d2
2023-01-09
needed_packages <- c("psych", "REdaS", "Hmisc", "corrplot", "ggcorrplot", "factoextra", "nFactors")
# Extract not installed packages
not_installed <- needed_packages[!(needed_packages %in% installed.packages()[ , "Package"])]
# Install not installed packages
if(length(not_installed)) install.packages(not_installed, repos = "http://cran.us.r-project.org")
library(psych)
library(REdaS)## Loading required package: gridlibrary(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha##
## Attaching package: 'Hmisc'## The following object is masked from 'package:psych':
##
## describe## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(corrplot)## corrplot 0.92 loadedlibrary(ggcorrplot)
library(factoextra)#Used for principal component analysis to get a different view of eigenvalues## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(nFactors)##
## Attaching package: 'nFactors'## The following object is masked from 'package:lattice':
##
## parallellibrary(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:Hmisc':
##
## src, summarize## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readr)#We read the dat and get its dimensions and structure
studentdata <- read.csv("studentpartII.csv")
head(studentdata)## id school sex age.x address famsize Pstatus Medu Fedu Mjob Fjob
## 1 1 GP F 15 R GT3 T 1 1 at_home other
## 2 10 GP F 15 U GT3 A 3 3 other health
## 3 100 GP F 17 R LE3 T 2 2 services services
## 4 101 GP F 17 R LE3 T 3 1 services other
## 5 102 GP F 17 R LE3 T 4 4 services other
## 6 103 GP F 17 U GT3 A 2 1 other other
## reason nursery internet guardian.x traveltime.x studytime.x failures.x
## 1 home yes yes mother 2 4 1
## 2 reputation yes no father 1 4 0
## 3 course yes yes mother 1 3 0
## 4 reputation yes no mother 2 4 0
## 5 other yes no mother 1 1 0
## 6 course yes yes mother 2 3 0
## schoolsup.x famsup.x paid.x activities.x higher.x romantic.x famrel.x
## 1 yes yes yes yes yes no 3
## 2 yes no no no yes no 4
## 3 no yes yes yes yes no 3
## 4 no yes yes no yes no 3
## 5 no yes yes no yes no 5
## 6 no no no yes yes yes 3
## freetime.x goout.x Dalc.x Walc.x health.x absences.x G1.x G2.x G3.x
## 1 1 2 1 1 1 2 7 10 10
## 2 3 3 1 1 4 10 10 11 11
## 3 3 2 2 2 3 3 11 11 11
## 4 1 2 1 1 3 6 18 18 18
## 5 2 1 1 2 3 12 8 10 10
## 6 2 3 1 2 3 10 12 10 12
## guardian.y traveltime.y studytime.y failures.y schoolsup.y famsup.y paid.y
## 1 mother 2 4 0 yes yes yes
## 2 father 1 4 0 yes no no
## 3 mother 1 3 0 no yes no
## 4 mother 2 4 0 no yes no
## 5 mother 1 1 0 no yes no
## 6 mother 2 3 0 no no no
## activities.y higher.y romantic.y famrel.y freetime.y goout.y Dalc.y Walc.y
## 1 yes yes no 3 1 2 1 1
## 2 no yes no 4 3 3 1 1
## 3 yes yes no 3 3 2 2 2
## 4 no yes no 3 1 2 1 1
## 5 no yes no 5 2 1 1 2
## 6 yes yes yes 3 2 3 1 2
## health.y absences.y G1.y G2.y G3.y A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 B1 B2 B3 B4
## 1 1 4 13 13 13 4 3 4 2 4 2 3 5 2 3 4 4 4 4
## 2 4 10 10 10 10 3 4 2 4 4 4 3 3 2 3 5 5 5 5
## 3 3 0 11 11 10 5 5 5 5 5 5 5 2 1 2 4 3 4 4
## 4 3 0 18 19 19 4 5 4 4 4 5 4 3 1 2 5 5 4 5
## 5 3 6 12 11 11 3 3 2 4 3 4 4 3 4 4 4 5 5 5
## 6 3 0 15 15 16 4 4 4 3 4 3 4 3 3 3 4 3 4 5
## B5 B6 B7 B8 B9 B10 B11 B12 B13 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 D1 D2 D3 D4 D5
## 1 4 4 4 4 1 2 2 2 2 2 1 4 2 2 4 5 5 4 2 2 2 5 4 2
## 2 4 5 2 4 2 1 1 2 3 4 5 5 4 3 1 2 1 1 1 4 4 5 5 4
## 3 4 3 5 5 3 2 4 1 2 4 3 4 4 4 1 2 2 2 3 3 3 3 3 3
## 4 5 4 4 4 2 2 4 1 1 2 3 3 2 2 2 3 3 4 2 4 3 3 5 4
## 5 4 5 2 4 4 4 3 1 2 2 3 2 3 1 5 4 4 3 2 5 5 4 4 3
## 6 4 4 4 4 5 2 1 2 1 3 4 3 3 3 4 3 1 2 2 4 3 2 3 5
## D6 D7 D8 D9 D10 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10
## 1 4 2 2 3 5 2 3 4 2 5 5 1 2 3 1 1 2 1 1 1 4 4 4 4 4
## 2 4 1 1 2 1 4 4 5 5 5 4 1 1 1 1 2 2 1 3 5 3 4 5 3 5
## 3 4 3 3 4 4 3 3 5 2 5 1 1 3 2 2 4 5 5 4 5 2 2 3 1 1
## 4 4 3 2 4 1 3 2 4 4 4 2 2 3 1 4 3 3 1 4 2 3 3 5 3 4
## 5 2 2 2 2 2 2 2 3 1 4 3 5 5 4 3 3 3 2 2 2 4 4 5 3 4
## 6 5 2 2 2 2 3 3 4 2 4 3 2 3 2 3 3 3 2 4 2 3 4 3 3 4
## G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 I1 I2 I3 I4 I5
## 1 4 2 1 2 4 2 3 2 4 5 3 2 2 1 1 2 3 3 3 4 4 3 4 3 5
## 2 5 5 5 3 5 1 1 2 1 1 4 5 4 1 1 4 2 3 1 2 1 2 2 1 4
## 3 4 4 2 5 5 1 2 2 2 3 4 3 3 2 4 5 4 3 2 1 2 2 2 2 3
## 4 4 4 4 4 4 3 3 2 4 3 5 5 4 3 3 3 2 2 1 4 2 3 4 3 4
## 5 2 4 2 2 4 5 5 2 5 4 4 5 2 5 1 2 4 3 4 2 4 4 3 4 4
## 6 3 2 4 3 4 2 3 1 4 2 5 4 5 2 4 4 2 2 3 2 2 4 3 3 3
## I6 I7 I8 I9 I10 J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 K1 K2 K3 K4 K5 K6 K7 K8 K9 K10
## 1 2 3 3 3 3 5 4 3 4 5 3 5 1 2 2 5 4 4 5 2 2 4 1 4 4
## 2 2 3 5 4 4 4 3 2 2 4 4 5 1 3 3 1 2 1 1 1 5 4 4 4 5
## 3 1 4 4 4 3 2 3 2 5 2 1 2 4 2 2 2 1 3 2 2 5 4 4 3 4
## 4 3 3 3 3 3 4 5 5 5 4 3 3 3 1 2 3 3 1 4 4 3 2 1 2 4
## 5 2 3 4 3 3 4 2 2 2 2 4 4 2 4 4 4 2 2 4 3 2 3 4 3 3
## 6 3 2 2 3 3 4 4 5 5 3 3 4 3 1 1 3 4 4 3 3 3 3 3 3 4
## L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 N1 N2 N3 N4 N5
## 1 2 2 3 4 5 1 4 2 2 4 2 4 5 4 2 3 2 3 2 2 2 5 4 1 3
## 2 1 1 1 2 2 1 2 4 4 4 4 5 5 5 5 1 1 1 1 1 3 3 4 3 4
## 3 5 0 3 3 2 4 3 3 4 3 2 4 5 3 3 2 2 2 2 3 2 2 4 3 4
## 4 4 3 2 4 4 4 5 1 3 4 5 4 5 4 3 1 1 1 1 1 3 4 4 3 4
## 5 5 4 4 5 4 5 4 1 1 3 3 5 3 4 2 2 2 2 4 2 4 4 5 4 5
## 6 2 3 3 4 4 3 2 2 2 4 5 5 5 4 4 2 1 2 2 3 3 4 4 4 4
## N6 N7 N8 N9 N10 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
## 1 2 4 2 3 2 4 3 4 4 4 4 4 2 2 4 4 4 2 2 2 4 2 2 4 2
## 2 4 3 3 3 2 1 2 3 2 2 4 4 3 4 4 2 2 5 4 1 2 5 3 4 3
## 3 3 3 5 5 3 5 4 4 3 4 4 3 3 3 4 2 2 3 2 2 4 2 4 4 5
## 4 3 4 5 3 2 4 3 4 4 4 2 2 4 2 2 4 3 3 4 3 3 2 2 5 5
## 5 4 5 4 3 2 5 2 5 4 4 5 1 5 3 5 5 5 4 5 3 3 3 1 4 4
## 6 4 5 4 3 2 4 3 4 4 4 2 2 2 3 3 3 2 3 3 3 3 3 2 3 3str(studentdata)## 'data.frame': 382 obs. of 217 variables:
## $ id : int 1 10 100 101 102 103 104 105 106 107 ...
## $ school : chr "GP" "GP" "GP" "GP" ...
## $ sex : chr "F" "F" "F" "F" ...
## $ age.x : int 15 15 17 17 17 17 17 17 17 17 ...
## $ address : chr "R" "U" "R" "R" ...
## $ famsize : chr "GT3" "GT3" "LE3" "LE3" ...
## $ Pstatus : chr "T" "A" "T" "T" ...
## $ Medu : int 1 3 2 3 4 2 2 3 4 4 ...
## $ Fedu : int 1 3 2 1 4 1 2 3 3 4 ...
## $ Mjob : chr "at_home" "other" "services" "services" ...
## $ Fjob : chr "other" "health" "services" "other" ...
## $ reason : chr "home" "reputation" "course" "reputation" ...
## $ nursery : chr "yes" "yes" "yes" "yes" ...
## $ internet : chr "yes" "no" "yes" "no" ...
## $ guardian.x : chr "mother" "father" "mother" "mother" ...
## $ traveltime.x: int 2 1 1 2 1 2 1 1 1 2 ...
## $ studytime.x : int 4 4 3 4 1 3 2 2 2 2 ...
## $ failures.x : int 1 0 0 0 0 0 1 0 0 0 ...
## $ schoolsup.x : chr "yes" "yes" "no" "no" ...
## $ famsup.x : chr "yes" "no" "yes" "yes" ...
## $ paid.x : chr "yes" "no" "yes" "yes" ...
## $ activities.x: chr "yes" "no" "yes" "no" ...
## $ higher.x : chr "yes" "yes" "yes" "yes" ...
## $ romantic.x : chr "no" "no" "no" "no" ...
## $ famrel.x : int 3 4 3 3 5 3 3 3 5 4 ...
## $ freetime.x : int 1 3 3 1 2 2 3 3 2 1 ...
## $ goout.x : int 2 3 2 2 1 3 1 3 2 4 ...
## $ Dalc.x : int 1 1 2 1 1 1 1 1 1 1 ...
## $ Walc.x : int 1 1 2 1 2 2 2 3 2 1 ...
## $ health.x : int 1 4 3 3 3 3 4 3 5 1 ...
## $ absences.x : int 2 10 3 6 12 10 0 6 23 6 ...
## $ G1.x : int 7 10 11 18 8 12 9 8 13 6 ...
## $ G2.x : int 10 11 11 18 10 10 8 7 13 5 ...
## $ G3.x : int 10 11 11 18 10 12 0 9 13 6 ...
## $ guardian.y : chr "mother" "father" "mother" "mother" ...
## $ traveltime.y: int 2 1 1 2 1 2 1 1 1 2 ...
## $ studytime.y : int 4 4 3 4 1 3 2 2 2 2 ...
## $ failures.y : int 0 0 0 0 0 0 0 0 0 0 ...
## $ schoolsup.y : chr "yes" "yes" "no" "no" ...
## $ famsup.y : chr "yes" "no" "yes" "yes" ...
## $ paid.y : chr "yes" "no" "no" "no" ...
## $ activities.y: chr "yes" "no" "yes" "no" ...
## $ higher.y : chr "yes" "yes" "yes" "yes" ...
## $ romantic.y : chr "no" "no" "no" "no" ...
## $ famrel.y : int 3 4 3 3 5 3 3 3 5 4 ...
## $ freetime.y : int 1 3 3 1 2 2 3 3 2 1 ...
## $ goout.y : int 2 3 2 2 1 3 1 3 2 4 ...
## $ Dalc.y : int 1 1 2 1 1 1 1 1 1 1 ...
## $ Walc.y : int 1 1 2 1 2 2 2 3 2 1 ...
## $ health.y : int 1 4 3 3 3 3 4 3 5 1 ...
## $ absences.y : int 4 10 0 0 6 0 18 10 14 2 ...
## $ G1.y : int 13 10 11 18 12 15 10 12 15 10 ...
## $ G2.y : int 13 10 11 19 11 15 12 13 14 13 ...
## $ G3.y : int 13 10 10 19 11 16 14 14 17 13 ...
## $ A1 : int 4 3 5 4 3 4 4 5 5 4 ...
## $ A2 : int 3 4 5 5 3 4 4 5 3 4 ...
## $ A3 : int 4 2 5 4 2 4 4 4 3 5 ...
## $ A4 : int 2 4 5 4 4 3 4 3 4 4 ...
## $ A5 : int 4 4 5 4 3 4 4 5 4 5 ...
## $ A6 : int 2 4 5 5 4 3 4 5 1 4 ...
## $ A7 : int 3 3 5 4 4 4 5 4 2 5 ...
## $ A8 : int 5 3 2 3 3 3 3 4 3 1 ...
## $ A9 : int 2 2 1 1 4 3 2 2 2 1 ...
## $ A10 : int 3 3 2 2 4 3 3 2 2 2 ...
## $ B1 : int 4 5 4 5 4 4 3 4 5 4 ...
## $ B2 : int 4 5 3 5 5 3 3 2 5 4 ...
## $ B3 : int 4 5 4 4 5 4 4 5 5 4 ...
## $ B4 : int 4 5 4 5 5 5 4 5 5 4 ...
## $ B5 : int 4 4 4 5 4 4 4 3 4 4 ...
## $ B6 : int 4 5 3 4 5 4 2 3 5 4 ...
## $ B7 : int 4 2 5 4 2 4 4 5 4 4 ...
## $ B8 : int 4 4 5 4 4 4 5 5 4 4 ...
## $ B9 : int 1 2 3 2 4 5 4 4 2 2 ...
## $ B10 : int 2 1 2 2 4 2 2 2 2 4 ...
## $ B11 : int 2 1 4 4 3 1 2 4 1 4 ...
## $ B12 : int 2 2 1 1 1 2 2 1 1 1 ...
## $ B13 : int 2 3 2 1 2 1 3 2 1 1 ...
## $ C1 : int 2 4 4 2 2 3 3 1 4 2 ...
## $ C2 : int 1 5 3 3 3 4 4 4 5 4 ...
## $ C3 : int 4 5 4 3 2 3 4 4 4 4 ...
## $ C4 : int 2 4 4 2 3 3 3 5 3 2 ...
## $ C5 : int 2 3 4 2 1 3 5 5 2 1 ...
## $ C6 : int 4 1 1 2 5 4 2 1 2 4 ...
## $ C7 : int 5 2 2 3 4 3 3 1 2 3 ...
## $ C8 : int 5 1 2 3 4 1 3 2 1 2 ...
## $ C9 : int 4 1 2 4 3 2 3 1 1 2 ...
## $ C10 : int 2 1 3 2 2 2 3 2 3 2 ...
## $ D1 : int 2 4 3 4 5 4 4 3 4 4 ...
## $ D2 : int 2 4 3 3 5 3 3 4 2 4 ...
## $ D3 : int 5 5 3 3 4 2 3 3 5 4 ...
## $ D4 : int 4 5 3 5 4 3 3 4 5 4 ...
## $ D5 : int 2 4 3 4 3 5 4 3 5 4 ...
## $ D6 : int 4 4 4 4 2 5 4 4 5 4 ...
## $ D7 : int 2 1 3 3 2 2 3 4 3 2 ...
## $ D8 : int 2 1 3 2 2 2 2 2 1 2 ...
## $ D9 : int 3 2 4 4 2 2 3 4 4 2 ...
## $ D10 : int 5 1 4 1 2 2 3 1 1 2 ...
## $ E1 : int 2 4 3 3 2 3 3 2 2 5 ...
## $ E2 : int 3 4 3 2 2 3 4 5 2 4 ...
## [list output truncated]dim(studentdata)## [1] 382 217This information is not considered statistical, it is just to get an idea of the actual dataset.
#We need to reverse code the negative columns into positive values.
ragdataNegative <- subset(studentdata, select = c("A1","A3","A5", "A7","C2", "C4","C6", "C8","E2", "E4","E6", "E8","E10"))
# Reverse the values in all columns
reverse_values <- function(col) {
max_val <- max(col) + 1
return(max_val - col)
}
ragDataNegative <- data.frame(apply(ragdataNegative, 2 , reverse_values))
raqDataPositive <- subset(studentdata, select = c("A2", "A4","A6","A8","A9", "A10","C1", "C3","C5", "C7","C9","C10","E1", "E3","E5", "E7","E9"))
raqData <- merge(raqDataPositive,ragDataNegative)
head(raqData)## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10 E1 E3 E5 E7 E9 A1 A3 A5 A7 C2 C4 C6 C8
## 1 3 2 2 5 2 3 2 4 2 5 4 2 2 4 5 1 3 2 2 2 3 5 4 2 1
## 2 4 4 4 3 2 3 4 5 3 2 1 1 4 5 5 1 1 2 2 2 3 5 4 2 1
## 3 5 5 5 2 1 2 4 4 4 2 2 3 3 5 5 1 2 2 2 2 3 5 4 2 1
## 4 5 4 5 3 1 2 2 3 2 3 4 2 3 4 4 2 1 2 2 2 3 5 4 2 1
## 5 3 4 4 3 4 4 2 2 1 4 3 2 2 3 4 5 4 2 2 2 3 5 4 2 1
## 6 4 3 3 3 3 3 3 3 3 3 2 2 3 4 4 2 2 2 2 2 3 5 4 2 1
## E2 E4 E6 E8 E10
## 1 3 4 1 4 5
## 2 3 4 1 4 5
## 3 3 4 1 4 5
## 4 3 4 1 4 5
## 5 3 4 1 4 5
## 6 3 4 1 4 5##Step 1: Screen the correlation matrix
#create a correlation matrix (these are just some methods)
raqMatrix<-cor(raqData)
round(raqMatrix, 2)## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10
## A2 1.00 0.40 0.51 -0.17 -0.27 -0.08 0.00 0.20 0.04 0.03 0.02 -0.01
## A4 0.40 1.00 0.34 -0.24 -0.39 -0.18 0.06 0.11 0.08 0.06 -0.09 0.02
## A6 0.51 0.34 1.00 -0.09 -0.27 -0.07 0.15 0.36 0.19 -0.14 -0.15 -0.15
## A8 -0.17 -0.24 -0.09 1.00 0.30 0.24 0.03 0.10 0.01 0.00 0.05 -0.01
## A9 -0.27 -0.39 -0.27 0.30 1.00 0.30 -0.03 -0.03 -0.13 0.15 0.15 0.11
## A10 -0.08 -0.18 -0.07 0.24 0.30 1.00 -0.01 -0.02 -0.01 0.07 0.14 0.10
## C1 0.00 0.06 0.15 0.03 -0.03 -0.01 1.00 0.22 0.32 -0.45 -0.28 -0.26
## C3 0.20 0.11 0.36 0.10 -0.03 -0.02 0.22 1.00 0.34 -0.28 -0.30 -0.46
## C5 0.04 0.08 0.19 0.01 -0.13 -0.01 0.32 0.34 1.00 -0.35 -0.28 -0.41
## C7 0.03 0.06 -0.14 0.00 0.15 0.07 -0.45 -0.28 -0.35 1.00 0.62 0.53
## C9 0.02 -0.09 -0.15 0.05 0.15 0.14 -0.28 -0.30 -0.28 0.62 1.00 0.48
## C10 -0.01 0.02 -0.15 -0.01 0.11 0.10 -0.26 -0.46 -0.41 0.53 0.48 1.00
## E1 0.36 0.18 0.29 -0.06 -0.16 -0.03 0.17 0.34 0.15 -0.17 -0.07 -0.24
## E3 0.36 0.26 0.23 0.03 -0.14 0.08 0.10 0.14 0.07 -0.01 0.09 0.06
## E5 0.43 0.34 0.43 -0.06 -0.15 -0.05 0.06 0.24 0.11 0.03 0.03 -0.05
## E7 -0.13 -0.09 -0.08 0.14 0.24 0.17 -0.01 0.01 -0.06 0.13 0.08 0.00
## E9 -0.08 -0.15 -0.14 0.13 0.15 0.15 -0.06 -0.13 -0.12 0.10 0.14 0.25
## A1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E1 E3 E5 E7 E9 A1 A3 A5 A7 C2 C4 C6
## A2 0.36 0.36 0.43 -0.13 -0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A4 0.18 0.26 0.34 -0.09 -0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A6 0.29 0.23 0.43 -0.08 -0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A8 -0.06 0.03 -0.06 0.14 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A9 -0.16 -0.14 -0.15 0.24 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A10 -0.03 0.08 -0.05 0.17 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C1 0.17 0.10 0.06 -0.01 -0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C3 0.34 0.14 0.24 0.01 -0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C5 0.15 0.07 0.11 -0.06 -0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C7 -0.17 -0.01 0.03 0.13 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C9 -0.07 0.09 0.03 0.08 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C10 -0.24 0.06 -0.05 0.00 0.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E1 1.00 0.32 0.40 -0.10 -0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E3 0.32 1.00 0.53 -0.43 -0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E5 0.40 0.53 1.00 -0.26 -0.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E7 -0.10 -0.43 -0.26 1.00 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E9 -0.07 -0.12 -0.20 0.24 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A1 0.00 0.00 0.00 0.00 0.00 1.00 0.56 0.42 0.31 0.10 0.04 0.13
## A3 0.00 0.00 0.00 0.00 0.00 0.56 1.00 0.30 0.41 0.08 0.03 0.10
## A5 0.00 0.00 0.00 0.00 0.00 0.42 0.30 1.00 0.26 0.16 0.14 -0.10
## A7 0.00 0.00 0.00 0.00 0.00 0.31 0.41 0.26 1.00 0.00 0.06 -0.03
## C2 0.00 0.00 0.00 0.00 0.00 0.10 0.08 0.16 0.00 1.00 0.44 -0.24
## C4 0.00 0.00 0.00 0.00 0.00 0.04 0.03 0.14 0.06 0.44 1.00 -0.30
## C6 0.00 0.00 0.00 0.00 0.00 0.13 0.10 -0.10 -0.03 -0.24 -0.30 1.00
## C8 0.00 0.00 0.00 0.00 0.00 -0.04 0.08 -0.13 0.01 -0.63 -0.38 0.37
## E2 0.00 0.00 0.00 0.00 0.00 0.12 0.04 0.21 0.15 0.17 0.17 -0.06
## E4 0.00 0.00 0.00 0.00 0.00 0.13 0.09 0.24 0.19 0.14 0.11 -0.05
## E6 0.00 0.00 0.00 0.00 0.00 0.15 0.17 0.18 0.12 0.06 0.08 0.28
## E8 0.00 0.00 0.00 0.00 0.00 -0.03 0.05 -0.25 -0.11 -0.05 -0.07 0.25
## E10 0.00 0.00 0.00 0.00 0.00 0.02 0.05 -0.10 -0.06 0.12 0.08 -0.04
## C8 E2 E4 E6 E8 E10
## A2 0.00 0.00 0.00 0.00 0.00 0.00
## A4 0.00 0.00 0.00 0.00 0.00 0.00
## A6 0.00 0.00 0.00 0.00 0.00 0.00
## A8 0.00 0.00 0.00 0.00 0.00 0.00
## A9 0.00 0.00 0.00 0.00 0.00 0.00
## A10 0.00 0.00 0.00 0.00 0.00 0.00
## C1 0.00 0.00 0.00 0.00 0.00 0.00
## C3 0.00 0.00 0.00 0.00 0.00 0.00
## C5 0.00 0.00 0.00 0.00 0.00 0.00
## C7 0.00 0.00 0.00 0.00 0.00 0.00
## C9 0.00 0.00 0.00 0.00 0.00 0.00
## C10 0.00 0.00 0.00 0.00 0.00 0.00
## E1 0.00 0.00 0.00 0.00 0.00 0.00
## E3 0.00 0.00 0.00 0.00 0.00 0.00
## E5 0.00 0.00 0.00 0.00 0.00 0.00
## E7 0.00 0.00 0.00 0.00 0.00 0.00
## E9 0.00 0.00 0.00 0.00 0.00 0.00
## A1 -0.04 0.12 0.13 0.15 -0.03 0.02
## A3 0.08 0.04 0.09 0.17 0.05 0.05
## A5 -0.13 0.21 0.24 0.18 -0.25 -0.10
## A7 0.01 0.15 0.19 0.12 -0.11 -0.06
## C2 -0.63 0.17 0.14 0.06 -0.05 0.12
## C4 -0.38 0.17 0.11 0.08 -0.07 0.08
## C6 0.37 -0.06 -0.05 0.28 0.25 -0.04
## C8 1.00 -0.13 -0.12 0.03 0.17 -0.13
## E2 -0.13 1.00 0.65 0.38 -0.53 -0.20
## E4 -0.12 0.65 1.00 0.34 -0.55 -0.22
## E6 0.03 0.38 0.34 1.00 -0.14 -0.15
## E8 0.17 -0.53 -0.55 -0.14 1.00 0.26
## E10 -0.13 -0.20 -0.22 -0.15 0.26 1.00Hmisc::rcorr(as.matrix(raqData))## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10
## A2 1.00 0.40 0.51 -0.17 -0.27 -0.08 0.00 0.20 0.04 0.03 0.02 -0.01
## A4 0.40 1.00 0.34 -0.24 -0.39 -0.18 0.06 0.11 0.08 0.06 -0.09 0.02
## A6 0.51 0.34 1.00 -0.09 -0.27 -0.07 0.15 0.36 0.19 -0.14 -0.15 -0.15
## A8 -0.17 -0.24 -0.09 1.00 0.30 0.24 0.03 0.10 0.01 0.00 0.05 -0.01
## A9 -0.27 -0.39 -0.27 0.30 1.00 0.30 -0.03 -0.03 -0.13 0.15 0.15 0.11
## A10 -0.08 -0.18 -0.07 0.24 0.30 1.00 -0.01 -0.02 -0.01 0.07 0.14 0.10
## C1 0.00 0.06 0.15 0.03 -0.03 -0.01 1.00 0.22 0.32 -0.45 -0.28 -0.26
## C3 0.20 0.11 0.36 0.10 -0.03 -0.02 0.22 1.00 0.34 -0.28 -0.30 -0.46
## C5 0.04 0.08 0.19 0.01 -0.13 -0.01 0.32 0.34 1.00 -0.35 -0.28 -0.41
## C7 0.03 0.06 -0.14 0.00 0.15 0.07 -0.45 -0.28 -0.35 1.00 0.62 0.53
## C9 0.02 -0.09 -0.15 0.05 0.15 0.14 -0.28 -0.30 -0.28 0.62 1.00 0.48
## C10 -0.01 0.02 -0.15 -0.01 0.11 0.10 -0.26 -0.46 -0.41 0.53 0.48 1.00
## E1 0.36 0.18 0.29 -0.06 -0.16 -0.03 0.17 0.34 0.15 -0.17 -0.07 -0.24
## E3 0.36 0.26 0.23 0.03 -0.14 0.08 0.10 0.14 0.07 -0.01 0.09 0.06
## E5 0.43 0.34 0.43 -0.06 -0.15 -0.05 0.06 0.24 0.11 0.03 0.03 -0.05
## E7 -0.13 -0.09 -0.08 0.14 0.24 0.17 -0.01 0.01 -0.06 0.13 0.08 0.00
## E9 -0.08 -0.15 -0.14 0.13 0.15 0.15 -0.06 -0.13 -0.12 0.10 0.14 0.25
## A1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E1 E3 E5 E7 E9 A1 A3 A5 A7 C2 C4 C6
## A2 0.36 0.36 0.43 -0.13 -0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A4 0.18 0.26 0.34 -0.09 -0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A6 0.29 0.23 0.43 -0.08 -0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A8 -0.06 0.03 -0.06 0.14 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A9 -0.16 -0.14 -0.15 0.24 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A10 -0.03 0.08 -0.05 0.17 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C1 0.17 0.10 0.06 -0.01 -0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C3 0.34 0.14 0.24 0.01 -0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C5 0.15 0.07 0.11 -0.06 -0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C7 -0.17 -0.01 0.03 0.13 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C9 -0.07 0.09 0.03 0.08 0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## C10 -0.24 0.06 -0.05 0.00 0.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E1 1.00 0.32 0.40 -0.10 -0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E3 0.32 1.00 0.53 -0.43 -0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E5 0.40 0.53 1.00 -0.26 -0.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E7 -0.10 -0.43 -0.26 1.00 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## E9 -0.07 -0.12 -0.20 0.24 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## A1 0.00 0.00 0.00 0.00 0.00 1.00 0.56 0.42 0.31 0.10 0.04 0.13
## A3 0.00 0.00 0.00 0.00 0.00 0.56 1.00 0.30 0.41 0.08 0.03 0.10
## A5 0.00 0.00 0.00 0.00 0.00 0.42 0.30 1.00 0.26 0.16 0.14 -0.10
## A7 0.00 0.00 0.00 0.00 0.00 0.31 0.41 0.26 1.00 0.00 0.06 -0.03
## C2 0.00 0.00 0.00 0.00 0.00 0.10 0.08 0.16 0.00 1.00 0.44 -0.24
## C4 0.00 0.00 0.00 0.00 0.00 0.04 0.03 0.14 0.06 0.44 1.00 -0.30
## C6 0.00 0.00 0.00 0.00 0.00 0.13 0.10 -0.10 -0.03 -0.24 -0.30 1.00
## C8 0.00 0.00 0.00 0.00 0.00 -0.04 0.08 -0.13 0.01 -0.63 -0.38 0.37
## E2 0.00 0.00 0.00 0.00 0.00 0.12 0.04 0.21 0.15 0.17 0.17 -0.06
## E4 0.00 0.00 0.00 0.00 0.00 0.13 0.09 0.24 0.19 0.14 0.11 -0.05
## E6 0.00 0.00 0.00 0.00 0.00 0.15 0.17 0.18 0.12 0.06 0.08 0.28
## E8 0.00 0.00 0.00 0.00 0.00 -0.03 0.05 -0.25 -0.11 -0.05 -0.07 0.25
## E10 0.00 0.00 0.00 0.00 0.00 0.02 0.05 -0.10 -0.06 0.12 0.08 -0.04
## C8 E2 E4 E6 E8 E10
## A2 0.00 0.00 0.00 0.00 0.00 0.00
## A4 0.00 0.00 0.00 0.00 0.00 0.00
## A6 0.00 0.00 0.00 0.00 0.00 0.00
## A8 0.00 0.00 0.00 0.00 0.00 0.00
## A9 0.00 0.00 0.00 0.00 0.00 0.00
## A10 0.00 0.00 0.00 0.00 0.00 0.00
## C1 0.00 0.00 0.00 0.00 0.00 0.00
## C3 0.00 0.00 0.00 0.00 0.00 0.00
## C5 0.00 0.00 0.00 0.00 0.00 0.00
## C7 0.00 0.00 0.00 0.00 0.00 0.00
## C9 0.00 0.00 0.00 0.00 0.00 0.00
## C10 0.00 0.00 0.00 0.00 0.00 0.00
## E1 0.00 0.00 0.00 0.00 0.00 0.00
## E3 0.00 0.00 0.00 0.00 0.00 0.00
## E5 0.00 0.00 0.00 0.00 0.00 0.00
## E7 0.00 0.00 0.00 0.00 0.00 0.00
## E9 0.00 0.00 0.00 0.00 0.00 0.00
## A1 -0.04 0.12 0.13 0.15 -0.03 0.02
## A3 0.08 0.04 0.09 0.17 0.05 0.05
## A5 -0.13 0.21 0.24 0.18 -0.25 -0.10
## A7 0.01 0.15 0.19 0.12 -0.11 -0.06
## C2 -0.63 0.17 0.14 0.06 -0.05 0.12
## C4 -0.38 0.17 0.11 0.08 -0.07 0.08
## C6 0.37 -0.06 -0.05 0.28 0.25 -0.04
## C8 1.00 -0.13 -0.12 0.03 0.17 -0.13
## E2 -0.13 1.00 0.65 0.38 -0.53 -0.20
## E4 -0.12 0.65 1.00 0.34 -0.55 -0.22
## E6 0.03 0.38 0.34 1.00 -0.14 -0.15
## E8 0.17 -0.53 -0.55 -0.14 1.00 0.26
## E10 -0.13 -0.20 -0.22 -0.15 0.26 1.00
##
## n= 145924
##
##
## P
## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7
## A2 0.0000 0.0000 0.0000 0.0000 0.0000 0.3844 0.0000 0.0000 0.0000
## A4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.5363
## A9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0016 0.0000 0.0000 0.0000
## C1 0.3844 0.0000 0.0000 0.0000 0.0000 0.0016 0.0000 0.0000 0.0000
## C3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C5 0.0000 0.0000 0.0000 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000
## C7 0.0000 0.0000 0.0000 0.5363 0.0000 0.0000 0.0000 0.0000 0.0000
## C9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C10 0.0352 0.0000 0.0000 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0000 0.0000
## E9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C9 C10 E1 E3 E5 E7 E9 A1 A3 A5
## A2 0.0000 0.0352 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A8 0.0000 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## C1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## C3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0000 1.0000 1.0000 1.0000
## C5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## C7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## C9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## C10 0.0000 0.0000 0.0000 0.0000 0.0997 0.0000 1.0000 1.0000 1.0000
## E1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## E3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## E5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## E7 0.0000 0.0997 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## E9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
## A1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000
## A3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000
## A5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000
## A7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## C2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## C4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## C6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## C8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## E2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## E4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## E6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## E8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## E10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
## A7 C2 C4 C6 C8 E2 E4 E6 E8 E10
## A2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## C10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## E9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
## A1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## A7 0.6695 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C2 0.6695 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## E10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000###Using ggcorrplot
#Using ggcorrplot. Note these are examples you need to choose a style for yourself, you do not need to create multiple correlation matrices
p.mat <- ggcorrplot::cor_pmat(raqData)
ggcorrplot::ggcorrplot(raqMatrix, title = "Correlation matrix for RAQ data")
#Showing Xs for non-significant correlations
ggcorrplot::ggcorrplot(raqMatrix, title = "Correlation matrix for RAQ data", p.mat = p.mat, sig.level = .05)
#Showing lower diagonal
ggcorrplot::ggcorrplot(raqMatrix, title = "Correlation matrix for RAQ data", p.mat = p.mat, sig.level = .05, type="lower")
#Overlay plot with a white grid to space things out.
#t1.cex is the text size, pch is controlling what is shown for non-significant correlations
ggcorrplot(raqMatrix, sig.level=0.05, lab_size = 4.5, p.mat = NULL,
insig = c("pch", "blank"), pch = 1, pch.col = "black", pch.cex =1,
tl.cex = 10) +
theme(axis.text.x = element_text(margin=margin(-2,0,0,0)),
axis.text.y = element_text(margin=margin(0,-2,0,0)),
panel.grid.minor = element_line(size=10)) +
geom_tile(fill="white") +
geom_tile(height=0.8, width=0.8)## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
#Showing the co-coefficients (this will be messy given the number of variables)
ggcorrplot::ggcorrplot(raqMatrix, lab=TRUE, title = "Correlation matrix for RAQ data", type="lower")
###Using corrplot
#Visualization of correlations using circles
#corrplot parameters method = c("circle", "square", "ellipse", "number", "shade",
#"color", "pie")
#type = c("full", "lower", "upper"),
corrplot::corrplot(raqMatrix, method="circle")
corrplot::corrplot(raqMatrix, method="circle", type="upper")
#Visualization using numbers
corrplot::corrplot(raqMatrix, method="number")
#Visualization of significance levels at 0.05
res1 <- corrplot::cor.mtest(raqMatrix, conf.level = .95)
corrplot::corrplot(raqMatrix, p.mat = res1$p, type="lower", sig.level = .05)
#Showing p-value for non-significant results
corrplot::corrplot(raqMatrix, p.mat = res1$p, type="lower",insig = "p-value")
##Step 2: Check if data is suitable - look at the relevant Statistics
###Bartlett’s test
psych::cortest.bartlett(raqData)## R was not square, finding R from data## $chisq
## [1] 1193147
##
## $p.value
## [1] 0
##
## $df
## [1] 435psych::cortest.bartlett(raqMatrix, n=nrow(raqData))## $chisq
## [1] 1193147
##
## $p.value
## [1] 0
##
## $df
## [1] 435###KMO
#KMO (execute one of these):
REdaS::KMOS(raqData)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: REdaS::KMOS(x = raqData)
##
## Measures of Sampling Adequacy (MSA):
## A2 A4 A6 A8 A9 A10 C1 C3
## 0.8163262 0.7587018 0.7965148 0.7254769 0.7654068 0.6972584 0.7668660 0.8084286
## C5 C7 C9 C10 E1 E3 E5 E7
## 0.8587635 0.7152644 0.7505997 0.7782528 0.8291699 0.6867382 0.8102849 0.6191747
## E9 A1 A3 A5 A7 C2 C4 C6
## 0.7610301 0.6684919 0.6400395 0.7976396 0.7705462 0.6398434 0.7826940 0.6283490
## C8 E2 E4 E6 E8 E10
## 0.6513312 0.7569315 0.7705208 0.7062560 0.7345008 0.7968214
##
## KMO-Criterion: 0.7436294psych::KMO(raqData)## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = raqData)
## Overall MSA = 0.74
## MSA for each item =
## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10 E1 E3 E5 E7
## 0.82 0.76 0.80 0.73 0.77 0.70 0.77 0.81 0.86 0.72 0.75 0.78 0.83 0.69 0.81 0.62
## E9 A1 A3 A5 A7 C2 C4 C6 C8 E2 E4 E6 E8 E10
## 0.76 0.67 0.64 0.80 0.77 0.64 0.78 0.63 0.65 0.76 0.77 0.71 0.73 0.80###Determinant
#Determinant (execute one of these):
det(raqMatrix)## [1] 0.0002809986det(cor(raqData))## [1] 0.0002809986##Step 3: Do the Dimension Reduction (PRINCIPAL COMPONENTS ANALYSIS)
library(FactoMineR)
library(factoextra)
pc1 <- principal(raqData, nfactors = 23, rotate = "none")
pc1 <- principal(raqData, nfactors = length(raqData), rotate = "none")
pc1## Principal Components Analysis
## Call: principal(r = raqData, nfactors = length(raqData), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12
## A2 0.54 0.00 0.49 0.00 0.00 0.11 0.29 0.00 0.03 -0.08 0.00 0.00
## A4 0.48 0.00 0.41 0.00 0.00 -0.21 0.29 0.00 0.13 0.33 0.00 0.00
## A6 0.64 0.00 0.21 0.00 0.00 0.14 0.34 0.00 -0.02 0.12 0.00 0.00
## A8 -0.20 0.00 -0.23 0.00 0.00 0.60 -0.15 0.00 -0.09 0.02 0.00 0.00
## A9 -0.47 0.00 -0.21 0.00 0.00 0.51 -0.09 0.00 -0.18 0.00 0.00 0.00
## A10 -0.24 0.00 -0.05 0.00 0.00 0.62 -0.04 0.00 0.15 0.31 0.00 0.00
## C1 0.39 0.00 -0.41 0.00 0.00 0.13 -0.08 0.00 0.48 0.25 0.00 0.00
## C3 0.57 0.00 -0.28 0.00 0.00 0.34 0.20 0.00 -0.30 -0.10 0.00 0.00
## C5 0.47 0.00 -0.40 0.00 0.00 0.10 -0.01 0.00 0.05 0.34 0.00 0.00
## C7 -0.49 0.00 0.64 0.00 0.00 0.09 0.15 0.00 -0.26 0.14 0.00 0.00
## C9 -0.45 0.00 0.58 0.00 0.00 0.23 -0.01 0.00 -0.09 0.07 0.00 0.00
## C10 -0.51 0.00 0.60 0.00 0.00 0.01 -0.02 0.00 0.30 0.10 0.00 0.00
## E1 0.57 0.00 0.12 0.00 0.00 0.31 0.08 0.00 -0.01 -0.46 0.00 0.00
## E3 0.46 0.00 0.46 0.00 0.00 0.33 -0.46 0.00 0.18 0.00 0.00 0.00
## E5 0.58 0.00 0.46 0.00 0.00 0.28 -0.12 0.00 -0.11 0.01 0.00 0.00
## E7 -0.35 0.00 -0.25 0.00 0.00 0.22 0.73 0.00 -0.07 0.13 0.00 0.00
## E9 -0.37 0.00 0.00 0.00 0.00 0.24 0.33 0.00 0.60 -0.39 0.00 0.00
## A1 0.00 0.42 0.00 0.40 0.56 0.00 0.00 -0.04 0.00 0.00 -0.09 -0.27
## A3 0.00 0.34 0.00 0.45 0.61 0.00 0.00 -0.06 0.00 0.00 0.07 0.06
## A5 0.00 0.58 0.00 0.17 0.28 0.00 0.00 -0.22 0.00 0.00 -0.33 -0.30
## A7 0.00 0.40 0.00 0.34 0.33 0.00 0.00 -0.32 0.00 0.00 0.27 0.50
## C2 0.00 0.45 0.00 -0.58 0.31 0.00 0.00 0.31 0.00 0.00 -0.14 -0.03
## C4 0.00 0.40 0.00 -0.51 0.22 0.00 0.00 0.19 0.00 0.00 -0.08 0.44
## C6 0.00 -0.22 0.00 0.62 -0.01 0.00 0.00 0.56 0.00 0.00 -0.06 -0.09
## C8 0.00 -0.41 0.00 0.69 -0.19 0.00 0.00 -0.10 0.00 0.00 0.08 0.14
## E2 0.00 0.72 0.00 0.07 -0.41 0.00 0.00 0.14 0.00 0.00 0.22 -0.02
## E4 0.00 0.72 0.00 0.12 -0.40 0.00 0.00 0.05 0.00 0.00 0.23 -0.06
## E6 0.00 0.44 0.00 0.36 -0.14 0.00 0.00 0.61 0.00 0.00 -0.08 0.14
## E8 0.00 -0.62 0.00 0.04 0.48 0.00 0.00 0.31 0.00 0.00 -0.11 0.19
## E10 0.00 -0.21 0.00 -0.26 0.46 0.00 0.00 0.21 0.00 0.00 0.69 -0.29
## PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24
## A2 -0.09 -0.15 -0.01 0.00 0.15 -0.14 0.00 -0.13 0.00 0.47 0.00 -0.14
## A4 -0.11 0.06 0.08 0.00 -0.36 0.35 0.00 0.02 0.00 0.09 0.00 0.08
## A6 -0.24 -0.10 0.07 0.00 0.36 -0.25 0.00 0.02 0.00 -0.21 0.00 0.14
## A8 -0.52 0.32 0.10 0.00 -0.26 -0.20 0.00 -0.11 0.00 0.06 0.00 0.06
## A9 0.14 -0.09 0.29 0.00 0.30 0.36 0.00 -0.16 0.00 0.19 0.00 0.09
## A10 0.05 -0.54 -0.29 0.00 -0.15 -0.05 0.00 0.09 0.00 -0.06 0.00 0.02
## C1 0.26 0.15 0.44 0.00 0.05 -0.14 0.00 0.16 0.00 0.03 0.00 -0.05
## C3 -0.06 0.11 -0.06 0.00 0.07 0.20 0.00 0.49 0.00 0.02 0.00 0.02
## C5 0.19 0.35 -0.47 0.00 0.15 0.03 0.00 -0.22 0.00 0.09 0.00 0.14
## C7 0.10 0.20 -0.05 0.00 0.00 0.07 0.00 0.11 0.00 0.00 0.00 0.05
## C9 0.31 0.27 -0.07 0.00 0.05 -0.26 0.00 0.14 0.00 0.02 0.00 -0.15
## C10 -0.08 0.03 0.13 0.00 0.10 0.01 0.00 0.04 0.00 -0.01 0.00 0.35
## E1 0.39 -0.02 0.03 0.00 -0.30 -0.11 0.00 -0.08 0.00 0.00 0.00 0.30
## E3 -0.03 0.02 -0.03 0.00 -0.09 0.11 0.00 0.05 0.00 0.06 0.00 -0.21
## E5 0.04 0.06 0.10 0.00 0.08 0.17 0.00 -0.25 0.00 -0.38 0.00 -0.14
## E7 0.13 0.02 0.15 0.00 -0.18 -0.03 0.00 -0.15 0.00 -0.09 0.00 -0.18
## E9 -0.12 0.17 -0.23 0.00 0.12 0.20 0.00 0.02 0.00 -0.07 0.00 -0.09
## A1 0.00 0.00 0.00 -0.06 0.00 0.00 0.26 0.00 0.11 0.00 -0.30 0.00
## A3 0.00 0.00 0.00 -0.11 0.00 0.00 0.27 0.00 -0.30 0.00 0.16 0.00
## A5 0.00 0.00 0.00 0.38 0.00 0.00 -0.33 0.00 0.11 0.00 0.21 0.00
## A7 0.00 0.00 0.00 -0.19 0.00 0.00 -0.36 0.00 0.15 0.00 -0.06 0.00
## C2 0.00 0.00 0.00 -0.29 0.00 0.00 -0.03 0.00 -0.01 0.00 0.23 0.00
## C4 0.00 0.00 0.00 0.40 0.00 0.00 0.26 0.00 0.22 0.00 -0.09 0.00
## C6 0.00 0.00 0.00 -0.16 0.00 0.00 -0.06 0.00 0.39 0.00 -0.03 0.00
## C8 0.00 0.00 0.00 0.30 0.00 0.00 0.19 0.00 0.01 0.00 0.22 0.00
## E2 0.00 0.00 0.00 -0.01 0.00 0.00 0.14 0.00 0.08 0.00 0.11 0.00
## E4 0.00 0.00 0.00 -0.09 0.00 0.00 0.08 0.00 0.09 0.00 0.21 0.00
## E6 0.00 0.00 0.00 0.18 0.00 0.00 -0.23 0.00 -0.37 0.00 -0.17 0.00
## E8 0.00 0.00 0.00 -0.03 0.00 0.00 -0.03 0.00 0.04 0.00 0.27 0.00
## E10 0.00 0.00 0.00 0.24 0.00 0.00 -0.11 0.00 0.01 0.00 -0.01 0.00
## PC25 PC26 PC27 PC28 PC29 PC30 h2 u2 com
## A2 0.00 0.01 -0.18 0.00 0.00 -0.03 1 -4.4e-16 5.0
## A4 0.00 -0.18 0.12 0.00 0.00 -0.10 1 4.4e-16 7.3
## A6 0.00 -0.08 0.24 0.00 0.00 0.09 1 -6.7e-16 4.8
## A8 0.00 -0.07 -0.04 0.00 0.00 -0.02 1 8.9e-16 4.5
## A9 0.00 -0.09 0.14 0.00 0.00 -0.02 1 -6.7e-16 6.4
## A10 0.00 -0.08 -0.08 0.00 0.00 -0.01 1 7.8e-16 3.9
## C1 0.00 -0.08 -0.13 0.00 0.00 0.08 1 -8.9e-16 6.6
## C3 0.00 0.13 -0.09 0.00 0.00 -0.10 1 3.3e-16 5.1
## C5 0.00 0.08 0.00 0.00 0.00 0.01 1 -2.0e-15 6.3
## C7 0.00 -0.09 -0.15 0.00 0.00 0.37 1 0.0e+00 4.0
## C9 0.00 -0.13 0.16 0.00 0.00 -0.24 1 -1.1e-15 5.4
## C10 0.00 0.30 -0.10 0.00 0.00 -0.13 1 -4.4e-16 4.3
## E1 0.00 -0.02 0.04 0.00 0.00 0.04 1 1.1e-16 5.1
## E3 0.00 0.26 0.24 0.00 0.00 0.16 1 -6.7e-16 6.3
## E5 0.00 -0.03 -0.24 0.00 0.00 -0.11 1 -4.4e-16 5.1
## E7 0.00 0.28 0.06 0.00 0.00 0.02 1 -4.4e-16 3.2
## E9 0.00 -0.12 0.01 0.00 0.00 0.03 1 4.4e-16 5.1
## A1 0.25 0.00 0.00 -0.05 0.14 0.00 1 2.2e-16 5.5
## A3 -0.24 0.00 0.00 0.03 -0.17 0.00 1 -1.3e-15 4.7
## A5 -0.03 0.00 0.00 0.02 -0.06 0.00 1 0.0e+00 5.7
## A7 0.03 0.00 0.00 0.04 0.06 0.00 1 -6.7e-16 6.8
## C2 -0.06 0.00 0.00 0.13 0.30 0.00 1 -4.4e-16 5.2
## C4 -0.11 0.00 0.00 -0.04 -0.03 0.00 1 -8.9e-16 6.0
## C6 -0.24 0.00 0.00 0.05 -0.07 0.00 1 -2.2e-16 3.7
## C8 0.00 0.00 0.00 0.09 0.30 0.00 1 -8.9e-16 3.5
## E2 0.25 0.00 0.00 0.34 -0.16 0.00 1 -2.2e-16 3.1
## E4 0.01 0.00 0.00 -0.42 0.03 0.00 1 -2.2e-16 3.0
## E6 0.06 0.00 0.00 -0.04 0.06 0.00 1 1.1e-16 4.6
## E8 0.36 0.00 0.00 -0.12 -0.12 0.00 1 0.0e+00 4.3
## E10 -0.03 0.00 0.00 0.01 0.03 0.00 1 0.0e+00 3.5
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 3.78 3.03 2.57 2.19 1.84 1.68 1.26 1.15 0.98 0.83 0.82
## Proportion Var 0.13 0.10 0.09 0.07 0.06 0.06 0.04 0.04 0.03 0.03 0.03
## Cumulative Var 0.13 0.23 0.31 0.39 0.45 0.50 0.54 0.58 0.62 0.64 0.67
## Proportion Explained 0.13 0.10 0.09 0.07 0.06 0.06 0.04 0.04 0.03 0.03 0.03
## Cumulative Proportion 0.13 0.23 0.31 0.39 0.45 0.50 0.54 0.58 0.62 0.64 0.67
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.78 0.78 0.75 0.73 0.66 0.65 0.60 0.58 0.51 0.49 0.48
## Proportion Var 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Var 0.70 0.72 0.75 0.77 0.79 0.82 0.84 0.86 0.87 0.89 0.90
## Proportion Explained 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Proportion 0.70 0.72 0.75 0.77 0.79 0.82 0.84 0.86 0.87 0.89 0.90
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.44 0.42 0.39 0.36 0.34 0.34 0.29 0.29
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.92 0.93 0.95 0.96 0.97 0.98 0.99 1.00
## Proportion Explained 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Proportion 0.92 0.93 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 4.9
## Test of the hypothesis that 30 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1##Step 4: Decide which components to retain (PRINCIPAL COMPONENTS ANALYSIS)
#Create the scree plot
plot(pc1$values, type = "b") 
#Print the variance explained by each component
pc1$Vaccounted ## PC1 PC2 PC3 PC4 PC5
## SS loadings 3.7811572 3.0314434 2.56674193 2.18807980 1.84295321
## Proportion Var 0.1260386 0.1010481 0.08555806 0.07293599 0.06143177
## Cumulative Var 0.1260386 0.2270867 0.31264475 0.38558074 0.44701252
## Proportion Explained 0.1260386 0.1010481 0.08555806 0.07293599 0.06143177
## Cumulative Proportion 0.1260386 0.2270867 0.31264475 0.38558074 0.44701252
## PC6 PC7 PC8 PC9 PC10
## SS loadings 1.67911966 1.25559669 1.14676396 0.9840960 0.83216797
## Proportion Var 0.05597066 0.04185322 0.03822547 0.0328032 0.02773893
## Cumulative Var 0.50298317 0.54483639 0.58306186 0.6158651 0.64360399
## Proportion Explained 0.05597066 0.04185322 0.03822547 0.0328032 0.02773893
## Cumulative Proportion 0.50298317 0.54483639 0.58306186 0.6158651 0.64360399
## PC11 PC12 PC13 PC14 PC15
## SS loadings 0.82135862 0.78162824 0.77752237 0.74986122 0.72938034
## Proportion Var 0.02737862 0.02605427 0.02591741 0.02499537 0.02431268
## Cumulative Var 0.67098261 0.69703689 0.72295430 0.74794967 0.77226235
## Proportion Explained 0.02737862 0.02605427 0.02591741 0.02499537 0.02431268
## Cumulative Proportion 0.67098261 0.69703689 0.72295430 0.74794967 0.77226235
## PC16 PC17 PC18 PC19 PC20
## SS loadings 0.65975589 0.65082581 0.60036339 0.58248721 0.50672605
## Proportion Var 0.02199186 0.02169419 0.02001211 0.01941624 0.01689087
## Cumulative Var 0.79425422 0.81594841 0.83596052 0.85537676 0.87226763
## Proportion Explained 0.02199186 0.02169419 0.02001211 0.01941624 0.01689087
## Cumulative Proportion 0.79425422 0.81594841 0.83596052 0.85537676 0.87226763
## PC21 PC22 PC23 PC24 PC25
## SS loadings 0.49015671 0.48443053 0.43872338 0.41813928 0.39221813
## Proportion Var 0.01633856 0.01614768 0.01462411 0.01393798 0.01307394
## Cumulative Var 0.88860619 0.90475387 0.91937798 0.93331596 0.94638990
## Proportion Explained 0.01633856 0.01614768 0.01462411 0.01393798 0.01307394
## Cumulative Proportion 0.88860619 0.90475387 0.91937798 0.93331596 0.94638990
## PC26 PC27 PC28 PC29 PC30
## SS loadings 0.36075432 0.33724836 0.33601327 0.28841819 0.285868905
## Proportion Var 0.01202514 0.01124161 0.01120044 0.00961394 0.009528964
## Cumulative Var 0.95841504 0.96965665 0.98085710 0.99047104 1.000000000
## Proportion Explained 0.01202514 0.01124161 0.01120044 0.00961394 0.009528964
## Cumulative Proportion 0.95841504 0.96965665 0.98085710 0.99047104 1.000000000#Print the Eigenvalues
pc1$values## [1] 3.7811572 3.0314434 2.5667419 2.1880798 1.8429532 1.6791197 1.2555967
## [8] 1.1467640 0.9840960 0.8321680 0.8213586 0.7816282 0.7775224 0.7498612
## [15] 0.7293803 0.6597559 0.6508258 0.6003634 0.5824872 0.5067261 0.4901567
## [22] 0.4844305 0.4387234 0.4181393 0.3922181 0.3607543 0.3372484 0.3360133
## [29] 0.2884182 0.2858689#Another way to look at eigen values plus variance explained (need to use princomp function of PCA to get right class for use with factoextra functions)
pcf=princomp(raqData)
factoextra::get_eigenvalue(pcf)## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.5131374 11.9571129 11.95711
## Dim.2 4.4539971 11.8004266 23.75754
## Dim.3 3.2091308 8.5022759 32.25982
## Dim.4 3.0518290 8.0855203 40.34534
## Dim.5 2.3205171 6.1479815 46.49332
## Dim.6 1.9376089 5.1335040 51.62682
## Dim.7 1.6444247 4.3567411 55.98356
## Dim.8 1.4317998 3.7934126 59.77697
## Dim.9 1.1900148 3.1528270 62.92980
## Dim.10 1.1266262 2.9848851 65.91469
## Dim.11 1.0748000 2.8475767 68.76226
## Dim.12 0.9950349 2.6362469 71.39851
## Dim.13 0.9921160 2.6285135 74.02702
## Dim.14 0.8974046 2.3775851 76.40461
## Dim.15 0.8697062 2.3042009 78.70881
## Dim.16 0.8121870 2.1518095 80.86062
## Dim.17 0.6934753 1.8372944 82.69791
## Dim.18 0.6921428 1.8337641 84.53168
## Dim.19 0.6336039 1.6786712 86.21035
## Dim.20 0.6088227 1.6130159 87.82337
## Dim.21 0.5572879 1.4764794 89.29984
## Dim.22 0.5365033 1.4214128 90.72126
## Dim.23 0.5270572 1.3963862 92.11764
## Dim.24 0.5028285 1.3321946 93.44984
## Dim.25 0.4832574 1.2803429 94.73018
## Dim.26 0.4675009 1.2385977 95.96878
## Dim.27 0.4288483 1.1361914 97.10497
## Dim.28 0.3930651 1.0413874 98.14636
## Dim.29 0.3843323 1.0182505 99.16461
## Dim.30 0.3153135 0.8353921 100.00000factoextra::fviz_eig(pcf, addlabels = TRUE, ylim = c(0, 50))#Visualize the Eigenvalues
factoextra::fviz_pca_var(pcf, col.var = "black")
factoextra::fviz_pca_var(pcf, col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
#Print the loadings above the level of 0.3
psych::print.psych(pc1, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = raqData, nfactors = length(raqData), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## A6 3 0.64 0.34
## E5 15 0.58 0.46
## C3 8 0.57 0.34 -0.30
## E1 13 0.57 0.31 -0.46
## A2 1 0.54 0.49
## A4 2 0.48 0.41 0.33
## E4 27 0.72 -0.40
## E2 26 0.72 -0.41
## E8 29 -0.62 0.48 0.31
## A5 20 0.58 -0.33
## C7 10 -0.49 0.64
## C10 12 -0.51 0.60
## C9 11 -0.45 0.58
## C8 25 -0.41 0.69
## C6 24 0.62 0.56
## C2 22 0.45 -0.58 0.31 0.31
## C4 23 0.40 -0.51
## A3 19 0.34 0.45 0.61
## A1 18 0.42 0.40 0.56
## A10 6 0.62 0.31
## A8 4 0.60
## A9 5 -0.47 0.51
## E7 16 -0.35 0.73
## E3 14 0.46 0.46 0.33 -0.46
## E6 28 0.44 0.36 0.61
## E9 17 -0.37 0.33 0.60 -0.39
## C1 7 0.39 -0.41 0.48
## E10 30 0.46 0.69
## A7 21 0.40 0.34 0.33 -0.32
## C5 9 0.47 -0.40 0.34
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23
## A6 0.36
## E5 -0.38
## C3 0.49
## E1 0.39
## A2 0.47
## A4 -0.36 0.35
## E4
## E2
## E8
## A5 0.38 -0.33
## C7
## C10
## C9 0.31
## C8 0.30
## C6 0.39
## C2
## C4 0.44 0.40
## A3 -0.30
## A1 -0.30
## A10 -0.54
## A8 -0.52 0.32
## A9 0.36
## E7
## E3
## E6 -0.37
## E9
## C1 0.44
## E10
## A7 0.50 -0.36
## C5 0.35 -0.47
## PC24 PC25 PC26 PC27 PC28 PC29 PC30 h2 u2 com
## A6 1 -6.7e-16 4.8
## E5 1 -4.4e-16 5.1
## C3 1 3.3e-16 5.1
## E1 0.30 1 1.1e-16 5.1
## A2 1 -4.4e-16 5.0
## A4 1 4.4e-16 7.3
## E4 -0.42 1 -2.2e-16 3.0
## E2 0.34 1 -2.2e-16 3.1
## E8 0.36 1 0.0e+00 4.3
## A5 1 0.0e+00 5.7
## C7 0.37 1 0.0e+00 4.0
## C10 0.35 0.30 1 -4.4e-16 4.3
## C9 1 -1.1e-15 5.4
## C8 0.30 1 -8.9e-16 3.5
## C6 1 -2.2e-16 3.7
## C2 1 -4.4e-16 5.2
## C4 1 -8.9e-16 6.0
## A3 1 -1.3e-15 4.7
## A1 1 2.2e-16 5.5
## A10 1 7.8e-16 3.9
## A8 1 8.9e-16 4.5
## A9 1 -6.7e-16 6.4
## E7 1 -4.4e-16 3.2
## E3 1 -6.7e-16 6.3
## E6 1 1.1e-16 4.6
## E9 1 4.4e-16 5.1
## C1 1 -8.9e-16 6.6
## E10 1 0.0e+00 3.5
## A7 1 -6.7e-16 6.8
## C5 1 -2.0e-15 6.3
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 3.78 3.03 2.57 2.19 1.84 1.68 1.26 1.15 0.98 0.83 0.82
## Proportion Var 0.13 0.10 0.09 0.07 0.06 0.06 0.04 0.04 0.03 0.03 0.03
## Cumulative Var 0.13 0.23 0.31 0.39 0.45 0.50 0.54 0.58 0.62 0.64 0.67
## Proportion Explained 0.13 0.10 0.09 0.07 0.06 0.06 0.04 0.04 0.03 0.03 0.03
## Cumulative Proportion 0.13 0.23 0.31 0.39 0.45 0.50 0.54 0.58 0.62 0.64 0.67
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.78 0.78 0.75 0.73 0.66 0.65 0.60 0.58 0.51 0.49 0.48
## Proportion Var 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Var 0.70 0.72 0.75 0.77 0.79 0.82 0.84 0.86 0.87 0.89 0.90
## Proportion Explained 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Proportion 0.70 0.72 0.75 0.77 0.79 0.82 0.84 0.86 0.87 0.89 0.90
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.44 0.42 0.39 0.36 0.34 0.34 0.29 0.29
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.92 0.93 0.95 0.96 0.97 0.98 0.99 1.00
## Proportion Explained 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Proportion 0.92 0.93 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 4.9
## Test of the hypothesis that 30 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1#create a diagram showing the components and how the manifest variables load
fa.diagram(pc1) 
#Show the loadings of variables on to components
fa.sort(pc1$loading)##
## Loadings:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## A6 0.636 0.210 0.140 0.338 0.117
## E5 0.582 0.457 0.283 -0.123 -0.108
## C3 0.569 -0.282 0.340 0.198 -0.305 -0.102
## E1 0.565 0.123 0.307 -0.460
## A2 0.541 0.488 0.115 0.290
## A4 0.484 0.413 -0.208 0.287 0.132 0.328
## E4 0.724 0.124 -0.397
## E2 0.722 -0.408 0.143
## E8 -0.618 0.484 0.312
## A5 0.576 0.167 0.281 -0.225
## C7 -0.487 0.642 0.149 -0.257 0.138
## C10 -0.511 0.601 0.300 0.104
## C9 -0.449 0.584 0.231
## C8 -0.407 0.695 -0.190
## C6 -0.224 0.619 0.559
## C2 0.447 -0.582 0.308 0.309
## C4 0.400 -0.508 0.215 0.188
## A3 0.338 0.452 0.611
## A1 0.423 0.397 0.564
## A10 -0.238 0.623 0.152 0.312
## A8 -0.203 -0.226 0.598 -0.149
## A9 -0.473 -0.211 0.513 -0.183
## E7 -0.349 -0.248 0.216 0.727 0.133
## E3 0.463 0.459 0.330 -0.464 0.177
## E6 0.442 0.361 -0.142 0.607
## E9 -0.370 0.245 0.330 0.602 -0.392
## C1 0.393 -0.405 0.132 0.480 0.245
## E10 -0.213 -0.263 0.458 0.213
## A7 0.404 0.338 0.326 -0.321
## C5 0.470 -0.401 0.343
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## A6 -0.244 -0.104 0.364 -0.245
## E5 0.170 -0.250
## C3 0.109 0.200 0.489
## E1 0.386 -0.299 -0.112
## A2 -0.155 0.151 -0.137 -0.131
## A4 -0.112 -0.356 0.348
## E4 0.232
## E2 0.219 0.140
## E8 -0.109 0.193
## A5 -0.329 -0.300 0.381 -0.326
## C7 0.197 0.110
## C10 0.125 0.104
## C9 0.313 0.271 -0.265 0.145
## C8 0.140 0.303 0.191
## C6 -0.156
## C2 -0.141 -0.294
## C4 0.439 0.402 0.264
## A3 -0.106 0.274
## A1 -0.273 0.265
## A10 -0.541 -0.291 -0.147
## A8 -0.523 0.323 0.105 -0.255 -0.201 -0.106
## A9 0.141 0.292 0.297 0.359 -0.155
## E7 0.131 0.155 -0.183 -0.152
## E3 0.107
## E6 0.137 0.183 -0.233
## E9 -0.118 0.170 -0.233 0.120 0.199
## C1 0.259 0.154 0.441 -0.136 0.164
## E10 0.689 -0.286 0.242 -0.114
## A7 0.266 0.501 -0.186 -0.356
## C5 0.188 0.353 -0.473 0.148 -0.221
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## A6 -0.206 0.144 0.239
## E5 -0.381 -0.141 -0.236 -0.109
## C3 0.127
## E1 0.300
## A2 0.470 -0.136 -0.184
## A4 -0.183 0.125 -0.101
## E4 0.210 -0.416
## E2 0.114 0.248 0.336 -0.161
## E8 0.270 0.361 -0.119 -0.124
## A5 0.114 0.209
## C7 -0.150 0.365
## C10 0.349 0.303 -0.102 -0.127
## C9 -0.146 -0.125 0.155 -0.244
## C8 0.225 0.304
## C6 0.386 -0.243
## C2 0.234 0.128 0.295
## C4 0.220 -0.106
## A3 -0.305 0.163 -0.242 -0.174
## A1 0.114 -0.302 0.247 0.139
## A10
## A8
## A9 0.186 0.140
## E7 -0.177 0.275
## E3 -0.208 0.257 0.242 0.159
## E6 -0.369 -0.169
## E9 -0.116
## C1 -0.131
## E10
## A7 0.146
## C5 0.140
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## SS loadings 3.781 3.031 2.567 2.188 1.843 1.679 1.256 1.147 0.984 0.832
## Proportion Var 0.126 0.101 0.086 0.073 0.061 0.056 0.042 0.038 0.033 0.028
## Cumulative Var 0.126 0.227 0.313 0.386 0.447 0.503 0.545 0.583 0.616 0.644
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## SS loadings 0.821 0.782 0.778 0.750 0.729 0.660 0.651 0.600 0.582 0.507
## Proportion Var 0.027 0.026 0.026 0.025 0.024 0.022 0.022 0.020 0.019 0.017
## Cumulative Var 0.671 0.697 0.723 0.748 0.772 0.794 0.816 0.836 0.855 0.872
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.490 0.484 0.439 0.418 0.392 0.361 0.337 0.336 0.288 0.286
## Proportion Var 0.016 0.016 0.015 0.014 0.013 0.012 0.011 0.011 0.010 0.010
## Cumulative Var 0.889 0.905 0.919 0.933 0.946 0.958 0.970 0.981 0.990 1.000#Output the communalities of variables across components (will be one for PCA since all the variance is used)
pc1$communality ## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10 E1 E3 E5 E7 E9 A1 A3 A5
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## A7 C2 C4 C6 C8 E2 E4 E6 E8 E10
## 1 1 1 1 1 1 1 1 1 1#Visualize contribution of variables to each component
var <- factoextra::get_pca_var(pcf)
corrplot::corrplot(var$contrib, is.corr=FALSE) 
# Contributions of variables to PC1
factoextra::fviz_contrib(pcf, choice = "var", axes = 1, top = 10)
# Contributions of variables to PC2
factoextra::fviz_contrib(pcf, choice = "var", axes = 2, top = 10)
##Step 5: Apply rotation
#Apply rotation to try to refine the component structure
pc2 <- principal(raqData, nfactors = 4, rotate = "varimax")#Extracting 4 factors
#output the components
psych::print.psych(pc2, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = raqData, nfactors = 4, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item RC1 RC3 RC2 RC4 h2 u2 com
## E5 15 0.74 0.547 0.45 1.0
## A2 1 0.73 0.530 0.47 1.0
## E3 14 0.65 0.425 0.58 1.0
## A4 2 0.64 0.405 0.60 1.0
## A6 3 0.63 0.448 0.55 1.3
## E1 13 0.52 0.334 0.67 1.5
## A9 5 -0.50 0.268 0.73 1.1
## E7 16 -0.43 0.183 0.82 1.0
## A8 4 0.092 0.91 1.1
## E9 17 0.137 0.86 1.9
## A10 6 0.059 0.94 1.5
## C7 10 0.81 0.649 0.35 1.0
## C10 12 0.79 0.623 0.38 1.0
## C9 11 0.74 0.542 0.46 1.0
## C5 9 -0.61 0.382 0.62 1.1
## C3 8 -0.58 0.403 0.60 1.4
## C1 7 -0.56 0.318 0.68 1.0
## E4 27 0.68 0.539 0.46 1.3
## E2 26 0.64 0.33 0.526 0.47 1.5
## A5 20 0.57 0.360 0.64 1.2
## A1 18 0.57 0.337 0.66 1.1
## E6 28 0.57 0.325 0.67 1.0
## A3 19 0.53 0.319 0.68 1.3
## A7 21 0.52 0.277 0.72 1.0
## E8 29 -0.50 -0.37 0.384 0.62 1.8
## E10 30 -0.32 0.114 0.89 1.2
## C8 25 -0.80 0.648 0.35 1.0
## C2 22 0.73 0.539 0.46 1.0
## C4 23 0.64 0.418 0.58 1.0
## C6 24 -0.64 0.433 0.57 1.1
##
## RC1 RC3 RC2 RC4
## SS loadings 3.31 3.04 2.78 2.43
## Proportion Var 0.11 0.10 0.09 0.08
## Cumulative Var 0.11 0.21 0.30 0.39
## Proportion Explained 0.29 0.26 0.24 0.21
## Cumulative Proportion 0.29 0.55 0.79 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.08
## with the empirical chi square 730418.6 with prob < 0
##
## Fit based upon off diagonal values = 0.77#output the communalities
pc2$communality## A2 A4 A6 A8 A9 A10 C1
## 0.53012409 0.40492762 0.44830621 0.09195115 0.26848736 0.05922192 0.31842729
## C3 C5 C7 C9 C10 E1 E3
## 0.40344971 0.38183330 0.64938704 0.54248756 0.62253630 0.33449514 0.42455675
## E5 E7 E9 A1 A3 A5 A7
## 0.54732492 0.18334598 0.13703675 0.33662626 0.31906643 0.35966898 0.27726618
## C2 C4 C6 C8 E2 E4 E6
## 0.53893561 0.41779499 0.43307883 0.64813252 0.52570779 0.53938739 0.32548441
## E8 E10
## 0.38389165 0.11448214#NOTE: you can do all the other things done for the model created in pc1##Step 6: Reliability Analysis
#If you know that variables are grouped, test each group as a separate scale
Agreeableness <- raqData[,c("A1","A2","A3","A4","A5","A6","A7","A8","A9","A10")]
Conscientiousness <- raqData[,c("C1","C2","C3","C4","C5","C6","C7","C8","C9","C10")]
Extraversion <- raqData[,c("E1","E2","E3","E4","E5","E6","E7","E8","E9","E10")]
head(raqData)## A2 A4 A6 A8 A9 A10 C1 C3 C5 C7 C9 C10 E1 E3 E5 E7 E9 A1 A3 A5 A7 C2 C4 C6 C8
## 1 3 2 2 5 2 3 2 4 2 5 4 2 2 4 5 1 3 2 2 2 3 5 4 2 1
## 2 4 4 4 3 2 3 4 5 3 2 1 1 4 5 5 1 1 2 2 2 3 5 4 2 1
## 3 5 5 5 2 1 2 4 4 4 2 2 3 3 5 5 1 2 2 2 2 3 5 4 2 1
## 4 5 4 5 3 1 2 2 3 2 3 4 2 3 4 4 2 1 2 2 2 3 5 4 2 1
## 5 3 4 4 3 4 4 2 2 1 4 3 2 2 3 4 5 4 2 2 2 3 5 4 2 1
## 6 4 3 3 3 3 3 3 3 3 3 2 2 3 4 4 2 2 2 2 2 3 5 4 2 1
## E2 E4 E6 E8 E10
## 1 3 4 1 4 5
## 2 3 4 1 4 5
## 3 3 4 1 4 5
## 4 3 4 1 4 5
## 5 3 4 1 4 5
## 6 3 4 1 4 5#Output our Cronbach Alpha values
psych::alpha(Agreeableness)## Warning in psych::alpha(Agreeableness): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( A1 A3 A5 A7 A8 A9 A10 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = Agreeableness)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.37 0.38 0.51 0.057 0.61 0.0025 2.7 0.39 3.2e-21
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.37 0.37 0.37
## Duhachek 0.37 0.37 0.37
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## A1 0.23 0.25 0.39 0.036 0.34 0.0031 0.043 3.0e-22
## A2 0.37 0.37 0.48 0.061 0.58 0.0025 0.042 3.1e-21
## A3 0.24 0.25 0.39 0.036 0.34 0.0030 0.043 3.0e-22
## A4 0.42 0.42 0.52 0.073 0.71 0.0023 0.040 3.4e-21
## A5 0.29 0.29 0.45 0.044 0.42 0.0028 0.049 3.1e-21
## A6 0.36 0.37 0.48 0.060 0.58 0.0025 0.044 3.4e-21
## A7 0.29 0.29 0.45 0.044 0.42 0.0028 0.049 3.3e-21
## A8 0.41 0.41 0.53 0.071 0.68 0.0023 0.048 3.2e-21
## A9 0.42 0.44 0.54 0.081 0.79 0.0023 0.040 3.3e-21
## A10 0.38 0.39 0.52 0.066 0.63 0.0024 0.051 3.4e-21
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## A1 145924 0.60 0.59 0.599 0.365 2.3 1.13
## A2 145924 0.34 0.36 0.259 0.091 3.9 1.00
## A3 145924 0.59 0.58 0.592 0.367 2.2 1.08
## A4 145924 0.23 0.24 0.074 -0.035 3.8 1.02
## A5 145924 0.48 0.51 0.423 0.285 2.1 0.87
## A6 145924 0.34 0.36 0.253 0.109 3.7 0.92
## A7 145924 0.48 0.51 0.421 0.283 2.1 0.86
## A8 145924 0.31 0.26 0.059 0.010 3.0 1.16
## A9 145924 0.18 0.17 -0.028 -0.068 2.0 0.98
## A10 145924 0.33 0.31 0.120 0.067 2.4 1.05
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 miss
## A1 0.00 0.23 0.47 0.14 0.12 0.03 0.01 0
## A2 0.01 0.02 0.06 0.18 0.48 0.26 0.00 0
## A3 0.00 0.25 0.47 0.15 0.08 0.03 0.01 0
## A4 0.01 0.02 0.08 0.17 0.51 0.20 0.00 0
## A5 0.00 0.25 0.52 0.17 0.05 0.01 0.00 0
## A6 0.01 0.02 0.05 0.25 0.49 0.18 0.00 0
## A7 0.00 0.22 0.59 0.10 0.07 0.01 0.00 0
## A8 0.01 0.07 0.30 0.26 0.25 0.10 0.00 0
## A9 0.02 0.31 0.43 0.15 0.08 0.01 0.00 0
## A10 0.01 0.17 0.43 0.21 0.15 0.03 0.00 0#If some items are to be reversed keyed, then either recode or get alpha to reverse code as needed by setting check.keys=TRUE (be careful with this - make sure you know it makes sense)
psych::alpha(Extraversion)## Warning in psych::alpha(Extraversion): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( E7 E8 E10 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = Extraversion)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.029 0.034 0.31 0.0035 0.035 0.0038 3.1 0.37 -4.7e-21
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.02 0.03 0.04
## Duhachek 0.02 0.03 0.04
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## E1 -0.088 -0.109 0.22 -0.0110 -0.098 0.0042 0.060 -6.2e-21
## E2 -0.077 -0.040 0.21 -0.0042 -0.038 0.0043 0.043 -4.8e-21
## E3 -0.019 -0.036 0.22 -0.0039 -0.035 0.0040 0.051 -8.6e-21
## E4 -0.058 -0.020 0.22 -0.0021 -0.019 0.0042 0.043 -6.0e-21
## E5 -0.060 -0.085 0.20 -0.0088 -0.078 0.0041 0.052 -4.5e-21
## E6 -0.118 -0.072 0.25 -0.0075 -0.067 0.0044 0.060 -7.6e-21
## E7 0.132 0.154 0.38 0.0198 0.182 0.0034 0.058 -4.5e-21
## E8 0.256 0.223 0.41 0.0309 0.287 0.0029 0.048 -4.5e-21
## E9 0.055 0.073 0.35 0.0086 0.079 0.0037 0.065 -3.3e-21
## E10 0.109 0.104 0.37 0.0128 0.116 0.0034 0.063 -3.7e-21
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## E1 145924 0.4570 0.483 0.411 0.158 2.6 1.17
## E2 145924 0.4699 0.407 0.453 0.127 3.1 1.33
## E3 145924 0.3514 0.404 0.387 0.078 3.9 1.04
## E4 145924 0.4367 0.384 0.411 0.113 3.3 1.25
## E5 145924 0.3960 0.458 0.464 0.152 3.9 0.95
## E6 145924 0.5021 0.444 0.337 0.176 3.2 1.30
## E7 145924 0.1451 0.138 -0.185 -0.153 2.1 1.11
## E8 145924 -0.0058 0.013 -0.328 -0.322 2.9 1.25
## E9 145924 0.2349 0.263 -0.044 -0.038 2.0 1.01
## E10 145924 0.2046 0.217 -0.124 -0.110 3.7 1.17
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 miss
## E1 0.01 0.20 0.31 0.27 0.15 0.06 0.00 0
## E2 0.00 0.13 0.28 0.19 0.23 0.16 0.01 0
## E3 0.01 0.02 0.07 0.15 0.45 0.31 0.00 0
## E4 0.00 0.07 0.24 0.21 0.27 0.20 0.01 0
## E5 0.02 0.01 0.04 0.13 0.54 0.25 0.00 0
## E6 0.00 0.12 0.22 0.20 0.29 0.16 0.01 0
## E7 0.01 0.35 0.37 0.12 0.12 0.03 0.00 0
## E8 0.00 0.16 0.25 0.22 0.28 0.08 0.01 0
## E9 0.01 0.29 0.46 0.14 0.07 0.03 0.00 0
## E10 0.00 0.05 0.12 0.15 0.39 0.27 0.01 0psych::alpha(Conscientiousness)## Warning in psych::alpha(Conscientiousness): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( C1 C2 C3 C5 C6 C8 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = Conscientiousness)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## -0.37 -0.39 0.11 -0.029 -0.28 0.0055 2.9 0.32 -9.7e-21
##
## 95% confidence boundaries
## lower alpha upper
## Feldt -0.38 -0.37 -0.36
## Duhachek -0.38 -0.37 -0.36
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## C1 -0.23 -0.27 0.189 -0.024 -0.21 0.0048 0.079 -5.1e-21
## C2 -0.23 -0.27 0.127 -0.024 -0.21 0.0049 0.074 -1.4e-20
## C3 -0.25 -0.25 0.194 -0.023 -0.20 0.0049 0.077 -7.7e-21
## C4 -0.31 -0.35 0.140 -0.030 -0.26 0.0052 0.080 -9.2e-21
## C5 -0.25 -0.29 0.175 -0.026 -0.22 0.0049 0.076 -4.3e-21
## C6 -0.37 -0.38 0.134 -0.032 -0.28 0.0055 0.084 -7.7e-21
## C7 -0.50 -0.49 -0.025 -0.038 -0.33 0.0060 0.062 -1.1e-20
## C8 -0.18 -0.20 0.172 -0.018 -0.16 0.0047 0.074 -7.7e-21
## C9 -0.61 -0.59 -0.046 -0.043 -0.37 0.0065 0.067 -9.2e-21
## C10 -0.42 -0.39 0.071 -0.032 -0.28 0.0057 0.065 -1.4e-20
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## C1 145924 0.18 0.20 -0.2326 -0.1822 2.8 1.2
## C2 145924 0.19 0.21 0.0129 -0.1831 2.3 1.2
## C3 145924 0.13 0.19 -0.2582 -0.1762 3.4 1.0
## C4 145924 0.25 0.28 -0.0018 -0.1047 2.6 1.1
## C5 145924 0.20 0.23 -0.1515 -0.1608 2.9 1.2
## C6 145924 0.34 0.31 0.0023 -0.0555 3.1 1.3
## C7 145924 0.42 0.39 0.6570 0.0388 2.8 1.3
## C8 145924 0.16 0.13 -0.2044 -0.2178 3.6 1.2
## C9 145924 0.48 0.46 0.7466 0.1292 2.3 1.2
## C10 145924 0.34 0.32 0.3273 -0.0087 2.5 1.1
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 miss
## C1 0.01 0.12 0.30 0.26 0.23 0.09 0.00 0
## C2 0.00 0.25 0.43 0.13 0.12 0.06 0.01 0
## C3 0.01 0.03 0.13 0.26 0.47 0.10 0.00 0
## C4 0.00 0.12 0.44 0.20 0.18 0.05 0.02 0
## C5 0.00 0.09 0.35 0.20 0.26 0.10 0.00 0
## C6 0.00 0.13 0.21 0.21 0.30 0.14 0.01 0
## C7 0.01 0.13 0.36 0.21 0.16 0.13 0.00 0
## C8 0.00 0.08 0.12 0.20 0.30 0.31 0.00 0
## C9 0.01 0.27 0.37 0.15 0.15 0.05 0.00 0
## C10 0.01 0.15 0.42 0.19 0.19 0.05 0.00 0psych::alpha(Agreeableness)## Warning in psych::alpha(Agreeableness): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( A1 A3 A5 A7 A8 A9 A10 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = Agreeableness)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.37 0.38 0.51 0.057 0.61 0.0025 2.7 0.39 3.2e-21
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.37 0.37 0.37
## Duhachek 0.37 0.37 0.37
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## A1 0.23 0.25 0.39 0.036 0.34 0.0031 0.043 3.0e-22
## A2 0.37 0.37 0.48 0.061 0.58 0.0025 0.042 3.1e-21
## A3 0.24 0.25 0.39 0.036 0.34 0.0030 0.043 3.0e-22
## A4 0.42 0.42 0.52 0.073 0.71 0.0023 0.040 3.4e-21
## A5 0.29 0.29 0.45 0.044 0.42 0.0028 0.049 3.1e-21
## A6 0.36 0.37 0.48 0.060 0.58 0.0025 0.044 3.4e-21
## A7 0.29 0.29 0.45 0.044 0.42 0.0028 0.049 3.3e-21
## A8 0.41 0.41 0.53 0.071 0.68 0.0023 0.048 3.2e-21
## A9 0.42 0.44 0.54 0.081 0.79 0.0023 0.040 3.3e-21
## A10 0.38 0.39 0.52 0.066 0.63 0.0024 0.051 3.4e-21
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## A1 145924 0.60 0.59 0.599 0.365 2.3 1.13
## A2 145924 0.34 0.36 0.259 0.091 3.9 1.00
## A3 145924 0.59 0.58 0.592 0.367 2.2 1.08
## A4 145924 0.23 0.24 0.074 -0.035 3.8 1.02
## A5 145924 0.48 0.51 0.423 0.285 2.1 0.87
## A6 145924 0.34 0.36 0.253 0.109 3.7 0.92
## A7 145924 0.48 0.51 0.421 0.283 2.1 0.86
## A8 145924 0.31 0.26 0.059 0.010 3.0 1.16
## A9 145924 0.18 0.17 -0.028 -0.068 2.0 0.98
## A10 145924 0.33 0.31 0.120 0.067 2.4 1.05
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 6 miss
## A1 0.00 0.23 0.47 0.14 0.12 0.03 0.01 0
## A2 0.01 0.02 0.06 0.18 0.48 0.26 0.00 0
## A3 0.00 0.25 0.47 0.15 0.08 0.03 0.01 0
## A4 0.01 0.02 0.08 0.17 0.51 0.20 0.00 0
## A5 0.00 0.25 0.52 0.17 0.05 0.01 0.00 0
## A6 0.01 0.02 0.05 0.25 0.49 0.18 0.00 0
## A7 0.00 0.22 0.59 0.10 0.07 0.01 0.00 0
## A8 0.01 0.07 0.30 0.26 0.25 0.10 0.00 0
## A9 0.02 0.31 0.43 0.15 0.08 0.01 0.00 0
## A10 0.01 0.17 0.43 0.21 0.15 0.03 0.00 0A principal component analysis (PCA) was conducted on the 23 items with orthogonal rotation (varimax). Bartlett’s test of sphericity, Χ2(253) = 19334.49, p< .001, indicated that correlations between items were sufficiently large for PCA. An initial analysis was run to obtain eigenvalues for each component in the data. Four components had eigenvalues over Kaiser’s criterion of 1 and in combination explained 50.94% of the variance. The scree plot was slightly ambiguous and showed inflexions that would justify retaining either 2 or 4 factors. Given the large sample size, and the convergence of the scree plot and Kaiser’s criterion on four components, four components were retained in the final analysis. Component 1 represents a fear of computers, component 2 a fear of statistics, component 3 a fear of math, and component 4 peer evaluation concerns. The fear of computers, and fear of math subscales of the RAQ all had high reliabilities, all Cronbach’s α= .82. The fear of statistics had an acceptable reliability of Cronbach’s α= .61 of However, the fear of negative peer evaluation subscale had a relatively low reliability, Cronbach’s α= .57.