Analisis Multivariat PCA & FA
Umi_Putri
2026-03-04
1. Putri Sofyatus Salwa (24031554112)
2. Umi Imro’atus Sholekhah (24031554150)
STAGE 1 : Objective (Tujuan Analisis)
(Tahap ini dijelaskan dalam laporan)
STAGE 2 : Research Design & Data Preparation
2.1 Load Library
library(psych)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.2.0 ✔ readr 2.2.0
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.2 ✔ tibble 3.3.1
## ✔ lubridate 1.9.5 ✔ tidyr 1.3.2
## ✔ purrr 1.2.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ ggplot2::%+%() masks psych::%+%()
## ✖ ggplot2::alpha() masks psych::alpha()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa2.2 Import Dataset
data <- read.csv("C:/Users/MSI-PC/Downloads/brisbane_water_quality.csv")2.3 Exploratory Data Analysis (EDA) Awal
str(data)## 'data.frame': 30894 obs. of 20 variables:
## $ Timestamp : chr "2023-08-04 23:00:00" "2023-08-04 23:30:00" "2023-08-04 23:00:00" "2023-08-04 23:30:00" ...
## $ Record.number : int 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 ...
## $ Average.Water.Speed : num 4.83 2.54 1.26 0.76 3.4 ...
## $ Average.Water.Direction : num 73.5 106.4 156.8 281.8 244.6 ...
## $ Chlorophyll : num 1.62 1.96 1.62 1.76 1.64 ...
## $ Chlorophyll..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Temperature : num 20 20 20 20 20 ...
## $ Temperature..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Dissolved.Oxygen : num 7.47 7.46 7.43 7.42 7.43 ...
## $ Dissolved.Oxygen..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Dissolved.Oxygen...Saturation. : num 101 101 101 100 101 ...
## $ Dissolved.Oxygen...Saturation...quality.: num NA NA NA NA NA NA NA NA NA NA ...
## $ pH : num 8.18 8.18 8.17 8.17 8.17 ...
## $ pH..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Salinity : num 35.2 35.2 35.2 35.2 35.2 ...
## $ Salinity..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Specific.Conductance : num 53.3 53.3 53.3 53.3 53.3 ...
## $ Specific.Conductance..quality. : num NA NA NA NA NA NA NA NA NA NA ...
## $ Turbidity : num 2.07 1.99 2.03 1.97 1.94 ...
## $ Turbidity..quality. : num NA NA NA NA NA NA NA NA NA NA ...dim(data)## [1] 30894 20summary(data)## Timestamp Record.number Average.Water.Speed Average.Water.Direction
## Length:30894 Min. : 1468 Min. : 0.000 Min. : 0.00
## Class :character 1st Qu.: 9191 1st Qu.: 6.594 1st Qu.: 86.31
## Mode :character Median :16915 Median :13.390 Median :176.33
## Mean :16915 Mean :16.799 Mean :177.54
## 3rd Qu.:24638 3rd Qu.:23.600 3rd Qu.:267.87
## Max. :32361 Max. :89.912 Max. :359.99
## NA's :20 NA's :1
## Chlorophyll Chlorophyll..quality. Temperature Temperature..quality.
## Min. : 0.100 Min. :1020 Min. :17.00 Min. :1020
## 1st Qu.: 1.451 1st Qu.:1020 1st Qu.:21.29 1st Qu.:1020
## Median : 2.371 Median :1020 Median :25.25 Median :1020
## Mean : 2.782 Mean :1020 Mean :24.42 Mean :1022
## 3rd Qu.: 3.650 3rd Qu.:1020 3rd Qu.:27.25 3rd Qu.:1020
## Max. :43.301 Max. :1220 Max. :32.06 Max. :2010
## NA's :585 NA's :808 NA's :5164 NA's :5344
## Dissolved.Oxygen Dissolved.Oxygen..quality. Dissolved.Oxygen...Saturation.
## Min. :3.030 Min. :1020 Min. : 51.84
## 1st Qu.:6.387 1st Qu.:1020 1st Qu.: 92.23
## Median :6.814 Median :1020 Median : 96.51
## Mean :6.815 Mean :1020 Mean : 96.64
## 3rd Qu.:7.254 3rd Qu.:1020 3rd Qu.:101.67
## Max. :9.260 Max. :2010 Max. :134.08
## NA's :4300 NA's :4524 NA's :5749
## Dissolved.Oxygen...Saturation...quality. pH pH..quality.
## Min. :1020 Min. :7.309 Min. :1020
## 1st Qu.:1020 1st Qu.:7.980 1st Qu.:1020
## Median :1020 Median :8.073 Median :1020
## Mean :1023 Mean :8.063 Mean :1020
## 3rd Qu.:1020 3rd Qu.:8.140 3rd Qu.:1020
## Max. :2010 Max. :8.255 Max. :1020
## NA's :5950 NA's :1084 NA's :1308
## Salinity Salinity..quality. Specific.Conductance
## Min. : 0.057 Min. :1020 Min. : 0.021
## 1st Qu.:29.151 1st Qu.:1020 1st Qu.:45.046
## Median :30.604 Median :1020 Median :47.420
## Mean :31.003 Mean :1020 Mean :47.927
## 3rd Qu.:33.918 3rd Qu.:1020 3rd Qu.:53.361
## Max. :36.000 Max. :1020 Max. :54.996
## NA's :3958 NA's :4182 NA's :1367
## Specific.Conductance..quality. Turbidity Turbidity..quality.
## Min. :1020 Min. : 0.335 Min. :1020
## 1st Qu.:1020 1st Qu.: 2.354 1st Qu.:1020
## Median :1020 Median : 3.093 Median :1020
## Mean :1020 Mean : 3.942 Mean :1020
## 3rd Qu.:1020 3rd Qu.: 4.005 3rd Qu.:1020
## Max. :1020 Max. :49.869 Max. :1020
## NA's :1591 NA's :2000 NA's :2224colSums(is.na(data))## Timestamp
## 0
## Record.number
## 0
## Average.Water.Speed
## 20
## Average.Water.Direction
## 1
## Chlorophyll
## 585
## Chlorophyll..quality.
## 808
## Temperature
## 5164
## Temperature..quality.
## 5344
## Dissolved.Oxygen
## 4300
## Dissolved.Oxygen..quality.
## 4524
## Dissolved.Oxygen...Saturation.
## 5749
## Dissolved.Oxygen...Saturation...quality.
## 5950
## pH
## 1084
## pH..quality.
## 1308
## Salinity
## 3958
## Salinity..quality.
## 4182
## Specific.Conductance
## 1367
## Specific.Conductance..quality.
## 1591
## Turbidity
## 2000
## Turbidity..quality.
## 22242.4 Seleksi Variabel Numerik (Data Mentah)
data_numeric_all <- data %>% select(where(is.numeric))
describe(data_numeric_all)## vars n mean sd median
## Record.number 1 30894 16914.50 8918.47 16914.50
## Average.Water.Speed 2 30874 16.80 13.17 13.39
## Average.Water.Direction 3 30893 177.54 103.62 176.33
## Chlorophyll 4 30309 2.78 1.86 2.37
## Chlorophyll..quality. 5 30086 1020.01 1.15 1020.00
## Temperature 6 25730 24.42 3.49 25.25
## Temperature..quality. 7 25550 1021.67 40.60 1020.00
## Dissolved.Oxygen 8 26594 6.82 0.62 6.81
## Dissolved.Oxygen..quality. 9 26370 1020.49 21.98 1020.00
## Dissolved.Oxygen...Saturation. 10 25145 96.64 8.11 96.51
## Dissolved.Oxygen...Saturation...quality. 11 24944 1022.98 54.20 1020.00
## pH 12 29810 8.06 0.09 8.07
## pH..quality. 13 29586 1020.00 0.00 1020.00
## Salinity 14 26936 31.00 3.47 30.60
## Salinity..quality. 15 26712 1020.00 0.00 1020.00
## Specific.Conductance 16 29527 47.93 5.16 47.42
## Specific.Conductance..quality. 17 29303 1020.00 0.00 1020.00
## Turbidity 18 28894 3.94 4.07 3.09
## Turbidity..quality. 19 28670 1020.00 0.00 1020.00
## trimmed mad min max
## Record.number 16914.50 11450.86 1468.00 32361.00
## Average.Water.Speed 15.00 11.56 0.00 89.91
## Average.Water.Direction 176.99 134.62 0.00 359.99
## Chlorophyll 2.55 1.55 0.10 43.30
## Chlorophyll..quality. 1020.00 0.00 1020.00 1220.00
## Temperature 24.57 3.61 17.00 32.06
## Temperature..quality. 1020.00 0.00 1020.00 2010.00
## Dissolved.Oxygen 6.82 0.64 3.03 9.26
## Dissolved.Oxygen..quality. 1020.00 0.00 1020.00 2010.00
## Dissolved.Oxygen...Saturation. 96.73 6.92 51.84 134.08
## Dissolved.Oxygen...Saturation...quality. 1020.00 0.00 1020.00 2010.00
## pH 8.06 0.12 7.31 8.26
## pH..quality. 1020.00 0.00 1020.00 1020.00
## Salinity 31.20 2.56 0.06 36.00
## Salinity..quality. 1020.00 0.00 1020.00 1020.00
## Specific.Conductance 48.31 4.46 0.02 55.00
## Specific.Conductance..quality. 1020.00 0.00 1020.00 1020.00
## Turbidity 3.22 1.21 0.34 49.87
## Turbidity..quality. 1020.00 0.00 1020.00 1020.00
## range skew kurtosis se
## Record.number 30893.00 0.00 -1.20 50.74
## Average.Water.Speed 89.91 1.31 1.95 0.07
## Average.Water.Direction 359.99 0.04 -1.23 0.59
## Chlorophyll 43.20 2.26 20.51 0.01
## Chlorophyll..quality. 200.00 173.44 30079.00 0.01
## Temperature 15.06 -0.38 -0.93 0.02
## Temperature..quality. 990.00 24.28 588.04 0.25
## Dissolved.Oxygen 6.23 -0.23 0.65 0.00
## Dissolved.Oxygen..quality. 990.00 45.00 2023.31 0.14
## Dissolved.Oxygen...Saturation. 82.25 -0.08 1.38 0.05
## Dissolved.Oxygen...Saturation...quality. 990.00 18.15 327.56 0.34
## pH 0.95 -0.19 -0.35 0.00
## pH..quality. 0.00 NaN NaN 0.00
## Salinity 35.94 -0.99 3.98 0.02
## Salinity..quality. 0.00 NaN NaN 0.00
## Specific.Conductance 54.98 -1.14 4.83 0.03
## Specific.Conductance..quality. 0.00 NaN NaN 0.00
## Turbidity 49.53 5.32 36.99 0.02
## Turbidity..quality. 0.00 NaN NaN 0.002.5 Visualisasi Distribusi Awal
data_long <- data_numeric_all %>%
pivot_longer(cols = everything(),
names_to = "Variabel",
values_to = "Nilai")— Histogram
ggplot(data_long, aes(x = Nilai)) +
geom_histogram(bins = 30, fill = "skyblue", color = "black") +
facet_wrap(~ Variabel, scales = "free") +
labs(
title = "Distribusi Variabel Kualitas Air",
x = "Nilai",
y = "Frekuensi"
)## Warning: Removed 50159 rows containing non-finite outside the scale range
## (`stat_bin()`).
— Boxplot
ggplot(data_long, aes(x = Variabel, y = Nilai)) +
geom_boxplot(fill = "salmon") +
coord_flip() +
labs(
title = "Boxplot Variabel Kualitas Air",
x = "Variabel",
y = "Nilai"
)## Warning: Removed 50159 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
2.6 Seleksi Variabel untuk PCA & FA
data_num <- data %>%
select(
Temperature,
pH,
Dissolved.Oxygen,
Dissolved.Oxygen...Saturation.,
Salinity,
Turbidity,
Chlorophyll,
Specific.Conductance,
Average.Water.Speed,
Average.Water.Direction
)2.7 Penanganan Missing Value
prop_na <- colMeans(is.na(data_num))
data_clean <- data_num[, prop_na <= 0.5]
data_clean <- data_clean %>%
mutate(across(everything(),
~ ifelse(is.na(.), mean(., na.rm = TRUE), .)))
colSums(is.na(data_clean))## Temperature pH
## 0 0
## Dissolved.Oxygen Dissolved.Oxygen...Saturation.
## 0 0
## Salinity Turbidity
## 0 0
## Chlorophyll Specific.Conductance
## 0 0
## Average.Water.Speed Average.Water.Direction
## 0 02.8 Statistik Deskriptif Setelah Cleaning
describe(data_clean)## vars n mean sd median trimmed mad
## Temperature 1 30894 24.42 3.19 24.42 24.57 3.59
## pH 2 30894 8.06 0.09 8.07 8.06 0.12
## Dissolved.Oxygen 3 30894 6.82 0.58 6.82 6.82 0.53
## Dissolved.Oxygen...Saturation. 4 30894 96.64 7.32 96.64 96.71 5.18
## Salinity 5 30894 31.00 3.24 31.00 31.15 2.52
## Turbidity 6 30894 3.94 3.94 3.19 3.27 1.11
## Chlorophyll 7 30894 2.78 1.84 2.41 2.56 1.54
## Specific.Conductance 8 30894 47.93 5.04 47.66 48.28 4.44
## Average.Water.Speed 9 30894 16.80 13.16 13.40 15.00 11.56
## Average.Water.Direction 10 30894 177.54 103.62 176.33 176.99 134.62
## min max range skew kurtosis se
## Temperature 17.00 32.06 15.06 -0.42 -0.51 0.02
## pH 7.31 8.26 0.95 -0.20 -0.25 0.00
## Dissolved.Oxygen 3.03 9.26 6.23 -0.24 1.24 0.00
## Dissolved.Oxygen...Saturation. 51.84 134.08 82.25 -0.09 2.38 0.04
## Salinity 0.06 36.00 35.94 -1.06 5.00 0.02
## Turbidity 0.34 49.87 49.53 5.50 39.75 0.02
## Chlorophyll 0.10 43.30 43.20 2.28 20.97 0.01
## Specific.Conductance 0.02 55.00 54.98 -1.17 5.19 0.03
## Average.Water.Speed 0.00 89.91 89.91 1.32 1.95 0.07
## Average.Water.Direction 0.00 359.99 359.99 0.04 -1.23 0.592.9 Visualisasi Setelah Cleaning & Imputasi
data_clean_long <- data_clean %>%
pivot_longer(
cols = everything(),
names_to = "Variabel",
values_to = "Nilai"
)— Histogram
ggplot(data_clean_long, aes(x = Nilai)) +
geom_histogram(bins = 30, fill = "steelblue", color = "black") +
facet_wrap(~ Variabel, scales = "free") +
labs(
title = "Distribusi Variabel Kualitas Air Setelah Cleaning & Imputasi",
x = "Nilai",
y = "Frekuensi"
)
— Boxplot
ggplot(data_clean_long, aes(x = Variabel, y = Nilai)) +
geom_boxplot(fill = "orange") +
coord_flip() +
labs(
title = "Boxplot Variabel Kualitas Air Setelah Cleaning & Imputasi",
x = "Variabel",
y = "Nilai"
)
2.10 Standarisasi Data
data_scaled <- scale(data_clean)STAGE 3 : Assumption Testing (Uji Asumsi)
3.1 Matriks Korelasi
cor_matrix <- cor(data_scaled)
cor_matrix ## Temperature pH Dissolved.Oxygen
## Temperature 1.000000000 -0.49240828 -0.353587645
## pH -0.492408283 1.00000000 0.345585762
## Dissolved.Oxygen -0.353587645 0.34558576 1.000000000
## Dissolved.Oxygen...Saturation. 0.242942133 -0.08325193 0.631901391
## Salinity -0.052703138 -0.18793072 -0.130492835
## Turbidity -0.108563401 0.21117544 0.046123022
## Chlorophyll 0.200101059 -0.02636365 0.209959555
## Specific.Conductance -0.032884191 -0.22030838 -0.146478809
## Average.Water.Speed 0.009350559 0.04806107 -0.056891770
## Average.Water.Direction -0.040042127 0.02465841 -0.004656729
## Dissolved.Oxygen...Saturation. Salinity
## Temperature 0.24294213 -0.052703138
## pH -0.08325193 -0.187930723
## Dissolved.Oxygen 0.63190139 -0.130492835
## Dissolved.Oxygen...Saturation. 1.00000000 0.055648951
## Salinity 0.05564895 1.000000000
## Turbidity -0.07520407 -0.259396223
## Chlorophyll 0.32627719 -0.246801529
## Specific.Conductance 0.06595632 0.892962626
## Average.Water.Speed -0.13493854 -0.109285465
## Average.Water.Direction -0.05223865 -0.006512387
## Turbidity Chlorophyll Specific.Conductance
## Temperature -0.10856340 0.200101059 -0.03288419
## pH 0.21117544 -0.026363652 -0.22030838
## Dissolved.Oxygen 0.04612302 0.209959555 -0.14647881
## Dissolved.Oxygen...Saturation. -0.07520407 0.326277185 0.06595632
## Salinity -0.25939622 -0.246801529 0.89296263
## Turbidity 1.00000000 0.085125417 -0.25870116
## Chlorophyll 0.08512542 1.000000000 -0.26618449
## Specific.Conductance -0.25870116 -0.266184494 1.00000000
## Average.Water.Speed 0.10228689 -0.048677120 -0.11776581
## Average.Water.Direction 0.01399139 -0.006064756 -0.01002414
## Average.Water.Speed Average.Water.Direction
## Temperature 0.009350559 -0.040042127
## pH 0.048061065 0.024658413
## Dissolved.Oxygen -0.056891770 -0.004656729
## Dissolved.Oxygen...Saturation. -0.134938542 -0.052238646
## Salinity -0.109285465 -0.006512387
## Turbidity 0.102286892 0.013991389
## Chlorophyll -0.048677120 -0.006064756
## Specific.Conductance -0.117765809 -0.010024138
## Average.Water.Speed 1.000000000 0.027425790
## Average.Water.Direction 0.027425790 1.0000000003.2 Uji KMO (Kaiser-Meyer-Olkin)
KMO(cor_matrix)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cor_matrix)
## Overall MSA = 0.51
## MSA for each item =
## Temperature pH
## 0.37 0.77
## Dissolved.Oxygen Dissolved.Oxygen...Saturation.
## 0.40 0.36
## Salinity Turbidity
## 0.57 0.84
## Chlorophyll Specific.Conductance
## 0.84 0.56
## Average.Water.Speed Average.Water.Direction
## 0.68 0.683.3 Uji Bartlett’s Test of Sphericity
cortest.bartlett(cor_matrix, n = nrow(data_scaled))## $chisq
## [1] 115088.4
##
## $p.value
## [1] 0
##
## $df
## [1] 45STAGE 4 : Factor Extraction
4.1 Principal Component Analysis (PCA)
pca <- prcomp(data_scaled)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.5376 1.3362 1.3070 0.9985 0.96942 0.91701 0.80712
## Proportion of Variance 0.2364 0.1785 0.1708 0.0997 0.09398 0.08409 0.06514
## Cumulative Proportion 0.2364 0.4150 0.5858 0.6855 0.77947 0.86356 0.92871
## PC8 PC9 PC10
## Standard deviation 0.69158 0.36029 0.32379
## Proportion of Variance 0.04783 0.01298 0.01048
## Cumulative Proportion 0.97653 0.98952 1.00000pca$rotation## PC1 PC2 PC3 PC4
## Temperature 0.13721108 -0.24087973 0.611301062 -0.03580942
## pH -0.33246275 0.17734912 -0.462410842 0.04554132
## Dissolved.Oxygen -0.31982198 -0.42506967 -0.423984767 -0.04069505
## Dissolved.Oxygen...Saturation. -0.09199094 -0.67639482 -0.073143809 -0.05733365
## Salinity 0.53891326 -0.11507008 -0.294344790 -0.04238309
## Turbidity -0.29833162 0.18923046 -0.001169295 0.02216107
## Chlorophyll -0.26459253 -0.38069114 0.230513523 -0.08346973
## Specific.Conductance 0.54928285 -0.11835094 -0.276906486 -0.03759107
## Average.Water.Speed -0.09216561 0.23987437 0.098807411 -0.15577744
## Average.Water.Direction -0.01576699 0.08251296 -0.034019293 -0.97814422
## PC5 PC6 PC7 PC8
## Temperature -0.08175712 -0.06237519 -0.19061766 0.57218237
## pH 0.02719840 0.03304206 0.21985140 0.76743451
## Dissolved.Oxygen -0.13209042 0.12219028 -0.19267696 -0.19771928
## Dissolved.Oxygen...Saturation. -0.19137719 -0.03148638 -0.29899545 0.13115705
## Salinity -0.14743919 -0.22486032 0.17793547 0.07809202
## Turbidity -0.14517529 -0.89078338 -0.23556789 -0.06204404
## Chlorophyll 0.02716109 -0.20734760 0.81753364 -0.10868236
## Specific.Conductance -0.14240222 -0.22869894 0.12713218 0.06006381
## Average.Water.Speed -0.91898936 0.19878723 0.11461649 -0.03788677
## Average.Water.Direction 0.17358332 -0.01503012 -0.06319433 0.02353224
## PC9 PC10
## Temperature -0.40991905 0.0764362156
## pH 0.05241432 0.0157750675
## Dissolved.Oxygen -0.64022803 0.1308545212
## Dissolved.Oxygen...Saturation. 0.60278634 -0.1334994905
## Salinity -0.22222493 -0.6696658840
## Turbidity -0.02785686 -0.0029998345
## Chlorophyll -0.01407892 0.0293136080
## Specific.Conductance 0.06478713 0.7138920755
## Average.Water.Speed 0.03613406 0.0006700977
## Average.Water.Direction 0.01070626 -0.0007779577— Scree Plot PCA
fviz_eig(pca)## Warning in geom_bar(stat = "identity", fill = barfill, color = barcolor, :
## Ignoring empty aesthetic: `width`.
4.2 Penentuan Jumlah Faktor (Parallel Analysis)
fa.parallel(data_scaled, fa = "fa")
## Parallel analysis suggests that the number of factors = 4 and the number of components = NA4.3 Ekstraksi Faktor dengan Rotasi Varimax
fa_result <- fa(
data_scaled,
nfactors = 4,
rotate = "varimax"
)
fa_result## Factor Analysis using method = minres
## Call: fa(r = data_scaled, nfactors = 4, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 h2 u2 com
## Temperature -0.12 0.13 -0.86 -0.01 0.7746 0.2254 1.1
## pH -0.16 0.01 0.60 0.11 0.3914 0.6086 1.2
## Dissolved.Oxygen -0.11 0.74 0.54 -0.01 0.8525 0.1475 1.9
## Dissolved.Oxygen...Saturation. 0.05 0.96 -0.14 -0.02 0.9414 0.0586 1.1
## Salinity 0.89 0.00 -0.06 -0.11 0.8163 0.1837 1.0
## Turbidity -0.16 -0.03 0.13 0.97 0.9952 0.0048 1.1
## Chlorophyll -0.28 0.34 -0.14 0.07 0.2179 0.7821 2.4
## Specific.Conductance 0.98 0.00 -0.10 -0.09 0.9781 0.0219 1.0
## Average.Water.Speed -0.11 -0.13 0.02 0.08 0.0348 0.9652 2.7
## Average.Water.Direction -0.01 -0.04 0.04 0.01 0.0036 0.9964 2.1
##
## MR1 MR2 MR3 MR4
## SS loadings 1.93 1.62 1.46 0.99
## Proportion Var 0.19 0.16 0.15 0.10
## Cumulative Var 0.19 0.36 0.50 0.60
## Proportion Explained 0.32 0.27 0.24 0.17
## Cumulative Proportion 0.32 0.59 0.83 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 3.73 with Chi Square = 115088.4
## df of the model are 11 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 30894 with the empirical chi square 108.73 with prob < 3.3e-18
## The total n.obs was 30894 with Likelihood Chi Square = 390.99 with prob < 5e-77
##
## Tucker Lewis Index of factoring reliability = 0.986
## RMSEA index = 0.033 and the 90 % confidence intervals are 0.031 0.036
## BIC = 277.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4
## Correlation of (regression) scores with factors 0.99 0.98 0.93 1.00
## Multiple R square of scores with factors 0.98 0.95 0.86 0.99
## Minimum correlation of possible factor scores 0.96 0.90 0.72 0.98STAGE 5 : Factor Interpretation
5.1 Matriks Factor Loadings
fa_result$loadings##
## Loadings:
## MR1 MR2 MR3 MR4
## Temperature -0.122 0.128 -0.862
## pH -0.157 0.595 0.111
## Dissolved.Oxygen -0.107 0.744 0.537
## Dissolved.Oxygen...Saturation. 0.958 -0.144
## Salinity 0.895 -0.106
## Turbidity -0.165 0.131 0.974
## Chlorophyll -0.278 0.342 -0.139
## Specific.Conductance 0.981
## Average.Water.Speed -0.110 -0.128
## Average.Water.Direction
##
## MR1 MR2 MR3 MR4
## SS loadings 1.932 1.624 1.458 0.992
## Proportion Var 0.193 0.162 0.146 0.099
## Cumulative Var 0.193 0.356 0.501 0.601