
## [9,] -0.2055649 -0.28294414 0.64515722 0.534379070 -0.32658140 0.25081081
## [10,] -0.3275581 -0.13625522 -0.18479225 0.124189478 -0.18854124 -0.61157504
## [11,] -0.3272064 0.35229519 0.11889293 -0.025512883 0.11670569 -0.01885018
## [,7] [,8] [,9] [,10] [,11]
## [1,] -0.08139002 -0.13136568 -0.5200527540 0.701966064 0.071716784
## [2,] 0.03572033 -0.34294643 0.2694081862 0.057878795 -0.701522881
## [3,] 0.03822224 -0.33276109 0.2578592961 -0.092320441 0.704599804
## [4,] -0.26792373 0.72870973 0.0543109872 0.027283869 -0.002325821
## [5,] 0.44008713 -0.07975782 -0.0153556104 -0.002013183 0.000175021
## [6,] 0.07521995 -0.19049418 -0.0050502030 -0.005461041 0.001914357
## [7,] 0.56669753 0.40507019 -0.0328525036 -0.015621285 -0.005635080
## [8,] 0.10991731 0.07942229 0.5629219779 0.070483467 0.012033113
## [9,] -0.06394614 0.04408765 0.0008029042 -0.017308390 -0.001527239
## [10,] -0.61472282 -0.02890034 0.1872913056 -0.034636005 0.000372313
## [11,] -0.06572493 -0.08697667 -0.4839657478 -0.698484906 -0.077931645## variance proportion and cumulative variance
sumvar <- sum(pc$values)
propvar <- sapply(pc$values, function(x) x/sumvar)*100
cumvar <- data.frame(cbind(pc$values, propvar)) %>% mutate(cum = cumsum(propvar))
colnames(cumvar)[1] <- "eigen_value"
row.names(cumvar) <- paste0("PC",c(1:ncol(data_nutrisi_fix)))
print(cumvar)## eigen_value propvar cum
## PC1 7.5599150202 68.726500184 68.72650
## PC2 1.3858015747 12.598196134 81.32470
## PC3 0.9136701166 8.306091969 89.63079
## PC4 0.5212132940 4.738302673 94.36909
## PC5 0.2449772090 2.227065537 96.59616
## PC6 0.2203330632 2.003027847 98.59918
## PC7 0.0862490454 0.784082231 99.38327
## PC8 0.0633738728 0.576126117 99.95939
## PC9 0.0038089610 0.034626918 99.99402
## PC10 0.0004001546 0.003637769 99.99766
## PC11 0.0002576885 0.002342623 100.00000PC1 adalah komponen pertama karena memiliki eigenvalue terbesar (7.5599) dan menjelaskan 68.73% variasi data.
PC2 adalah komponen kedua karena memiliki eigenvalue terbesar kedua (1.3858) dan menjelaskan tambahan 12.60% variasi.
Jumlah komponen yang dipilih adalah 2 karena hanya dua komponen yang memiliki eigenvalue lebih dari 1 dan secara kumulatif sudah menjelaskan lebih dari 80% variasi data.
Komponen pertama menjelaskan 68,73% variasi data dan memiliki loading besar pada hampir seluruh variabel nutrisi seperti kalori, lemak, sodium, dan protein. Oleh karena itu, PC1 merepresentasikan tingkat keseluruhan kandungan nutrisi suatu makanan. Semakin tinggi skor PC1, semakin tinggi kandungan nutrisi secara umum.
Komponen kedua menjelaskan 12,60% variasi data dan menggambarkan perbedaan komposisi antar jenis nutrisi. PC2 membedakan makanan berdasarkan dominasi jenis nutrisi tertentu, seperti karbohidrat dibandingkan lemak atau protein.
# PCA result
scores <- as.matrix(scale_data) %*% pc$vectors
scores_PC <- scores[,1:2]
head(scores_PC)## [,1] [,2]
## 1 0.1656522 -0.5125493
## 2 -0.5552259 -0.6194535
## 3 -2.8396936 -0.6705301
## 4 -1.8345695 -0.6558239
## 5 -3.5491080 -0.7043036
## 6 -6.6437623 -0.7076868Langkah ini digunakan untuk menghitung skor komponen utama bagi setiap item makanan.
Skor ini merupakan representasi baru dari data dalam bentuk komponen utama.
Kolom pertama (PC1) menunjukkan tingkat kandungan nutrisi secara keseluruhan. Produk dengan skor PC1 tinggi memiliki kandungan kalori, lemak, dan nutrisi lainnya yang relatif tinggi. Sebaliknya, skor negatif menunjukkan kandungan nutrisi yang lebih rendah.
Kolom kedua (PC2) menunjukkan perbedaan komposisi jenis nutrisi antar produk. Nilai positif atau negatif menunjukkan dominasi jenis nutrisi tertentu dibandingkan yang lain.
PCA WITH FUNCTION PRINCIPAL
pc <- principal(data_nutrisi_fix, nfactors = ncol(data_nutrisi_fix), rotate = "none")
pc## Principal Components Analysis
## Call: principal(r = data_nutrisi_fix, nfactors = ncol(data_nutrisi_fix),
## rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## Calories 0.95 0.29 0.10 0.00 -0.06 -0.02 -0.02 -0.03 -0.03 -0.01
## Calories.from.Fat 0.96 -0.19 -0.05 0.01 -0.18 0.09 0.01 -0.09 0.02 0.00
## Total.Fat..g. 0.96 -0.19 -0.06 0.01 -0.18 0.09 0.01 -0.08 0.02 0.00
## Saturated.Fat..g. 0.92 0.02 -0.23 -0.06 -0.04 0.21 -0.08 0.18 0.00 0.00
## Trans.Fat..g. 0.71 0.19 -0.54 0.33 0.21 0.02 0.13 -0.02 0.00 0.00
## Cholesterol..mg. 0.78 -0.21 0.06 -0.50 0.29 0.07 0.02 -0.05 0.00 0.00
## Sodium...mg. 0.86 -0.37 0.16 -0.07 -0.10 -0.23 0.17 0.10 0.00 0.00
## Carbs..g. 0.44 0.84 0.31 -0.05 0.04 -0.05 0.03 0.02 0.03 0.00
## Fiber..g. 0.57 -0.33 0.62 0.39 0.16 0.12 -0.02 0.01 0.00 0.00
## Protein..g. 0.90 -0.16 -0.18 0.09 0.09 -0.29 -0.18 -0.01 0.01 0.00
## Weight.Watchers.Pnts 0.90 0.41 0.11 -0.02 -0.06 -0.01 -0.02 -0.02 -0.03 0.01
## PC11 h2 u2 com
## Calories 0.00 1 7.8e-16 1.2
## Calories.from.Fat -0.01 1 6.1e-15 1.2
## Total.Fat..g. 0.01 1 3.7e-15 1.2
## Saturated.Fat..g. 0.00 1 3.7e-15 1.4
## Trans.Fat..g. 0.00 1 2.2e-15 2.8
## Cholesterol..mg. 0.00 1 2.9e-15 2.2
## Sodium...mg. 0.00 1 3.1e-15 1.8
## Carbs..g. 0.00 1 3.7e-15 1.9
## Fiber..g. 0.00 1 6.7e-16 3.5
## Protein..g. 0.00 1 3.7e-15 1.5
## Weight.Watchers.Pnts 0.00 1 3.9e-15 1.5
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 7.56 1.39 0.91 0.52 0.24 0.22 0.09 0.06 0 0 0
## Proportion Var 0.69 0.13 0.08 0.05 0.02 0.02 0.01 0.01 0 0 0
## Cumulative Var 0.69 0.81 0.90 0.94 0.97 0.99 0.99 1.00 1 1 1
## Proportion Explained 0.69 0.13 0.08 0.05 0.02 0.02 0.01 0.01 0 0 0
## Cumulative Proportion 0.69 0.81 0.90 0.94 0.97 0.99 0.99 1.00 1 1 1
##
## Mean item complexity = 1.8
## Test of the hypothesis that 11 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 = 1pc <- principal(data_nutrisi_fix, nfactors = 2, rotate = "none")
pc## Principal Components Analysis
## Call: principal(r = data_nutrisi_fix, nfactors = 2, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 h2 u2 com
## Calories 0.95 0.29 0.98 0.016 1.2
## Calories.from.Fat 0.96 -0.19 0.95 0.050 1.1
## Total.Fat..g. 0.96 -0.19 0.95 0.051 1.1
## Saturated.Fat..g. 0.92 0.02 0.86 0.144 1.0
## Trans.Fat..g. 0.71 0.19 0.54 0.463 1.1
## Cholesterol..mg. 0.78 -0.21 0.66 0.341 1.1
## Sodium...mg. 0.86 -0.37 0.87 0.131 1.4
## Carbs..g. 0.44 0.84 0.89 0.107 1.5
## Fiber..g. 0.57 -0.33 0.43 0.570 1.6
## Protein..g. 0.90 -0.16 0.84 0.163 1.1
## Weight.Watchers.Pnts 0.90 0.41 0.98 0.019 1.4
##
## PC1 PC2
## SS loadings 7.56 1.39
## Proportion Var 0.69 0.13
## Cumulative Var 0.69 0.81
## Proportion Explained 0.85 0.15
## Cumulative Proportion 0.85 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.05
## with the empirical chi square 123.41 with prob < 4.5e-12
##
## Fit based upon off diagonal values = 1Loading tinggi (mendekati 1) pada variabel Calories (0.95), Total Fat (0.96), dan Protein (0.90) menunjukkan bahwa PC1 merepresentasikan kandungan energi dan lemak secara umum. Artinya, komponen pertama menggambarkan tingkat kepadatan nutrisi suatu makanan. Semakin tinggi skor PC1, semakin tinggi kandungan kalori dan lemaknya.
Loading tertinggi pada PC2 terdapat pada variabel Carbohydrates (0.84). Hal ini menunjukkan bahwa komponen kedua membedakan makanan berdasarkan kandungan karbohidrat. Dengan demikian, PC2 dapat diinterpretasikan sebagai dimensi variasi karbohidrat.
Nilai h2 menunjukkan proporsi variasi suatu variabel yang dapat dijelaskan oleh komponen utama. Seperti nilai h2 sebesar 0.98 pada variabel Calories berarti 99% variasi Calories telah dijelaskan oleh komponen yang terbentuk.
# score PC principal
L <- as.matrix(pc$loadings) # loadings
lambda <- pc$values # eigenvalues
lambda_k <- lambda[1:ncol(L)]
V <- sweep(L, 2, sqrt(lambda_k), "/") # eigenvector
scores_PC <- scale_data %*% as.matrix(V)
scores_PC## PC1 PC2
## 1 -0.16565219 -0.512549295
## 2 0.55522591 -0.619453534
## 3 2.83969355 -0.670530084
## 4 1.83456951 -0.655823855
## 5 3.54910801 -0.704303599
## 6 6.64376231 -0.707686813
## 7 3.43006419 -0.419624647
## 8 2.58810138 -0.475560304
## 9 3.36374857 -0.618808101
## 10 6.86244452 -0.707488170
## 11 6.28182319 -0.539413134
## 12 6.21636211 -0.278531178
## 13 0.66579843 -0.530323452
## 14 0.56372250 -0.586038396
## 15 2.43203303 -0.794821281
## 16 0.88835951 -1.012766010
## 17 1.89797608 -0.426177731
## 18 2.22284978 -1.172738439
## 19 3.14232456 -0.543925026
## 20 1.30781260 -1.167576070
## 21 2.31174180 -0.537236726
## 22 0.98478953 -0.611366201
## 23 0.41893366 -0.584731184
## 24 0.01668375 -0.863128802
## 25 0.33130427 -0.543284617
## 26 -0.10109951 -0.824050906
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## 518 0.76982204 1.641017203PC1 memiliki eigenvalue sebesar ±7,56 dan mampu menjelaskan sekitar 68,73% variasi data. Loading terbesar pada PC1 terdapat pada variabel Calories (0,95), Calories from Fat (0,96), Total Fat (0,96), Protein (0,90), dan Sodium (0,86). Hal ini menunjukkan bahwa PC1 merepresentasikan dimensi kepadatan energi dan lemak. Semakin tinggi nilai PC1, semakin tinggi kandungan kalori dan lemak suatu produk.
PC2 memiliki eigenvalue sebesar ±1,39 dan menjelaskan sekitar 12,60% variasi data. Variabel dengan loading terbesar pada PC2 adalah Carbs (0,84). Hal ini menunjukkan bahwa PC2 merepresentasikan dimensi karbohidrat. Produk dengan skor PC2 tinggi memiliki kandungan karbohidrat yang lebih dominan.
Secara keseluruhan, dua komponen utama (PC1 dan PC2) sudah mampu menjelaskan sekitar 81,33% total variasi data, sehingga reduksi menjadi 2 PC sudah cukup representatif untuk menggambarkan struktur data nutrisi.
PCA with function FactoMineR
library('FactoMineR')
library('factoextra')## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa#using library FactoMineR
# https://rpubs.com/cahyaalkahfi/pca-with-r
pca_result <- PCA(scale_data,
scale.unit = TRUE,
graph = FALSE,
ncp=ncol(data))
# summary pca result
pca_result$eig # vs print(cumvar)## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 7.5599150202 68.726500184 68.72650
## comp 2 1.3858015747 12.598196134 81.32470
## comp 3 0.9136701166 8.306091969 89.63079
## comp 4 0.5212132940 4.738302673 94.36909
## comp 5 0.2449772090 2.227065537 96.59616
## comp 6 0.2203330632 2.003027847 98.59918
## comp 7 0.0862490454 0.784082231 99.38327
## comp 8 0.0633738728 0.576126117 99.95939
## comp 9 0.0038089610 0.034626918 99.99402
## comp 10 0.0004001546 0.003637769 99.99766
## comp 11 0.0002576885 0.002342623 100.00000Berdasarkan hasil PCA menggunakan FactoMineR, komponen utama pertama memiliki eigenvalue sebesar 7,56 dan mampu menjelaskan 68,73% variasi data. Komponen kedua memiliki eigenvalue 1,39 dan menjelaskan 12,60% variasi data. Secara kumulatif, dua komponen utama telah menjelaskan 81,32% variasi total, sehingga reduksi data menjadi dua dimensi dinilai sudah representatif. Komponen ketiga dan seterusnya tidak dipertahankan karena memiliki eigenvalue kurang dari 1
pca_result$svd$V # vs pc$vectors## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.3446145 0.24896683 0.10113517 -0.001578267 -0.11969342 -0.04963096
## [2,] 0.3478539 -0.15912536 -0.05723691 0.011385538 -0.35634942 0.19061187
## [3,] 0.3477525 -0.15948298 -0.05774151 0.011588059 -0.35971559 0.19262259
## [4,] 0.3363975 0.01897338 -0.24021540 -0.087328074 -0.07811748 0.45666647
## [5,] 0.2570856 0.16465013 -0.56811701 0.453543750 0.41890997 0.05074449
## [6,] 0.2846761 -0.18197847 0.06163207 -0.685869996 0.58942724 0.14898871
## [7,] 0.3111684 -0.31487366 0.16401115 -0.099067404 -0.19746030 -0.49167184
## [8,] 0.1599026 0.71048843 0.32785888 -0.067368722 0.07393845 -0.10842922
## [9,] 0.2055649 -0.28294414 0.64515722 0.534379070 0.32658140 0.25081081
## [10,] 0.3275581 -0.13625522 -0.18479225 0.124189478 0.18854124 -0.61157504
## [11,] 0.3272064 0.35229519 0.11889293 -0.025512883 -0.11670569 -0.01885018
## [,7] [,8] [,9] [,10] [,11]
## [1,] -0.08139002 -0.13136568 -0.5200527540 -0.701966064 0.071716784
## [2,] 0.03572033 -0.34294643 0.2694081862 -0.057878795 -0.701522881
## [3,] 0.03822224 -0.33276109 0.2578592961 0.092320441 0.704599804
## [4,] -0.26792373 0.72870973 0.0543109872 -0.027283869 -0.002325821
## [5,] 0.44008713 -0.07975782 -0.0153556104 0.002013183 0.000175021
## [6,] 0.07521995 -0.19049418 -0.0050502030 0.005461041 0.001914357
## [7,] 0.56669753 0.40507019 -0.0328525036 0.015621285 -0.005635080
## [8,] 0.10991731 0.07942229 0.5629219779 -0.070483467 0.012033113
## [9,] -0.06394614 0.04408765 0.0008029042 0.017308390 -0.001527239
## [10,] -0.61472282 -0.02890034 0.1872913056 0.034636005 0.000372313
## [11,] -0.06572493 -0.08697667 -0.4839657478 0.698484906 -0.077931645Berdasarkan matriks eigenvector dari FactoMineR, PC1 memiliki loading positif yang relatif besar pada hampir seluruh variabel nutrisi, sehingga merepresentasikan dimensi total kandungan energi dan lemak makanan. Sementara itu, PC2 didominasi oleh variabel karbohidrat dengan loading sebesar 0.71, sehingga merepresentasikan variasi kandungan karbohidrat
pca_result$ind['coord'] # vs head(scores)## $coord
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## 1 -0.16581677 -0.513058534 0.082281195 0.7754382074 0.486434872
## 2 0.55577755 -0.620068987 0.055213960 0.5904702273 0.326277303
## 3 2.84251491 -0.671196283 -1.033976946 0.9387019806 0.580411455
## 4 1.83639223 -0.656475443 -0.504196838 0.7575559503 0.458950681
## 5 3.55263420 -0.705003354 -0.590989995 1.2091548742 0.726408664
## 6 6.65036317 -0.708389930 -1.930702511 1.4500977180 1.026611805
## 7 3.43347211 -0.420041562 -0.449464738 1.3465826279 0.465079607
## 8 2.59067277 -0.476032793 -0.573087973 1.4902794805 0.851521259
## 9 3.36709060 -0.619422913 -0.631714695 1.2984876064 0.653895465
## 10 6.86926265 -0.708191089 -0.390431933 1.3241249044 0.690512009
## 11 6.28806444 -0.539949063 -0.451515022 1.4527424658 0.726603798
## 12 6.22253833 -0.278807911 -0.741701809 1.5879429342 0.912049896
## 13 0.66645993 -0.530850351 0.659898068 0.2712842751 -0.307854279
## 14 0.56428258 -0.586620650 0.773333415 0.2688890675 -0.302938458
## 15 2.43444936 -0.795610969 0.942693150 0.2607161054 -0.463010008
## 16 0.88924213 -1.013772236 1.542155473 0.8601648332 0.942852340
## 17 1.89986180 -0.426601157 1.326677231 0.5636819667 -0.304691327
## 18 2.22505827 -1.173903604 1.383659234 0.6237002475 0.646557436
## 19 3.14544659 -0.544465439 1.209263166 0.3254262766 -0.567735761
## 20 1.30911197 -1.168736106 1.511015801 0.7660214108 0.928832178
## 21 2.31403861 -0.537770493 1.317662002 0.4595957185 -0.341171446
## 22 0.98576796 -0.611973619 0.278138500 -0.1025908583 -0.420668931
## 23 0.41934988 -0.585312139 0.180912584 -0.0423192683 -0.588442148
## 24 0.01670032 -0.863986357 0.074031935 -0.1129464181 -0.030143499
## 25 0.33163344 -0.543824393 0.181438679 -0.0392721311 -0.514899606
## 26 -0.10119996 -0.824869635 0.095405697 -0.1021826444 0.050489824
## 27 0.33155174 -0.529924096 0.205094553 -0.0479834507 -0.500106083
## 28 -0.07656379 -0.820293005 0.115651220 -0.1102161646 0.040603418
## 29 1.93853263 -0.732588461 -0.963935506 0.2750615551 0.112414577
## 30 6.94496479 -0.578320297 -0.407743992 1.3108687954 0.691583067
## 31 2.04984277 -0.655304690 -0.985963588 0.2588910932 0.075783700
## 32 2.48250666 -0.764230872 -1.077123762 0.9949747952 0.476083478
## 33 2.47963914 -0.604235285 -1.184824995 1.0669758095 0.541142112
## 34 1.03523209 -0.498531718 -0.989470355 0.5831626507 0.125836501
## 35 -0.88697464 -0.590689632 1.009812853 0.9875055635 0.108979128
## 36 0.41271686 -0.429671162 2.103426499 1.6235216796 0.018040884
## 37 1.38456215 -0.191580042 2.694276987 1.9317167185 -0.138476060
## 38 -2.72761121 -0.818860889 -0.539751581 -0.0104662983 0.133051779
## 39 -2.68779004 -1.023128319 -0.532537924 -0.0337030946 0.079291850
## 40 -0.89793047 -0.966084041 -0.092221667 0.1258532788 -0.172764563
## 41 -0.01920702 -0.933429499 -0.033516163 -0.0239555403 -0.430887119
## 42 1.93641884 -1.044125375 0.494172455 0.0828254388 -0.788134998
## 43 -2.48504427 -0.619052501 -0.365522140 -0.0630155876 0.057581761
## 44 -2.64336043 -0.456113812 -0.449182258 -0.0122970303 0.158409776
## 45 -2.05696379 -1.108280045 0.429059057 0.6213901733 0.417930865
## 46 -2.55257869 -0.550713920 -0.401118288 -0.0415145009 0.100437543
## 47 1.09262821 -0.912597513 -0.371544531 -0.4687664798 -0.978316677
## 48 3.73947190 -0.960955996 -0.210780068 -0.8136712683 -1.766563098
## 49 -1.72650419 -1.490066147 0.042189407 0.2003798942 -0.259967054
## 50 -1.15640224 -0.955372387 -0.615635240 -0.1611697468 -0.911554937
## 51 -2.42700682 -0.623226698 -0.428951520 -0.0761047480 0.026327635
## 52 -2.33663061 -0.683527198 0.083799170 0.2921279904 0.289356948
## 53 1.24607274 -1.853765269 2.207137467 1.5390436715 1.404646912
## 54 1.98015003 -1.529977974 2.300354218 1.6058739460 0.606768835
## 55 -0.93038330 -1.471094939 2.104630206 2.0039325897 1.257631337
## 56 0.84790193 -1.964295109 0.628249943 0.3609383999 0.915498041
## 57 1.61630667 -1.623853697 0.684056095 0.4114830840 0.130114592
## 58 -0.93547777 -1.354009883 0.651200043 0.8218085500 0.530032830
## 59 0.32158648 -1.850481105 0.657443724 0.4960333002 1.006433606
## 60 1.05366790 -1.506198119 0.730861529 0.5562492650 0.232036920
## 61 -1.48016685 -1.293625073 0.647114482 0.9704421560 0.658393423
## 62 -2.60777680 -0.922661009 -0.148094081 0.3700413055 0.401776322
## 63 -2.29052342 -0.824867160 -0.039473819 0.3413404105 0.267541078
## 64 -1.19978461 -0.268386624 0.577662574 0.6126268096 0.150862708
## 65 -1.88367912 -0.756409746 -0.395644551 -0.2492335903 -0.148829979
## 66 -0.80347666 -1.063109970 -0.552918968 -0.2839048860 -0.942661851
## 67 -2.13697565 -1.181755938 -0.328575612 -0.1320712947 -0.270105027
## 68 -2.06300236 -1.050356111 -0.283705184 -0.1323170557 -0.237189466
## 69 -1.07434197 -0.930483906 -0.422950419 -0.2992617368 -0.747876283
## 70 1.17713799 -1.414501270 0.672610175 -1.6336718678 1.644367928
## 71 1.15425975 -0.941802413 0.431173017 0.1325927968 -0.619469733
## 72 2.83557699 -1.512386663 0.482114550 -1.9058360028 0.889039926
## 73 -1.52388824 -0.551999375 0.610890217 0.6476767339 0.336652660
## 74 2.51906959 -1.287441301 0.612888318 -1.6357024623 0.544631122
## 75 3.08908009 -1.342470719 1.160523539 -1.3177949274 0.495839803
## 76 3.46294654 -1.363980663 0.491990302 -1.7582749015 0.129540645
## 77 4.11936494 -1.426180101 0.993645456 -1.4549483224 0.039891572
## 78 1.81252801 -0.837740766 0.443880007 0.1131050247 -1.201208131
## 79 2.43666051 -0.946165973 0.926523015 0.4195862930 -1.283494322
## 80 1.45485692 -0.745986463 0.650481779 0.1971795107 -0.718873689
## 81 2.10636827 -0.829989193 1.142075680 0.5025734844 -0.810791766
## 82 5.27337195 -1.060322921 0.332818997 -1.0403020929 1.390302458
## 83 2.08724243 -0.916767611 0.924604183 -1.6393867437 0.931636305
## 84 3.75575524 -1.139267419 0.791221620 -1.9044641266 0.225551328
## 85 1.37576581 -0.523793779 0.732775223 0.1133255568 -0.833983727
## 86 6.79906810 -2.044976255 1.229922769 -4.0791754752 1.650649928
## 87 7.45540830 -2.136602717 1.724276453 -3.7756339528 1.555303341
## 88 9.64269730 -1.111790609 3.357582911 -3.4033153167 1.706375227
## 89 10.26685779 -1.185292405 3.852985317 -3.0986714675 1.641600811
## 90 0.63921198 -0.981458875 0.083685606 -0.8212871065 0.037505287
## 91 5.22185573 -1.683581093 0.648015338 -2.3817765973 1.704235979
## 92 0.01348010 0.067062681 1.503863275 0.6957124505 0.215996156
## 93 1.97980460 -0.160016727 1.361987210 0.3716196701 -0.519718850
## 94 -2.08570027 0.598095619 0.015673540 -0.1007112208 0.090463591
## 95 -2.41022881 -0.880709353 -0.663480190 -0.0122580967 -0.112405291
## 96 -1.37107190 -0.926110673 0.469159639 0.6181807825 -0.051429983
## 97 -2.70177114 -0.560979669 -0.493744815 -0.0042595189 0.166985531
## 98 -2.70177114 -0.560979669 -0.493744815 -0.0042595189 0.166985531
## 99 3.75471046 -0.933471362 0.907178409 -1.0611245400 1.155151182
## 100 -0.46055639 -0.067618488 2.217297003 1.5429457080 0.948744352
## 101 -0.63283307 -0.328914722 2.078663766 1.5750407432 0.981295454
## 105 -1.76310146 -0.103295743 0.178793544 0.2595985117 0.261310926
## 106 -2.51241791 -0.389174044 -0.390939304 -0.0695559083 0.144814070
## 107 -1.80952596 -0.134340777 -0.382208674 -0.1715188609 0.034112708
## 108 -2.54651561 -0.619879651 -0.531370900 -0.0452176711 0.144446075
## 109 -0.80438395 0.461506526 0.306859899 0.0145348057 0.106829410
## 110 -0.36950950 0.752860227 0.425503578 -0.0726054833 0.013588491
## 111 -0.04441902 0.366512328 0.670440278 0.3155997859 0.065109396
## 112 -2.34074237 -0.985917512 -0.213742292 0.3819973522 0.222850608
## 113 3.59864359 1.888799019 0.903169606 1.2607797395 0.403061153
## 114 2.30994333 1.469840513 0.545148108 1.0854452542 0.531603876
## 115 -0.28067300 -0.645224784 1.268243240 1.2353267909 0.132313159
## 116 1.05188265 0.484989140 1.259724363 0.6413894510 -0.450979163
## 117 -0.96559140 0.152277785 0.343646302 0.2115625456 -0.224738112
## 118 -1.43139419 -0.430122130 -0.035351234 0.1855849091 -0.071073640
## 119 -1.58812212 -0.422968585 0.037406687 0.1881819497 0.040189141
## 120 -1.65142302 -0.235922176 -0.428289116 -0.1234865619 -0.275506267
## 121 -2.38316112 -0.133013479 -0.280739225 -0.0899701062 0.131265631
## 122 1.86644460 2.079377297 -0.231148057 0.3599276376 0.209400805
## 123 2.84933837 2.824787600 0.009308779 0.2102950342 0.057966636
## 124 4.22103162 3.799260524 -0.191180609 0.3525850410 0.186323673
## 125 0.51172227 1.385599555 0.131588644 0.1799076922 0.283096644
## 126 1.70580205 2.289606559 -0.069002926 0.3883084540 0.434861750
## 127 3.05257574 3.251879082 0.237429308 0.1251315996 0.266220978
## 128 6.26991803 5.404160733 0.462556213 0.7676875417 0.720011707
## 129 0.98638955 0.863971232 0.207487811 0.5501620507 0.117221486
## 130 0.01413856 0.300101667 0.706927713 0.2879657461 0.023840715
## 131 1.65319601 2.244439865 -0.707811584 0.0258658170 0.025243975
## 132 2.60984435 2.982206268 -0.463608981 -0.1716616696 -0.100384921
## 133 3.95224979 3.944358851 -0.699324105 0.0293942936 0.024646176
## 134 0.26970598 1.495401491 -0.361803477 -0.1527496975 0.103341655
## 135 1.41828546 2.378961907 -0.585102996 0.0629151496 0.282573170
## 136 2.71696910 3.309858518 -0.291631953 -0.2032279102 0.088150731
## 137 5.64195551 5.595836364 -0.539601024 0.0950804745 0.369674880
## 138 1.46355906 2.098111791 -0.765626073 0.0704013967 0.022557701
## 139 2.46784753 2.779734643 -0.549973544 -0.1151165932 -0.115322180
## 140 3.70594672 3.724754748 -0.730919499 0.0490227328 0.069982392
## 141 5.61918273 5.529151804 -0.554143557 0.0955890184 0.370365717
## 142 0.23221029 1.467844858 -0.356505229 -0.1625273860 0.084659847
## 143 1.38255086 2.303377340 -0.603357884 0.0633868657 0.287753727
## 144 2.70958850 3.276266318 -0.292303388 -0.2056043044 0.087370816
## 145 -1.97605683 -0.581922046 -0.567867846 -0.0614054226 0.133732387
## 146 -1.51383553 -0.302744188 0.051452761 0.3032746217 0.252119182
## 147 -2.42886234 -0.087961649 -0.283661462 -0.0445309322 0.124223262
## 148 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 149 -2.20247809 0.181062822 -0.202341531 -0.0407043936 0.127499178
## 150 -2.01007109 0.474523097 -0.088110176 -0.0537696842 0.121909500
## 151 -1.61552318 1.119133708 0.177868478 -0.0949446450 0.084227752
## 152 -2.36900620 0.083371112 -0.214245456 -0.0567833006 0.128829097
## 153 -2.18802646 0.433313398 -0.060911567 -0.0859752636 0.108170449
## 154 -1.90876518 0.994601614 0.184086487 -0.1325289284 0.080858774
## 155 -1.45781160 1.885723990 0.570262940 -0.2051276467 0.033034906
## 156 -2.84434709 -0.864707063 -0.615056266 0.0161403334 0.178639346
## 157 -2.84127735 -0.867813362 -0.613438259 0.0151630113 0.176691355
## 158 -2.83513785 -0.874025960 -0.610202246 0.0132083670 0.172795375
## 159 -2.82592862 -0.883344857 -0.605348225 0.0102764007 0.166951405
## 160 -2.35987516 0.044625191 -0.216692905 -0.0595003237 0.117287611
## 161 -2.17582567 0.391461177 -0.061741009 -0.0896696088 0.094680973
## 162 -1.89664259 0.923322370 0.175955575 -0.1360083304 0.061671783
## 163 -1.43962772 1.778805123 0.558066573 -0.2103467496 0.004254419
## 164 -2.32604403 0.180543164 -0.175300122 -0.0634020356 0.126549806
## 165 -2.13884660 0.553699875 -0.011428750 -0.0947635861 0.107692693
## 166 -1.79239223 1.210261894 0.272546056 -0.1478310151 0.064720316
## 167 -1.30469416 2.175341896 0.687130361 -0.2248788809 0.012815623
## 168 -2.50288643 -0.266168746 -0.327375216 -0.0442269283 0.129636823
## 169 -2.36756834 -0.045647803 -0.221240592 -0.0663808272 0.106494889
## 170 -2.13105536 0.324258724 -0.036426735 -0.1064438634 0.063356908
## 171 -1.78967289 0.893370018 0.243952846 -0.1665961818 0.008656870
## 172 -2.85048658 -0.858494464 -0.618292279 0.0180949776 0.182535326
## 173 -2.84741684 -0.861600763 -0.616674272 0.0171176555 0.180587336
## 174 -2.84434709 -0.864707063 -0.615056266 0.0161403334 0.178639346
## 175 -2.83637030 -0.846010070 -0.603377007 0.0130956167 0.178960360
## 176 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
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## 399 -1.45603450 0.053795369 -0.294197941 -0.2570904893 -0.022133138
## 400 -1.53042041 -0.082262751 -0.352344735 -0.2466463219 -0.011945385
## 401 -0.98949684 0.417902996 0.373588832 0.0498346136 0.126382140
## 402 -1.15285404 0.355162404 -0.151966374 -0.3023739293 -0.121292565
## 403 -1.36500098 -0.384085324 -0.014689099 0.1648248341 -0.084993338
## 404 0.97716071 -0.834150804 0.051935757 -1.1879095367 0.280983635
## 405 2.92170038 -1.084652756 -0.101493745 -1.5500671250 -0.400301157
## 406 1.53506174 -1.109405969 0.150912541 -1.3497893699 0.260685237
## 407 1.42857724 -0.932724994 0.050385188 -1.2984495713 0.163206793
## 408 4.81054346 -1.439001755 -0.557593033 -1.5529003379 -0.468498057
## 409 4.18769222 -1.143610142 -0.595784630 -1.4217428525 -0.366070271
## 410 5.75368869 -1.326308900 -0.775878608 -1.6588909520 -0.962310573
## 411 4.43224658 -1.353943797 -0.562407872 -1.4758989212 -0.318934252
## 412 5.39697938 -1.905452852 -0.064205102 -2.0648684158 -1.307799761
## 413 2.39159126 -1.466173292 0.131671031 -1.5068448348 -0.256628765
## 414 3.77340104 -1.433796347 -0.123495038 -1.7052701386 -0.914186649
## 415 2.25334553 -1.268709126 0.044793457 -1.4644627603 -0.367402749
## 416 1.33363468 -0.863247907 0.168423669 -0.1583206764 -1.321158817
## 417 1.78097475 -1.497627842 0.919507399 -0.4179942661 0.303381156
## 418 6.24032368 -1.304865392 1.474400616 -2.4093369764 0.388049131
## 419 6.94678825 -0.353561547 2.874730084 -2.5399350249 0.539313606
## 420 6.80288370 -0.704140298 2.879999189 -1.9744955582 0.737156381
## 421 2.57218532 0.467944275 0.666801541 -0.6939428690 -1.263987004
## 422 -0.25719800 -1.001675487 1.005721379 0.8800066195 -0.385024995
## 423 2.45863819 -1.322552652 3.050693437 2.0976421236 -0.728222515
## 424 4.18388908 -1.393447123 4.166485462 2.6703520570 -1.118897498
## 425 -1.05631171 -0.265593175 0.173354171 0.2539008850 -0.371986469
## 426 0.13346145 0.083277248 0.864697558 0.5320266141 -0.634343867
## 427 -2.25823097 -0.960715095 -0.650725279 -0.1126099217 -0.007577336
## 428 -2.73209140 -0.840391025 -0.539373008 -0.0128546174 0.132023752
## 429 -2.09800034 -0.896483237 -0.596099473 -0.0864053288 -0.284156056
## 430 -2.72920658 -0.621030892 -0.519771458 0.0007254964 0.168665873
## 431 -2.34499784 0.107861813 -0.197235836 -0.0607685115 0.122712402
## 432 -2.48663271 -0.696341261 -0.368354218 -0.0696341196 0.045464741
## 433 -1.48192470 -0.894306419 -0.687509989 -0.1052484463 -0.663281795
## 434 -1.92375989 -1.011513682 -0.530729110 -0.1182864687 -0.393689238
## 435 -1.34206665 -0.933674835 -0.584606085 -0.2375982801 -0.671007211
## 436 -2.05540659 -0.717098070 -0.480264631 -0.1349136521 -0.202952278
## 437 -2.19061926 -0.542727360 -0.506207613 0.0109813379 0.260506834
## 438 -1.67914954 -0.144003593 -0.357058694 -0.1457741617 0.115324618
## 439 -0.99283375 0.850501482 1.617387831 0.9258800581 0.664963247
## 440 2.82678039 2.494928476 0.528004409 -0.2369311913 -0.325942255
## 441 3.16417177 2.473215984 0.556529523 -0.3182517491 -0.429897398
## 442 1.49544852 1.955149200 0.343097995 -0.8334715520 -0.555425770
## 443 1.81427588 1.894449729 0.869577651 -0.5094721210 -0.414171485
## 444 1.76395533 2.436064109 0.560861390 -0.8763462277 -0.593518551
## 446 -1.88727696 0.972857520 0.195412534 -0.1393701833 0.067222843
## 447 -1.62359901 1.461396161 0.410416147 -0.1803924077 0.032558573
## 448 -1.35452651 2.237571232 0.773607408 -0.2568804077 0.061203974
## 449 -0.52858951 3.522303953 1.327972031 -0.3582612091 -0.102934802
## 451 -2.81057989 -0.898876353 -0.597258192 0.0053897901 0.157211454
## 452 -2.80137065 -0.908195251 -0.592404172 0.0024578237 0.151367484
## 453 -2.77988242 -0.929939345 -0.581078125 -0.0043834311 0.137731553
## 454 -2.75532446 -0.954789738 -0.568134071 -0.0122020080 0.122147633
## 456 -1.87208463 0.898471977 0.188899629 -0.1438269073 0.046087862
## 457 -1.63279398 1.330054818 0.389268886 -0.1845242160 0.013409972
## 458 -1.07458421 2.334923156 0.850059117 -0.2767717725 -0.064003438
## 459 -0.51645265 3.310364470 1.303547879 -0.3688043857 -0.147114364
## 461 -1.97451195 0.777102283 0.117045634 -0.1260305203 0.072248894
## 462 -1.74757848 1.191683297 0.303641395 -0.1626035972 0.041665450
## 463 -1.24767963 2.114911079 0.717396258 -0.2433458082 -0.023728720
## 464 -0.76849347 3.031002244 1.133403255 -0.3259432482 -0.078702519
## 466 -1.73091911 1.177562935 0.312207659 -0.1675924008 0.031458030
## 467 -1.45488398 1.683103403 0.540984768 -0.2127388569 -0.005300686
## 468 -1.05109825 2.626873937 0.995042170 -0.3101779331 -0.010179198
## 469 -0.51655775 3.698969449 1.490618026 -0.4110988380 -0.059321161
## 471 -1.83817529 1.063816973 0.237593881 -0.1479435625 0.061047572
## 472 -1.57142759 1.549249315 0.454215501 -0.1899431090 0.024435312
## 473 -0.98568258 2.637394176 0.938559564 -0.2837078467 -0.051214954
## 474 -0.64012956 3.528951177 1.352883067 -0.3698565205 -0.038376710
## 476 -1.80281964 1.106936442 0.258224034 -0.1520755738 0.051736701
## 477 -1.56030285 1.594267032 0.474814235 -0.1941800911 0.028505852
## 478 -0.96658105 2.701108886 0.970837557 -0.2909895454 -0.046823400
## 479 -0.40199720 3.788045697 1.456768209 -0.3858365760 -0.111040245
## 481 -1.82229990 1.071783935 0.253650929 -0.1538180526 0.055992086
## 482 -1.55248245 1.554109978 0.471890556 -0.1967949212 0.017431836
## 483 -0.96059795 2.636042240 0.959470632 -0.2925143031 -0.062114410
## 484 -0.60714633 3.516869211 1.378171924 -0.3814927503 -0.054652667
## 486 -2.78772577 -0.816942738 -0.566121864 0.0010768856 0.162957259
## 487 -2.77667923 -0.801352045 -0.552824599 -0.0029451532 0.161330284
## 488 -2.74314773 -0.796137276 -0.529343007 -0.0118864851 0.147484763
## 489 -2.70777892 -0.766012917 -0.497418170 -0.0219178895 0.137856238
## 491 -2.30739096 0.250186440 -0.143687674 -0.0699107981 0.131954412
## 492 -2.11082789 0.672878301 0.039640656 -0.1046342016 0.118648359
## 493 -1.75500790 1.378975471 0.343072420 -0.1610634835 0.081227042
## 495 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 496 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 497 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 498 -2.49482298 -0.211251342 -0.329463453 -0.0379044177 0.133718979
## 499 -2.20285680 0.209625026 -0.174636642 -0.0497285712 0.136146118
## 500 -2.24931465 0.243545925 -0.118556713 -0.0807713139 0.102842624
## 501 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 502 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 503 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 504 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 505 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 506 -2.85355633 -0.855388165 -0.619910286 0.0190722998 0.184483316
## 507 -1.56657620 -0.240766352 -0.479580974 -0.3026861014 -0.169254049
## 508 -1.18216837 -0.050716429 -0.438943641 -0.3675146131 -0.272728693
## 509 -0.68944848 0.182711838 -0.404120799 -0.5041248539 -0.402145393
## 510 -1.28098243 -0.237187869 0.022261089 0.0428564347 0.042010141
## 511 -0.82156597 0.037097455 0.068780286 -0.0545171240 -0.099879453
## 512 -0.18012851 0.119056817 0.583248886 0.1813465372 -0.005555017
## 513 -0.48142915 0.396141542 0.296318113 -0.0542420401 -0.011431716
## 514 0.22914437 0.940259620 0.477148877 -0.2107045533 -0.098130735
## 515 0.98891287 1.478197957 0.695437332 -0.3439918701 -0.214201774
## 516 -0.59311714 0.565284853 -0.122466887 -0.4520201034 -0.193908957
## 517 0.09696211 1.118005928 0.053541932 -0.5652168397 -0.316679404
## 518 0.77058689 1.642647623 0.270830833 -0.7051893766 -0.414938113
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## 1 -0.2017425279 0.201167184 0.1409395362 6.843351e-03 -2.132705e-02
## 2 -0.2935350222 0.188503668 0.4174442408 6.739557e-03 -2.177750e-02
## 3 -0.4074395681 0.602036454 0.5017876463 7.068917e-03 -1.152898e-03
## 4 -0.4276687907 0.277326768 0.2770895588 -4.343358e-03 -5.393622e-03
## 5 -0.3648508324 0.346488463 0.4908638214 -9.972234e-03 5.888134e-03
## 6 -0.4277007471 -0.051336254 0.2606792834 -1.566672e-02 1.839069e-02
## 7 -0.1403306695 0.484756452 0.0014703992 -1.066427e-02 -4.987905e-03
## 8 -0.0195148372 0.267320339 -0.2284128161 7.922252e-04 -1.876856e-03
## 9 -0.0646675498 0.241388030 0.0950396209 3.920011e-03 5.361937e-03
## 10 -1.1664265459 0.592948186 0.8357763812 -4.377641e-02 2.500278e-03
## 11 -0.6248916461 0.498855166 0.4789882609 1.776930e-02 -8.230573e-03
## 12 -0.2128538416 -0.364987130 0.1043109960 5.707333e-02 -2.738060e-02
## 13 -0.3041147967 -0.174808995 -0.2716227270 -6.521224e-03 -3.291005e-02
## 14 -0.5406804860 0.117560375 -0.0505926186 9.433518e-04 -3.248933e-02
## 15 -0.1107619757 -0.499233018 0.3182793705 2.701265e-02 -1.051550e-02
## 16 -1.1025409664 -0.622175462 0.1103051534 -2.292238e-02 -1.038334e-02
## 17 -0.9447699502 -0.295949461 -0.2345428984 3.296478e-02 -3.596902e-02
## 18 -1.2012870961 -0.977944451 0.2759002797 3.971499e-02 -1.435823e-03
## 19 -1.0479243587 -0.601133417 -0.1018782478 -2.135802e-02 -2.733494e-02
## 20 -1.3674407819 -0.676751238 0.2829848312 -1.540334e-03 -2.896903e-03
## 21 -1.1501231186 -0.314969952 -0.0766364450 -4.016151e-03 -3.007373e-02
## 22 -1.4031471549 -0.159634475 -0.0260885329 2.136720e-03 -2.838148e-02
## 23 -0.5339529463 0.053497273 0.0870869210 -2.482884e-03 -3.271245e-02
## 24 -0.9093723948 -0.112923549 0.3510612733 -1.313847e-02 -2.401780e-02
## 25 -0.5327526984 0.023556988 0.1218462769 1.625892e-02 -3.099143e-02
## 26 -0.9482199580 -0.119214220 0.3220296707 1.805262e-03 -2.130075e-02
## 27 -0.5781482919 0.057900952 0.1706583677 1.423264e-02 -3.844386e-02
## 28 -0.9807256292 -0.082560781 0.3480952218 1.519694e-02 -1.974127e-02
## 29 -0.5256592289 0.507742553 0.3743835337 -3.187963e-02 -7.198929e-03
## 30 -1.0508458124 0.493069064 0.9207394324 -2.785432e-02 -2.226876e-04
## 31 -0.4228128308 0.440869908 0.4588361801 -1.588188e-02 -3.417993e-03
## 32 -0.0061674518 0.732684844 0.2096444451 -1.579302e-02 9.949788e-03
## 33 0.1624324654 0.329996931 -0.0680117378 -5.150032e-03 -7.917300e-04
## 34 -0.0785770679 0.473422902 0.0373063970 9.469170e-03 -1.409255e-02
## 35 0.6057903741 -0.039739234 -0.3097373690 8.246795e-04 -2.857716e-02
## 36 0.9558849704 -0.087874182 -0.4846309964 1.482891e-02 -4.226668e-02
## 37 1.0841294683 -0.186055174 -0.6015822232 2.695865e-02 -5.994584e-02
## 38 0.0568923164 0.245969400 0.0089661679 -2.894041e-02 -1.639766e-03
## 39 -0.0839729858 0.424280921 0.1436132688 -2.587314e-02 5.826464e-03
## 40 -0.0534417472 -0.076247948 -0.2707770798 5.085397e-03 -3.854473e-04
## 41 -0.2266468989 -0.124063718 -0.3722387669 1.272482e-02 -2.252753e-03
## 42 -0.4580401137 -0.322700292 -0.5708392786 2.618210e-02 -1.428611e-04
## 43 -0.1290092911 0.420927130 0.1167621993 -4.193177e-02 2.069027e-03
## 44 0.1231387514 0.129952768 -0.0913838102 -2.701725e-02 -3.146750e-03
## 45 0.2369527235 0.274012579 0.0306902549 -2.372042e-02 2.621704e-02
## 46 -0.0222993286 0.297933973 0.0288478213 -3.480163e-02 -1.321337e-03
## 47 -1.2171910124 -0.124307918 -0.3649326794 -3.396656e-02 -5.942850e-03
## 48 -2.0961084388 -0.272303309 -0.5628743071 3.284480e-03 -1.366975e-02
## 49 -0.2235090413 0.923530840 0.4100236132 -7.539130e-02 3.848737e-02
## 50 0.5821960311 0.285345909 -0.4586832547 -3.171064e-02 2.293347e-02
## 51 0.0552201077 0.289745689 -0.1003486004 -3.101822e-02 1.119365e-04
## 52 0.0721956813 0.326660713 0.1039438866 -2.919870e-02 7.168374e-03
## 53 -0.9281175217 -0.764741498 0.3974378820 -1.539198e-03 5.226349e-02
## 54 -0.3989553658 -0.644249698 -0.0446230045 1.594910e-02 4.573915e-02
## 55 0.8978837516 -0.360657167 0.1589419662 2.787460e-02 3.735540e-02
## 56 -1.4223060976 -0.789266789 0.4094926519 2.061508e-02 4.385205e-02
## 57 -0.8273174563 -0.718748228 0.1206865298 2.553172e-02 3.966843e-02
## 58 0.3545467853 -0.300051759 0.1838865171 1.629035e-02 2.487837e-02
## 59 -1.3265455850 -0.723816195 0.4082252910 1.860875e-02 3.928449e-02
## 60 -0.7619038491 -0.640829215 0.0476359943 2.037551e-02 3.578868e-02
## 61 0.3966544371 -0.286047765 0.1997992969 4.593648e-02 2.592311e-02
## 62 0.2620812019 0.039575823 -0.0460206575 -7.028185e-03 4.182419e-03
## 63 0.0931090781 0.136812900 -0.0367492723 2.749788e-03 -1.175099e-02
## 64 0.4093032215 -0.160924200 -0.2746398587 -2.009244e-02 1.961035e-02
## 65 -0.0028195545 0.426486733 -0.0490754576 -2.604811e-02 -3.169942e-03
## 66 0.3144361421 0.419979113 -0.2782737528 -3.634924e-02 2.203975e-02
## 67 -0.4804240518 0.941707987 0.3528846715 -5.361272e-02 2.317890e-02
## 68 -0.5654775233 0.888356718 0.3673736451 -6.315883e-02 5.990685e-03
## 69 0.1507541232 0.563493596 -0.1805110307 -3.237347e-02 2.042610e-02
## 70 -0.2191307695 -0.004833793 -0.1280361320 1.439749e-03 -5.523524e-03
## 71 0.0422600568 -0.100639660 0.2819389019 1.684053e-02 -1.122190e-02
## 72 0.3253061544 -0.277886410 -0.3053455184 1.639341e-02 3.218178e-03
## 73 -0.0390271660 0.073919021 0.0409917907 -1.089181e-02 -3.573657e-02
## 74 0.3511987097 0.185449668 0.5098616413 2.334927e-03 -1.451439e-02
## 75 0.4678231926 0.268497389 0.4209970539 -1.816833e-02 -4.586127e-03
## 76 0.5936976395 -0.052041266 0.2189338831 2.144677e-02 3.990156e-04
## 77 0.8046868811 -0.013618762 0.2319783650 2.870746e-02 4.002420e-03
## 78 0.3578315688 0.115787557 0.7623550856 -1.270932e-02 -1.733715e-02
## 79 0.5749588134 0.156840413 0.7818867685 1.820038e-02 -1.047644e-02
## 80 -0.5696171006 0.101658977 0.6644744526 1.727866e-02 -3.281139e-02
## 81 -0.3553004101 0.136708366 0.6750816432 7.264534e-03 -2.704500e-02
## 82 -0.5069577330 0.411966111 -0.0739116048 -3.460086e-02 -1.202863e-02
## 83 -0.0850060226 0.331174523 0.2105975130 -4.598695e-02 -7.369867e-03
## 84 0.1040095879 0.168152632 0.0779495863 -1.071669e-02 1.037517e-02
## 85 -0.0580415290 0.266553510 0.4435569219 -1.915293e-02 -8.470302e-03
## 86 0.9448713699 -0.051126491 -0.6729540567 3.965060e-02 1.840598e-02
## 87 1.1495626600 -0.004632641 -0.6540062611 3.092683e-02 2.168277e-02
## 88 0.5643846617 0.014851073 -0.4794908397 3.882988e-02 -4.409564e-02
## 89 0.7645077208 0.047489715 -0.4428624127 1.058650e-02 -3.679428e-02
## 90 -0.0814844923 0.138530662 0.2897025503 -2.110652e-02 -1.398790e-02
## 91 0.4395088952 0.169508179 -0.2578877525 -1.451889e-02 1.591017e-02
## 92 -0.1895698133 0.190938930 0.0988884980 8.163906e-03 -5.878287e-02
## 93 -0.1025189589 -0.031573285 0.1027712181 -7.085932e-03 -3.876773e-02
## 94 -0.0441916905 0.180054340 -0.1183033281 -3.096400e-02 -2.938072e-02
## 95 0.3489186721 0.111195867 -0.0760275421 -5.462501e-03 2.466726e-03
## 96 0.4146201212 0.265982278 -0.0812550772 -3.510840e-02 -4.833755e-04
## 97 0.1374879401 0.129365151 -0.0846121682 -1.357887e-02 -6.119598e-04
## 98 0.1374879401 0.129365151 -0.0846121682 -1.357887e-02 -6.119598e-04
## 99 -0.2532587017 0.347074179 -0.1227085633 -2.865666e-03 -2.111039e-02
## 100 0.6080332303 -0.226614587 0.0872281777 -1.648245e-02 2.347254e-03
## 101 0.6911230823 -0.285591907 0.0609785029 -1.912777e-02 -1.545931e-02
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## 503 0.1779514675 0.122388627 -0.0721765681 -8.371883e-03 -2.495340e-03
## 504 0.1779514675 0.122388627 -0.0721765681 -8.371883e-03 -2.495340e-03
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## 508 0.6004233100 -0.132837013 -0.0554711684 1.196646e-02 9.611509e-03
## 509 0.7963722960 -0.207994718 0.0263002753 -1.990751e-02 1.447593e-02
## 510 0.6278454808 -0.130433455 -0.0273016398 1.589351e-02 1.551699e-02
## 511 0.7932970891 -0.203922766 0.0952612656 -1.606918e-02 1.181558e-02
## 512 1.0213483342 -0.308876815 0.0613494406 3.086913e-02 2.521455e-02
## 513 0.2016022585 -0.253808875 0.1231951299 -1.375870e-03 -2.705879e-03
## 514 0.1581994473 -0.362148291 0.2843322488 -3.154642e-02 2.311815e-03
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## 518 -0.1259975844 -0.366067166 0.2724965994 -4.256936e-02 -1.732010e-02
## Dim.11
## 1 6.098005e-03
## 2 -1.215281e-02
## 3 -2.103969e-02
## 4 2.886935e-03
## 5 1.618430e-02
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## 518 -1.215629e-02Berdasarkan output pca_result\(ind\)coord, setiap produk memiliki skor pada masing-masing komponen utama. Karena dipilih 2 komponen, maka interpretasi difokuskan pada Dim.1 dan Dim.2.
Dimensi 1 (PC1) memiliki eigenvalue sebesar 7,56 dan mampu menjelaskan 68,73% variasi data. Contoh skor pada Dim.1 adalah -0,1658; 2,8425; hingga 6,8693. Nilai yang semakin besar menunjukkan produk dengan kandungan kalori dan lemak yang semakin tinggi, karena PC1 didominasi oleh variabel Calories, Total Fat, dan Protein.
Dimensi 2 (PC2) memiliki eigenvalue sebesar 1,39 dan menjelaskan 12,60% variasi data. Contoh skor pada Dim.2 adalah -0,5131; -0,7050; dan -0,7956. PC2 didominasi oleh variabel Carbs (loading 0,7105), sehingga komponen ini merepresentasikan variasi kandungan karbohidrat.
# scree plot
fviz_eig(pca_result,
addlabels = TRUE,
ncp = ncol(data),
barfill = "skyblue",
barcolor = "darkblue",
linecolor = "red")## Warning in geom_bar(stat = "identity", fill = barfill, color = barcolor, :
## Ignoring empty aesthetic: `width`.
Berdasarkan scree plot hasil fviz_eig(pca_result), terlihat bahwa:
PC1 menjelaskan 68,7% variasi data. PC2 menjelaskan 12,6% variasi data. PC3 hanya menjelaskan 8,3% variasi. Komponen ke-4 dan seterusnya masing-masing < 5%.
Terlihat adanya “elbow” (titik siku) setelah komponen ke-2, di mana penurunan persentase variasi menjadi sangat kecil. Secara kumulatif:
PC1 + PC2 = 81,3% variasi total
Karena sudah melebihi 80% dan eigenvalue PC1 (7,56) serta PC2 (1,39) > 1, maka cukup menggunakan 2 Principal Component untuk merepresentasikan data.
BIPLOT
#Biplot
fviz_pca_biplot(pca_result,
geom.ind = "point",
addEllipses = TRUE)
# correlation circle
contrib_circle <- fviz_pca_var(pca_result, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE) +
ggtitle("Kontribusi Variabel")## 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 factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## 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 factoextra package.
## Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.plot(contrib_circle)
- Setiap panah merepresentasikan variabel asli (misal: Calories,
Protein..g., Sodium..mg.).Arah panah menunjukkan korelasi variabel
dengan principal components: Panah menuju kanan → positif terhadap Dim1.
Panah ke atas → positif terhadap Dim2. Panah ke kiri/bawah → negatif
terhadap sumbu tersebut. Panah yang lebih panjang → variabel lebih kuat
berkontribusi terhadap komponen.
Warna panah menunjukkan kontribusi variabel terhadap komponen: Warna oranye/merah = kontribusi tinggi (10 atau mendekati 10). Warna hijau/biru = kontribusi lebih rendah (5–6). Jadi variabel seperti Calories, Protein..g., memiliki kontribusi paling tinggi ke Dim1.
Variabel yang berdekatan dan arah panahnya mirip → berkorelasi positif. Contoh: Calories dan Protein..g. cenderung naik bersama. Variabel yang saling berlawanan arah → berkorelasi negatif. Variabel yang mendekati pusat → kontribusi rendah atau tidak berkorelasi kuat dengan komponen pertama dan kedua.
Dim1 banyak dijelaskan oleh: Calories, Protein..g., Total.Fat..g., → ini variabel yang paling dominan.
Dim2 lebih sedikit kontribusi → misal Carbs..g. sedikit membedakan data.
# variable contribution
contrib_v_PC1 <- fviz_contrib(pca_result, choice = "var", axes = 1, top = 5) + ggtitle("PC1")
plot(contrib_v_PC1)
Berdasarkan grafik kontribusi variabel terhadap Principal Component 1 (PC1), variabel Calories.from.Fat dan Total.Fat.g memberikan kontribusi terbesar, masing-masing sekitar 12%, dan berada di atas garis kontribusi rata-rata. Variabel Calories juga memiliki kontribusi yang tinggi, yaitu sekitar 11–12%, diikuti oleh Saturated.Fat.g dengan kontribusi sekitar 11%. Sementara itu, Protein.g memiliki kontribusi paling rendah, yaitu sekitar 10–11%. Hal ini menunjukkan bahwa PC1 terutama dipengaruhi oleh variabel yang berkaitan dengan kandungan lemak dan kalori, sedangkan protein memiliki pengaruh yang relatif lebih kecil
contrib_v_PC2 <- fviz_contrib(pca_result, choice = "var", axes = 2, top = 5) + ggtitle("PC2")
plot(contrib_v_PC2)
Principal Component 2 (PC2) didominasi oleh variabel Carbs_g dengan
kontribusi sekitar 50%, menunjukkan bahwa komponen ini merepresentasikan
dimensi variasi kandungan karbohidrat dalam dataset. Variabel Weight
Watchers Points (±13%) dan Sodium (±10%) memberikan kontribusi sedang,
sedangkan Fiber (±8%) dan Calories (±7%) berkontribusi relatif kecil
terhadap pembentukan PC2.
Factor Analysis (FA)
Manual
# Factor Analysis
varcov = cov(scale_data)
pc = eigen(varcov)
cat("eigen value:")## eigen value:pc$values## [1] 7.5599150202 1.3858015747 0.9136701166 0.5212132940 0.2449772090
## [6] 0.2203330632 0.0862490454 0.0633738728 0.0038089610 0.0004001546
## [11] 0.0002576885Berdasarkan hasil eigenvalue, diperoleh dua faktor dengan nilai eigenvalue lebih dari 1, yaitu faktor pertama sebesar 7.5599 dan faktor kedua sebesar 1.3858.
cat("eigen vector:")## eigen vector:pc$vectors## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.3446145 0.24896683 0.10113517 -0.001578267 0.11969342 -0.04963096
## [2,] -0.3478539 -0.15912536 -0.05723691 0.011385538 0.35634942 0.19061187
## [3,] -0.3477525 -0.15948298 -0.05774151 0.011588059 0.35971559 0.19262259
## [4,] -0.3363975 0.01897338 -0.24021540 -0.087328074 0.07811748 0.45666647
## [5,] -0.2570856 0.16465013 -0.56811701 0.453543750 -0.41890997 0.05074449
## [6,] -0.2846761 -0.18197847 0.06163207 -0.685869996 -0.58942724 0.14898871
## [7,] -0.3111684 -0.31487366 0.16401115 -0.099067404 0.19746030 -0.49167184
## [8,] -0.1599026 0.71048843 0.32785888 -0.067368722 -0.07393845 -0.10842922
## [9,] -0.2055649 -0.28294414 0.64515722 0.534379070 -0.32658140 0.25081081
## [10,] -0.3275581 -0.13625522 -0.18479225 0.124189478 -0.18854124 -0.61157504
## [11,] -0.3272064 0.35229519 0.11889293 -0.025512883 0.11670569 -0.01885018
## [,7] [,8] [,9] [,10] [,11]
## [1,] -0.08139002 -0.13136568 -0.5200527540 0.701966064 0.071716784
## [2,] 0.03572033 -0.34294643 0.2694081862 0.057878795 -0.701522881
## [3,] 0.03822224 -0.33276109 0.2578592961 -0.092320441 0.704599804
## [4,] -0.26792373 0.72870973 0.0543109872 0.027283869 -0.002325821
## [5,] 0.44008713 -0.07975782 -0.0153556104 -0.002013183 0.000175021
## [6,] 0.07521995 -0.19049418 -0.0050502030 -0.005461041 0.001914357
## [7,] 0.56669753 0.40507019 -0.0328525036 -0.015621285 -0.005635080
## [8,] 0.10991731 0.07942229 0.5629219779 0.070483467 0.012033113
## [9,] -0.06394614 0.04408765 0.0008029042 -0.017308390 -0.001527239
## [10,] -0.61472282 -0.02890034 0.1872913056 -0.034636005 0.000372313
## [11,] -0.06572493 -0.08697667 -0.4839657478 -0.698484906 -0.077931645sp = sum(pc$values[1:2])
L1 = sqrt(pc$values[1])*pc$vectors[,1]
L2 = sqrt(pc$values[2])*pc$vectors[,2]
L = cbind(L1,L2)
cat("factor loading:")## factor loading:L## L1 L2
## [1,] -0.9475279 0.29308393
## [2,] -0.9564348 -0.18732250
## [3,] -0.9561559 -0.18774348
## [4,] -0.9249350 0.02233547
## [5,] -0.7068647 0.19382625
## [6,] -0.7827255 -0.21422519
## [7,] -0.8555669 -0.37066950
## [8,] -0.4396569 0.83638750
## [9,] -0.5652069 -0.33308205
## [10,] -0.9006307 -0.16039974
## [11,] -0.8996639 0.41472215dasarkan hasil perhitungan factor loading, Faktor 1 memiliki loading tinggi pada hampir seluruh variabel (>|0.7|), sehingga dapat diinterpretasikan sebagai faktor umum yang merepresentasikan karakteristik utama data. Faktor 2 menunjukkan loading sangat tinggi pada variabel ke-8 (karbohidrat) (0.8364), sehingga faktor ini lebih merepresentasikan dimensi spesifik dari variabel tersebut. Dengan dua faktor ini, struktur data sudah mampu dijelaskan secara optimal.
FA with function Principal
fa <- principal(scale_data, nfactors = 2, rotate = "none")
fa## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 2, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 h2 u2 com
## Calories 0.95 0.29 0.98 0.016 1.2
## Calories.from.Fat 0.96 -0.19 0.95 0.050 1.1
## Total.Fat..g. 0.96 -0.19 0.95 0.051 1.1
## Saturated.Fat..g. 0.92 0.02 0.86 0.144 1.0
## Trans.Fat..g. 0.71 0.19 0.54 0.463 1.1
## Cholesterol..mg. 0.78 -0.21 0.66 0.341 1.1
## Sodium...mg. 0.86 -0.37 0.87 0.131 1.4
## Carbs..g. 0.44 0.84 0.89 0.107 1.5
## Fiber..g. 0.57 -0.33 0.43 0.570 1.6
## Protein..g. 0.90 -0.16 0.84 0.163 1.1
## Weight.Watchers.Pnts 0.90 0.41 0.98 0.019 1.4
##
## PC1 PC2
## SS loadings 7.56 1.39
## Proportion Var 0.69 0.13
## Cumulative Var 0.69 0.81
## Proportion Explained 0.85 0.15
## Cumulative Proportion 0.85 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.05
## with the empirical chi square 123.41 with prob < 4.5e-12
##
## Fit based upon off diagonal values = 1Hasil analisis menunjukkan bahwa PC1 didominasi oleh variabel kalori, lemak, protein, dan sodium sehingga merepresentasikan faktor kandungan energi dan lemak makanan. PC2 didominasi oleh variabel karbohidrat, sehingga merepresentasikan faktor karbohidrat
# Factor Analysis with rotation varimax
fa_1 <- principal(scale_data, nfactors = 2, rotate = "varimax")
fa_1## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 2, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 h2 u2 com
## Calories 0.64 0.76 0.98 0.016 1.9
## Calories.from.Fat 0.91 0.36 0.95 0.050 1.3
## Total.Fat..g. 0.91 0.36 0.95 0.051 1.3
## Saturated.Fat..g. 0.77 0.52 0.86 0.144 1.8
## Trans.Fat..g. 0.49 0.54 0.54 0.463 2.0
## Cholesterol..mg. 0.77 0.24 0.66 0.341 1.2
## Sodium...mg. 0.92 0.15 0.87 0.131 1.1
## Carbs..g. -0.08 0.94 0.89 0.107 1.0
## Fiber..g. 0.66 0.02 0.43 0.570 1.0
## Protein..g. 0.84 0.35 0.84 0.163 1.3
## Weight.Watchers.Pnts 0.53 0.83 0.98 0.019 1.7
##
## RC1 RC2
## SS loadings 5.76 3.18
## Proportion Var 0.52 0.29
## Cumulative Var 0.52 0.81
## Proportion Explained 0.64 0.36
## Cumulative Proportion 0.64 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 2 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.05
## with the empirical chi square 123.41 with prob < 4.5e-12
##
## Fit based upon off diagonal values = 1Hasil rotasi varimax menghasilkan struktur faktor yang lebih jelas. Faktor pertama didominasi oleh variabel lemak, sodium, dan protein sehingga merepresentasikan faktor kandungan lemak dan mineral. Faktor kedua didominasi oleh karbohidrat dan kalori sehingga merepresentasikan faktor energi berbasis karbohidrat.
# scores FA
scores_FA = scale_data %*% solve(cor(scale_data)) %*% as.matrix(fa$loadings)
scores_FA## PC1 PC2
## 1 -0.060247458 -0.435396682
## 2 0.201934847 -0.526208925
## 3 1.032792365 -0.569597064
## 4 0.667230229 -0.557104523
## 5 1.290805359 -0.598286747
## 6 2.416326572 -0.601160695
## 7 1.247509298 -0.356459722
## 8 0.941288662 -0.403975541
## 9 1.223390404 -0.525660647
## 10 2.495860970 -0.600991953
## 11 2.284689845 -0.458216782
## 12 2.260881747 -0.236604658
## 13 0.242149910 -0.450495345
## 14 0.205025042 -0.497823674
## 15 0.884526833 -0.675179055
## 16 0.323095046 -0.860317173
## 17 0.690291106 -0.362026388
## 18 0.808447192 -0.996209399
## 19 1.142858816 -0.462049512
## 20 0.475649517 -0.991824107
## 21 0.840777089 -0.456367983
## 22 0.358166504 -0.519338955
## 23 0.152365554 -0.496713233
## 24 0.006067854 -0.733204436
## 25 0.120494876 -0.461505502
## 26 -0.036769744 -0.700008826
## 27 0.120465193 -0.449709298
## 28 -0.027818500 -0.696124962
## 29 0.704341670 -0.621696286
## 30 2.523366398 -0.490779749
## 31 0.744784824 -0.556110986
## 32 0.901987855 -0.648548974
## 33 0.900945976 -0.512771976
## 34 0.376138678 -0.423068795
## 35 -0.322271179 -0.501276733
## 36 0.149955529 -0.364631686
## 37 0.503063399 -0.162580503
## 38 -0.991043537 -0.694909626
## 39 -0.976575013 -0.868257023
## 40 -0.326251847 -0.819847557
## 41 -0.006978630 -0.792135945
## 42 0.703573652 -0.886075747
## 43 -0.902909864 -0.525346305
## 44 -0.960432067 -0.387071703
## 45 -0.747372158 -0.940519302
## 46 -0.927447652 -0.467352159
## 47 0.396992841 -0.774457304
## 48 1.358690509 -0.815495747
## 49 -0.627303780 -1.264514306
## 50 -0.420164339 -0.810757330
## 51 -0.881822680 -0.528888652
## 52 -0.848985612 -0.580061444
## 53 0.452745000 -1.573160163
## 54 0.719462835 -1.298384666
## 55 -0.338043177 -1.248414777
## 56 0.308074598 -1.666959062
## 57 0.587264885 -1.378050388
## 58 -0.339894189 -1.149052927
## 59 0.116844439 -1.570373124
## 60 0.382837097 -1.278204376
## 61 -0.537800179 -1.097808587
## 62 -0.947503197 -0.782997485
## 63 -0.832233136 -0.700006726
## 64 -0.435926785 -0.227760846
## 65 -0.684411332 -0.641911734
## 66 -0.291933231 -0.902186637
## 67 -0.776443467 -1.002873123
## 68 -0.749566196 -0.891363334
## 69 -0.390348765 -0.789636227
## 70 0.427698418 -1.200387711
## 71 0.419385894 -0.799241448
## 72 1.030271560 -1.283456158
## 73 -0.553685801 -0.468443034
## 74 0.915272539 -1.092560855
## 75 1.122378751 -1.139260451
## 76 1.258218465 -1.157514426
## 77 1.496719910 -1.210298714
## 78 0.658559463 -0.710931650
## 79 0.885330227 -0.802944494
## 80 0.528604128 -0.633066227
## 81 0.765322657 -0.704353435
## 82 1.916013975 -0.899821464
## 83 0.758373522 -0.777996173
## 84 1.364606858 -0.966816106
## 85 0.499867360 -0.444506929
## 86 2.470356655 -1.735427474
## 87 2.708829688 -1.813184406
## 88 3.503553885 -0.943498470
## 89 3.730334820 -1.005874273
## 90 0.232249705 -0.832895097
## 91 1.897296197 -1.428736826
## 92 0.004897825 0.056911379
## 93 0.719337327 -0.135794939
## 94 -0.757813200 0.507561673
## 95 -0.875726599 -0.747396066
## 96 -0.498161888 -0.785924972
## 97 -0.981654870 -0.476063978
## 98 -0.981654870 -0.476063978
## 99 1.364227248 -0.792171471
## 100 -0.167337425 -0.057383054
## 101 -0.229932008 -0.279126784
## 105 -0.640600942 -0.087659829
## 106 -0.912855736 -0.330264631
## 107 -0.657468706 -0.114005566
## 108 -0.925244710 -0.526048248
## 109 -0.292262882 0.391648120
## 110 -0.134256673 0.638899508
## 111 -0.016139096 0.311033227
## 112 -0.850479568 -0.836678829
## 113 1.307522296 1.602890842
## 114 0.839289120 1.247350234
## 115 -0.101979038 -0.547556880
## 116 0.382188450 0.411576162
## 117 -0.350835601 0.129227443
## 118 -0.520079239 -0.365014391
## 119 -0.577024379 -0.358943680
## 120 -0.600023973 -0.200210553
## 121 -0.865891890 -0.112879181
## 122 0.678149384 1.764621218
## 123 1.035271585 2.397198499
## 124 1.533659231 3.224165111
## 125 0.185927909 1.175860859
## 126 0.619781915 1.943028002
## 127 1.109115351 2.759640993
## 128 2.278096573 4.586131007
## 129 0.358392348 0.733191600
## 130 0.005137070 0.254675171
## 131 0.600668165 1.904698207
## 132 0.948254418 2.530788648
## 133 1.436000703 3.347299854
## 134 0.097994308 1.269042037
## 135 0.515316345 2.018857600
## 136 0.987176862 2.808844061
## 137 2.049934215 4.748792630
## 138 0.531765943 1.780519865
## 139 0.896661643 2.358965224
## 140 1.346509551 3.160937301
## 141 2.041660012 4.692202136
## 142 0.084370715 1.245656661
## 143 0.502332626 1.954714295
## 144 0.984495210 2.780336724
## 145 -0.717975621 -0.493836299
## 146 -0.550033271 -0.256917693
## 147 -0.882496860 -0.074646863
## 148 -1.036804128 -0.725907755
## 149 -0.800242962 0.153655279
## 150 -0.730334277 0.402694368
## 151 -0.586980212 0.949730042
## 152 -0.860748878 0.070751197
## 153 -0.794992144 0.367722595
## 154 -0.693526040 0.844048415
## 155 -0.529677676 1.600281281
## 156 -1.033458066 -0.733816048
## 157 -1.032342712 -0.736452146
## 158 -1.030112004 -0.741724341
## 159 -1.026765942 -0.749632633
## 160 -0.857431228 0.037870260
## 161 -0.790559140 0.332205560
## 162 -0.689121448 0.783558735
## 163 -0.523070788 1.509546761
## 164 -0.845139107 0.153214281
## 165 -0.777123253 0.469886129
## 166 -0.651243379 1.027064122
## 167 -0.474044363 1.846059622
## 168 -0.909392589 -0.225878688
## 169 -0.860226447 -0.038738079
## 170 -0.774292405 0.275175566
## 171 -0.650255340 0.758140281
## 172 -1.035688774 -0.728543853
## 173 -1.034573420 -0.731179950
## 174 -1.033458066 -0.733816048
## 175 -1.030559797 -0.717949226
## 176 -1.036804128 -0.725907755
## 177 -1.036804128 -0.725907755
## 178 -0.931741689 -0.744157654
## 179 -1.012846000 -0.616017501
## 180 -1.034545008 -0.706207306
## 181 -1.034545008 -0.706207306
## 182 -0.640311930 -0.218100069
## 183 -0.458675823 -0.064868958
## 184 -0.226673956 0.284017995
## 185 -0.648758558 -0.195813759
## 186 -0.466426477 0.003529014
## 187 -0.238886026 0.362960357
## 188 -0.636551673 -0.155387672
## 189 -0.454219592 0.043955101
## 190 -0.224420021 0.423086894
## 191 -0.648758558 -0.195813759
## 192 -0.466902681 0.002331485
## 193 -0.240001380 0.365596455
## 194 -0.744402781 -0.621198359
## 195 -0.601931297 -0.590202000
## 196 -0.443496712 -0.525598832
## 197 -0.865267118 0.031350298
## 198 -0.589255820 1.194665315
## 199 -0.744067704 0.517234248
## 200 -0.794243079 0.277753289
## 201 -0.872617241 -0.545764405
## 202 -0.820796492 -0.480727284
## 203 -0.794342646 -0.462013095
## 204 -0.797688708 -0.454104802
## 205 -0.757912623 -0.397600623
## 206 -0.717154992 -0.350653042
## 207 -0.731322747 0.105094417
## 208 -0.656504854 0.319814000
## 209 -0.582163165 0.533336054
## 210 -0.677910439 0.168692970
## 211 -0.581576320 0.411473603
## 212 -0.505003923 0.619723462
## 213 -0.739740963 0.152353372
## 214 -0.665370862 0.390848070
## 215 -0.595490589 0.614914514
## 216 -0.677972448 0.238116130
## 217 -0.593816802 0.465443321
## 218 -0.519446701 0.703938020
## 219 -0.739740963 0.152353372
## 220 -0.667629982 0.371147620
## 221 -0.595490589 0.614914514
## 222 -0.677972448 0.238116130
## 223 -0.593816802 0.465443321
## 224 -0.519446701 0.703938020
## 225 -0.878783202 -0.453410838
## 226 -0.824540387 -0.373704424
## 227 -0.794520710 -0.317984395
## 228 -0.815899333 -0.370284177
## 229 -0.771604283 -0.311303401
## 230 -0.715578553 -0.213094067
## 231 -0.453873937 0.335469537
## 232 -0.347053065 0.545646477
## 233 -0.252978066 0.768726660
## 234 -0.420421545 0.370658082
## 235 -0.269865411 0.657006529
## 236 -0.099078963 0.990249236
## 237 -0.900214853 -0.586815142
## 238 -0.871501887 -0.548400503
## 239 -0.843904276 -0.507349766
## 240 -0.776982749 0.066404086
## 241 -0.733105663 0.086591497
## 242 -0.658763974 0.300113551
## 243 -0.784733403 0.134802058
## 244 -0.742000083 0.132652922
## 245 -0.669860690 0.376419816
## 246 -0.786992523 0.115101608
## 247 -0.742000083 0.132652922
## 248 -0.671004456 0.354083268
## 249 -0.913350947 -0.485963286
## 250 -0.881518526 -0.474308818
## 251 -0.845226106 -0.385657614
## 252 -0.329195563 0.374316224
## 253 -0.262111935 0.493682720
## 254 -0.376925683 0.177544825
## 255 -0.484761267 0.007011110
## 256 -0.338617275 0.463900594
## 257 -0.445716107 0.298225958
## 258 -0.517798676 0.104404354
## 259 -0.589412096 -0.558823759
## 260 -0.505538858 -0.537753491
## 261 -0.370540325 -0.481895100
## 262 -0.495591092 -0.517027854
## 263 -0.360754780 -0.493062607
## 264 -0.263493280 -0.418386623
## 265 -0.518362230 0.089225125
## 266 -0.412656712 0.302038162
## 267 -0.251514804 0.476934497
## 268 -0.399195122 0.141205362
## 269 -0.279478705 0.348550552
## 270 -0.155748664 0.569126467
## 271 -0.526112884 0.157623097
## 272 -0.424420989 0.357205409
## 273 -0.275743127 0.572316562
## 274 -0.408089542 0.187266787
## 275 -0.288344713 0.419584622
## 276 -0.170859004 0.632202007
## 277 -0.526112884 0.157623097
## 278 -0.424420989 0.357205409
## 279 -0.275743127 0.572316562
## 280 -0.408089542 0.187266787
## 281 -0.290603833 0.399884172
## 282 -0.170859004 0.632202007
## 283 -0.659785279 -0.457029207
## 284 -0.582799316 -0.408924609
## 285 -0.463710129 -0.342492808
## 286 -0.546016427 -0.421133521
## 287 -0.446809066 -0.332985774
## 288 -0.328206256 -0.297388544
## 289 -0.238893601 0.285202158
## 290 -0.109325617 0.497195567
## 291 0.160816705 0.852213283
## 292 -0.148067065 0.295053822
## 293 0.156078928 0.718916053
## 294 0.387106257 0.947640815
## 295 -0.739592301 -0.621296255
## 296 -0.648109064 -0.590436885
## 297 -0.517583522 -0.546286433
## 298 -0.665405428 0.024833791
## 299 -0.571367757 0.049474286
## 300 -0.430881322 0.272505423
## 301 -0.673156082 0.093231763
## 302 -0.579118411 0.117872258
## 303 -0.443121804 0.326475141
## 304 -0.673156082 0.093231763
## 305 -0.558269747 0.124794291
## 306 -0.443121804 0.326475141
## 307 -0.795861555 -0.519408419
## 308 -0.681453554 -0.487346360
## 309 -0.607395689 -0.392540104
## 310 -0.105106620 0.327619228
## 311 0.113171015 0.536673622
## 312 -0.159575251 0.227298991
## 313 -0.269774859 0.067174868
## 314 0.181023430 0.577595580
## 315 -0.097458674 0.152963426
## 316 -0.263582315 -0.027032762
## 317 0.485006696 1.075065106
## 318 0.778256724 1.443201006
## 319 1.218141747 2.033650551
## 320 0.544288674 0.925331045
## 321 0.824643873 1.361031665
## 322 1.169846695 1.825836138
## 323 -0.263636275 0.743155929
## 324 -0.449333765 0.444992541
## 325 -0.578119498 0.291556012
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