portfolio_dimensionreduction
Dorothy
10/12/2020
needed_packages <- c("psych", "REdaS", "Hmisc", "corrplot", "ggcorrplot", "factoextra", "nFactors", "HDclassif","")
# 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") ## Installing package into 'C:/Users/dorot/OneDrive/Documents/R/win-library/4.0'
## (as 'lib' is unspecified)## Warning: package '' is not available (for R version 4.0.2)library(psych)## Warning: package 'psych' was built under R version 4.0.3library(REdaS)## Warning: package 'REdaS' was built under R version 4.0.3## Loading required package: gridlibrary(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.0.3##
## 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)## Warning: package 'corrplot' was built under R version 4.0.3## corrplot 0.84 loadedlibrary(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.0.3library(factoextra)#Used for principal component analysis to get a different view of eigenvalues## Warning: package 'factoextra' was built under R version 4.0.3## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(nFactors)## Warning: package 'nFactors' was built under R version 4.0.3##
## 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, union#load data
studentpIusepersonality <- read.csv('studentpIusepersonality.csv')
#### filtering some fields#####
sData <-select(studentpIusepersonality,E1,E2,E4,E5,E7,E8,E10,A1,A2,A3,A5,A6,A10,C1,C3,C4,C6,C8,C9,N1,N2,N4,N5,N6,N7,O3,O4,O7,O8,O9,O10)##Step 1: Screen the correlation matrix
#create a correlation matrix (these are just some methods)
sMatrix<-cor(sData)
round(sMatrix, 2)## E1 E2 E4 E5 E7 E8 E10 A1 A2 A3 A5 A6
## E1 1.00 0.57 0.52 0.40 -0.10 -0.39 -0.10 0.22 0.36 0.16 0.38 0.29
## E2 0.57 1.00 0.65 0.28 -0.02 -0.53 -0.20 0.12 0.37 0.04 0.21 0.20
## E4 0.52 0.65 1.00 0.20 -0.11 -0.55 -0.22 0.13 0.35 0.09 0.24 0.22
## E5 0.40 0.28 0.20 1.00 -0.26 -0.07 -0.01 0.39 0.43 0.28 0.41 0.43
## E7 -0.10 -0.02 -0.11 -0.26 1.00 0.15 0.06 -0.08 -0.13 -0.10 -0.21 -0.08
## E8 -0.39 -0.53 -0.55 -0.07 0.15 1.00 0.26 -0.03 -0.13 0.05 -0.25 -0.05
## E10 -0.10 -0.20 -0.22 -0.01 0.06 0.26 1.00 0.02 0.01 0.05 -0.10 0.10
## A1 0.22 0.12 0.13 0.39 -0.08 -0.03 0.02 1.00 0.39 0.56 0.42 0.45
## A2 0.36 0.37 0.35 0.43 -0.13 -0.13 0.01 0.39 1.00 0.43 0.44 0.51
## A3 0.16 0.04 0.09 0.28 -0.10 0.05 0.05 0.56 0.43 1.00 0.30 0.44
## A5 0.38 0.21 0.24 0.41 -0.21 -0.25 -0.10 0.42 0.44 0.30 1.00 0.46
## A6 0.29 0.20 0.22 0.43 -0.08 -0.05 0.10 0.45 0.51 0.44 0.46 1.00
## A10 -0.03 0.09 0.12 -0.05 0.17 0.07 -0.01 -0.16 -0.08 -0.16 -0.15 -0.07
## C1 0.17 0.06 0.03 0.06 -0.01 -0.11 0.09 -0.02 0.00 -0.06 0.15 0.15
## C3 0.34 0.22 0.18 0.24 0.01 -0.12 0.06 0.24 0.20 0.13 0.17 0.36
## C4 0.14 0.17 0.11 0.18 -0.04 -0.07 0.08 0.04 0.18 0.03 0.14 0.29
## C6 -0.06 -0.06 -0.05 0.04 0.10 0.25 -0.04 0.13 0.12 0.10 -0.10 -0.10
## C8 -0.30 -0.13 -0.12 -0.07 0.00 0.17 -0.13 -0.04 -0.05 0.08 -0.13 -0.18
## C9 -0.07 0.00 -0.01 0.03 0.08 0.15 0.01 -0.01 0.02 0.07 -0.09 -0.15
## N1 -0.34 -0.30 -0.27 -0.07 0.13 0.37 0.00 -0.12 -0.21 -0.05 -0.25 -0.22
## N2 -0.16 -0.16 -0.20 -0.01 0.13 0.28 0.12 0.02 -0.05 0.08 -0.11 -0.03
## N4 -0.32 -0.33 -0.33 -0.05 0.13 0.43 0.17 -0.03 -0.08 0.01 -0.17 0.00
## N5 -0.21 -0.29 -0.28 -0.03 0.11 0.34 0.16 0.03 -0.08 0.02 -0.09 0.04
## N6 -0.20 -0.19 -0.23 -0.02 0.15 0.35 0.12 0.03 -0.04 0.11 -0.16 0.02
## N7 -0.29 -0.23 -0.23 -0.16 0.11 0.23 0.12 -0.12 -0.21 -0.06 -0.21 -0.18
## O3 0.08 0.11 0.09 0.25 0.03 0.07 0.06 0.20 0.21 0.14 0.11 0.24
## O4 0.11 0.11 0.07 0.09 0.17 0.10 0.06 0.12 0.14 0.13 0.09 0.14
## O7 -0.04 -0.01 0.02 0.08 -0.02 0.08 0.01 0.04 0.08 0.07 0.01 0.05
## O8 -0.11 -0.07 -0.03 0.11 0.00 0.13 0.02 -0.11 0.04 -0.01 -0.07 -0.06
## O9 -0.06 -0.02 0.02 0.08 -0.07 0.08 0.07 0.00 0.06 0.09 -0.04 0.01
## O10 -0.13 -0.09 -0.04 0.12 -0.03 0.19 0.04 -0.01 -0.03 0.01 -0.09 0.01
## A10 C1 C3 C4 C6 C8 C9 N1 N2 N4 N5 N6
## E1 -0.03 0.17 0.34 0.14 -0.06 -0.30 -0.07 -0.34 -0.16 -0.32 -0.21 -0.20
## E2 0.09 0.06 0.22 0.17 -0.06 -0.13 0.00 -0.30 -0.16 -0.33 -0.29 -0.19
## E4 0.12 0.03 0.18 0.11 -0.05 -0.12 -0.01 -0.27 -0.20 -0.33 -0.28 -0.23
## E5 -0.05 0.06 0.24 0.18 0.04 -0.07 0.03 -0.07 -0.01 -0.05 -0.03 -0.02
## E7 0.17 -0.01 0.01 -0.04 0.10 0.00 0.08 0.13 0.13 0.13 0.11 0.15
## E8 0.07 -0.11 -0.12 -0.07 0.25 0.17 0.15 0.37 0.28 0.43 0.34 0.35
## E10 -0.01 0.09 0.06 0.08 -0.04 -0.13 0.01 0.00 0.12 0.17 0.16 0.12
## A1 -0.16 -0.02 0.24 0.04 0.13 -0.04 -0.01 -0.12 0.02 -0.03 0.03 0.03
## A2 -0.08 0.00 0.20 0.18 0.12 -0.05 0.02 -0.21 -0.05 -0.08 -0.08 -0.04
## A3 -0.16 -0.06 0.13 0.03 0.10 0.08 0.07 -0.05 0.08 0.01 0.02 0.11
## A5 -0.15 0.15 0.17 0.14 -0.10 -0.13 -0.09 -0.25 -0.11 -0.17 -0.09 -0.16
## A6 -0.07 0.15 0.36 0.29 -0.10 -0.18 -0.15 -0.22 -0.03 0.00 0.04 0.02
## A10 1.00 -0.01 -0.02 0.05 0.05 0.06 0.14 0.11 0.09 0.07 0.08 0.01
## C1 -0.01 1.00 0.22 0.24 -0.33 -0.30 -0.28 -0.15 -0.09 -0.10 0.02 -0.04
## C3 -0.02 0.22 1.00 0.34 -0.14 -0.44 -0.30 -0.18 0.05 0.04 0.04 0.10
## C4 0.05 0.24 0.34 1.00 -0.30 -0.38 -0.34 -0.12 0.02 0.04 0.10 0.17
## C6 0.05 -0.33 -0.14 -0.30 1.00 0.37 0.48 0.29 0.23 0.20 0.09 0.08
## C8 0.06 -0.30 -0.44 -0.38 0.37 1.00 0.51 0.27 0.12 0.08 0.04 0.01
## C9 0.14 -0.28 -0.30 -0.34 0.48 0.51 1.00 0.26 0.18 0.09 0.11 -0.04
## N1 0.11 -0.15 -0.18 -0.12 0.29 0.27 0.26 1.00 0.41 0.53 0.35 0.40
## N2 0.09 -0.09 0.05 0.02 0.23 0.12 0.18 0.41 1.00 0.39 0.36 0.42
## N4 0.07 -0.10 0.04 0.04 0.20 0.08 0.09 0.53 0.39 1.00 0.36 0.57
## N5 0.08 0.02 0.04 0.10 0.09 0.04 0.11 0.35 0.36 0.36 1.00 0.40
## N6 0.01 -0.04 0.10 0.17 0.08 0.01 -0.04 0.40 0.42 0.57 0.40 1.00
## N7 0.06 -0.08 -0.09 -0.07 0.08 0.09 0.06 0.43 0.39 0.35 0.27 0.37
## O3 -0.03 0.11 0.17 0.07 0.03 -0.13 -0.05 0.07 0.11 0.14 0.07 0.14
## O4 0.07 0.02 0.15 0.00 0.04 -0.05 0.05 0.09 0.29 0.16 0.12 0.26
## O7 0.10 0.00 0.07 0.21 0.07 0.09 0.08 -0.01 0.06 0.02 0.13 0.05
## O8 0.15 -0.10 -0.08 0.08 0.18 0.13 0.22 0.16 0.10 0.10 0.11 0.03
## O9 0.12 -0.12 -0.06 0.08 0.20 0.10 0.19 0.08 0.03 0.07 0.06 0.00
## O10 0.20 -0.05 -0.15 -0.01 0.13 0.14 0.17 0.14 0.07 0.13 0.09 0.05
## N7 O3 O4 O7 O8 O9 O10
## E1 -0.29 0.08 0.11 -0.04 -0.11 -0.06 -0.13
## E2 -0.23 0.11 0.11 -0.01 -0.07 -0.02 -0.09
## E4 -0.23 0.09 0.07 0.02 -0.03 0.02 -0.04
## E5 -0.16 0.25 0.09 0.08 0.11 0.08 0.12
## E7 0.11 0.03 0.17 -0.02 0.00 -0.07 -0.03
## E8 0.23 0.07 0.10 0.08 0.13 0.08 0.19
## E10 0.12 0.06 0.06 0.01 0.02 0.07 0.04
## A1 -0.12 0.20 0.12 0.04 -0.11 0.00 -0.01
## A2 -0.21 0.21 0.14 0.08 0.04 0.06 -0.03
## A3 -0.06 0.14 0.13 0.07 -0.01 0.09 0.01
## A5 -0.21 0.11 0.09 0.01 -0.07 -0.04 -0.09
## A6 -0.18 0.24 0.14 0.05 -0.06 0.01 0.01
## A10 0.06 -0.03 0.07 0.10 0.15 0.12 0.20
## C1 -0.08 0.11 0.02 0.00 -0.10 -0.12 -0.05
## C3 -0.09 0.17 0.15 0.07 -0.08 -0.06 -0.15
## C4 -0.07 0.07 0.00 0.21 0.08 0.08 -0.01
## C6 0.08 0.03 0.04 0.07 0.18 0.20 0.13
## C8 0.09 -0.13 -0.05 0.09 0.13 0.10 0.14
## C9 0.06 -0.05 0.05 0.08 0.22 0.19 0.17
## N1 0.43 0.07 0.09 -0.01 0.16 0.08 0.14
## N2 0.39 0.11 0.29 0.06 0.10 0.03 0.07
## N4 0.35 0.14 0.16 0.02 0.10 0.07 0.13
## N5 0.27 0.07 0.12 0.13 0.11 0.06 0.09
## N6 0.37 0.14 0.26 0.05 0.03 0.00 0.05
## N7 1.00 0.13 0.10 -0.07 0.03 -0.01 0.01
## O3 0.13 1.00 0.34 -0.35 -0.24 -0.20 -0.06
## O4 0.10 0.34 1.00 -0.22 -0.21 -0.22 -0.13
## O7 -0.07 -0.35 -0.22 1.00 0.47 0.40 0.29
## O8 0.03 -0.24 -0.21 0.47 1.00 0.60 0.47
## O9 -0.01 -0.20 -0.22 0.40 0.60 1.00 0.42
## O10 0.01 -0.06 -0.13 0.29 0.47 0.42 1.00Hmisc::rcorr(as.matrix(sData)) ## E1 E2 E4 E5 E7 E8 E10 A1 A2 A3 A5 A6
## E1 1.00 0.57 0.52 0.40 -0.10 -0.39 -0.10 0.22 0.36 0.16 0.38 0.29
## E2 0.57 1.00 0.65 0.28 -0.02 -0.53 -0.20 0.12 0.37 0.04 0.21 0.20
## E4 0.52 0.65 1.00 0.20 -0.11 -0.55 -0.22 0.13 0.35 0.09 0.24 0.22
## E5 0.40 0.28 0.20 1.00 -0.26 -0.07 -0.01 0.39 0.43 0.28 0.41 0.43
## E7 -0.10 -0.02 -0.11 -0.26 1.00 0.15 0.06 -0.08 -0.13 -0.10 -0.21 -0.08
## E8 -0.39 -0.53 -0.55 -0.07 0.15 1.00 0.26 -0.03 -0.13 0.05 -0.25 -0.05
## E10 -0.10 -0.20 -0.22 -0.01 0.06 0.26 1.00 0.02 0.01 0.05 -0.10 0.10
## A1 0.22 0.12 0.13 0.39 -0.08 -0.03 0.02 1.00 0.39 0.56 0.42 0.45
## A2 0.36 0.37 0.35 0.43 -0.13 -0.13 0.01 0.39 1.00 0.43 0.44 0.51
## A3 0.16 0.04 0.09 0.28 -0.10 0.05 0.05 0.56 0.43 1.00 0.30 0.44
## A5 0.38 0.21 0.24 0.41 -0.21 -0.25 -0.10 0.42 0.44 0.30 1.00 0.46
## A6 0.29 0.20 0.22 0.43 -0.08 -0.05 0.10 0.45 0.51 0.44 0.46 1.00
## A10 -0.03 0.09 0.12 -0.05 0.17 0.07 -0.01 -0.16 -0.08 -0.16 -0.15 -0.07
## C1 0.17 0.06 0.03 0.06 -0.01 -0.11 0.09 -0.02 0.00 -0.06 0.15 0.15
## C3 0.34 0.22 0.18 0.24 0.01 -0.12 0.06 0.24 0.20 0.13 0.17 0.36
## C4 0.14 0.17 0.11 0.18 -0.04 -0.07 0.08 0.04 0.18 0.03 0.14 0.29
## C6 -0.06 -0.06 -0.05 0.04 0.10 0.25 -0.04 0.13 0.12 0.10 -0.10 -0.10
## C8 -0.30 -0.13 -0.12 -0.07 0.00 0.17 -0.13 -0.04 -0.05 0.08 -0.13 -0.18
## C9 -0.07 0.00 -0.01 0.03 0.08 0.15 0.01 -0.01 0.02 0.07 -0.09 -0.15
## N1 -0.34 -0.30 -0.27 -0.07 0.13 0.37 0.00 -0.12 -0.21 -0.05 -0.25 -0.22
## N2 -0.16 -0.16 -0.20 -0.01 0.13 0.28 0.12 0.02 -0.05 0.08 -0.11 -0.03
## N4 -0.32 -0.33 -0.33 -0.05 0.13 0.43 0.17 -0.03 -0.08 0.01 -0.17 0.00
## N5 -0.21 -0.29 -0.28 -0.03 0.11 0.34 0.16 0.03 -0.08 0.02 -0.09 0.04
## N6 -0.20 -0.19 -0.23 -0.02 0.15 0.35 0.12 0.03 -0.04 0.11 -0.16 0.02
## N7 -0.29 -0.23 -0.23 -0.16 0.11 0.23 0.12 -0.12 -0.21 -0.06 -0.21 -0.18
## O3 0.08 0.11 0.09 0.25 0.03 0.07 0.06 0.20 0.21 0.14 0.11 0.24
## O4 0.11 0.11 0.07 0.09 0.17 0.10 0.06 0.12 0.14 0.13 0.09 0.14
## O7 -0.04 -0.01 0.02 0.08 -0.02 0.08 0.01 0.04 0.08 0.07 0.01 0.05
## O8 -0.11 -0.07 -0.03 0.11 0.00 0.13 0.02 -0.11 0.04 -0.01 -0.07 -0.06
## O9 -0.06 -0.02 0.02 0.08 -0.07 0.08 0.07 0.00 0.06 0.09 -0.04 0.01
## O10 -0.13 -0.09 -0.04 0.12 -0.03 0.19 0.04 -0.01 -0.03 0.01 -0.09 0.01
## A10 C1 C3 C4 C6 C8 C9 N1 N2 N4 N5 N6
## E1 -0.03 0.17 0.34 0.14 -0.06 -0.30 -0.07 -0.34 -0.16 -0.32 -0.21 -0.20
## E2 0.09 0.06 0.22 0.17 -0.06 -0.13 0.00 -0.30 -0.16 -0.33 -0.29 -0.19
## E4 0.12 0.03 0.18 0.11 -0.05 -0.12 -0.01 -0.27 -0.20 -0.33 -0.28 -0.23
## E5 -0.05 0.06 0.24 0.18 0.04 -0.07 0.03 -0.07 -0.01 -0.05 -0.03 -0.02
## E7 0.17 -0.01 0.01 -0.04 0.10 0.00 0.08 0.13 0.13 0.13 0.11 0.15
## E8 0.07 -0.11 -0.12 -0.07 0.25 0.17 0.15 0.37 0.28 0.43 0.34 0.35
## E10 -0.01 0.09 0.06 0.08 -0.04 -0.13 0.01 0.00 0.12 0.17 0.16 0.12
## A1 -0.16 -0.02 0.24 0.04 0.13 -0.04 -0.01 -0.12 0.02 -0.03 0.03 0.03
## A2 -0.08 0.00 0.20 0.18 0.12 -0.05 0.02 -0.21 -0.05 -0.08 -0.08 -0.04
## A3 -0.16 -0.06 0.13 0.03 0.10 0.08 0.07 -0.05 0.08 0.01 0.02 0.11
## A5 -0.15 0.15 0.17 0.14 -0.10 -0.13 -0.09 -0.25 -0.11 -0.17 -0.09 -0.16
## A6 -0.07 0.15 0.36 0.29 -0.10 -0.18 -0.15 -0.22 -0.03 0.00 0.04 0.02
## A10 1.00 -0.01 -0.02 0.05 0.05 0.06 0.14 0.11 0.09 0.07 0.08 0.01
## C1 -0.01 1.00 0.22 0.24 -0.33 -0.30 -0.28 -0.15 -0.09 -0.10 0.02 -0.04
## C3 -0.02 0.22 1.00 0.34 -0.14 -0.44 -0.30 -0.18 0.05 0.04 0.04 0.10
## C4 0.05 0.24 0.34 1.00 -0.30 -0.38 -0.34 -0.12 0.02 0.04 0.10 0.17
## C6 0.05 -0.33 -0.14 -0.30 1.00 0.37 0.48 0.29 0.23 0.20 0.09 0.08
## C8 0.06 -0.30 -0.44 -0.38 0.37 1.00 0.51 0.27 0.12 0.08 0.04 0.01
## C9 0.14 -0.28 -0.30 -0.34 0.48 0.51 1.00 0.26 0.18 0.09 0.11 -0.04
## N1 0.11 -0.15 -0.18 -0.12 0.29 0.27 0.26 1.00 0.41 0.53 0.35 0.40
## N2 0.09 -0.09 0.05 0.02 0.23 0.12 0.18 0.41 1.00 0.39 0.36 0.42
## N4 0.07 -0.10 0.04 0.04 0.20 0.08 0.09 0.53 0.39 1.00 0.36 0.57
## N5 0.08 0.02 0.04 0.10 0.09 0.04 0.11 0.35 0.36 0.36 1.00 0.40
## N6 0.01 -0.04 0.10 0.17 0.08 0.01 -0.04 0.40 0.42 0.57 0.40 1.00
## N7 0.06 -0.08 -0.09 -0.07 0.08 0.09 0.06 0.43 0.39 0.35 0.27 0.37
## O3 -0.03 0.11 0.17 0.07 0.03 -0.13 -0.05 0.07 0.11 0.14 0.07 0.14
## O4 0.07 0.02 0.15 0.00 0.04 -0.05 0.05 0.09 0.29 0.16 0.12 0.26
## O7 0.10 0.00 0.07 0.21 0.07 0.09 0.08 -0.01 0.06 0.02 0.13 0.05
## O8 0.15 -0.10 -0.08 0.08 0.18 0.13 0.22 0.16 0.10 0.10 0.11 0.03
## O9 0.12 -0.12 -0.06 0.08 0.20 0.10 0.19 0.08 0.03 0.07 0.06 0.00
## O10 0.20 -0.05 -0.15 -0.01 0.13 0.14 0.17 0.14 0.07 0.13 0.09 0.05
## N7 O3 O4 O7 O8 O9 O10
## E1 -0.29 0.08 0.11 -0.04 -0.11 -0.06 -0.13
## E2 -0.23 0.11 0.11 -0.01 -0.07 -0.02 -0.09
## E4 -0.23 0.09 0.07 0.02 -0.03 0.02 -0.04
## E5 -0.16 0.25 0.09 0.08 0.11 0.08 0.12
## E7 0.11 0.03 0.17 -0.02 0.00 -0.07 -0.03
## E8 0.23 0.07 0.10 0.08 0.13 0.08 0.19
## E10 0.12 0.06 0.06 0.01 0.02 0.07 0.04
## A1 -0.12 0.20 0.12 0.04 -0.11 0.00 -0.01
## A2 -0.21 0.21 0.14 0.08 0.04 0.06 -0.03
## A3 -0.06 0.14 0.13 0.07 -0.01 0.09 0.01
## A5 -0.21 0.11 0.09 0.01 -0.07 -0.04 -0.09
## A6 -0.18 0.24 0.14 0.05 -0.06 0.01 0.01
## A10 0.06 -0.03 0.07 0.10 0.15 0.12 0.20
## C1 -0.08 0.11 0.02 0.00 -0.10 -0.12 -0.05
## C3 -0.09 0.17 0.15 0.07 -0.08 -0.06 -0.15
## C4 -0.07 0.07 0.00 0.21 0.08 0.08 -0.01
## C6 0.08 0.03 0.04 0.07 0.18 0.20 0.13
## C8 0.09 -0.13 -0.05 0.09 0.13 0.10 0.14
## C9 0.06 -0.05 0.05 0.08 0.22 0.19 0.17
## N1 0.43 0.07 0.09 -0.01 0.16 0.08 0.14
## N2 0.39 0.11 0.29 0.06 0.10 0.03 0.07
## N4 0.35 0.14 0.16 0.02 0.10 0.07 0.13
## N5 0.27 0.07 0.12 0.13 0.11 0.06 0.09
## N6 0.37 0.14 0.26 0.05 0.03 0.00 0.05
## N7 1.00 0.13 0.10 -0.07 0.03 -0.01 0.01
## O3 0.13 1.00 0.34 -0.35 -0.24 -0.20 -0.06
## O4 0.10 0.34 1.00 -0.22 -0.21 -0.22 -0.13
## O7 -0.07 -0.35 -0.22 1.00 0.47 0.40 0.29
## O8 0.03 -0.24 -0.21 0.47 1.00 0.60 0.47
## O9 -0.01 -0.20 -0.22 0.40 0.60 1.00 0.42
## O10 0.01 -0.06 -0.13 0.29 0.47 0.42 1.00
##
## n= 382
##
##
## P
## E1 E2 E4 E5 E7 E8 E10 A1 A2 A3
## E1 0.0000 0.0000 0.0000 0.0624 0.0000 0.0606 0.0000 0.0000 0.0023
## E2 0.0000 0.0000 0.0000 0.6479 0.0000 0.0000 0.0231 0.0000 0.4290
## E4 0.0000 0.0000 0.0001 0.0274 0.0000 0.0000 0.0136 0.0000 0.0959
## E5 0.0000 0.0000 0.0001 0.0000 0.1619 0.8689 0.0000 0.0000 0.0000
## E7 0.0624 0.6479 0.0274 0.0000 0.0028 0.2656 0.1106 0.0102 0.0429
## E8 0.0000 0.0000 0.0000 0.1619 0.0028 0.0000 0.5017 0.0127 0.3520
## E10 0.0606 0.0000 0.0000 0.8689 0.2656 0.0000 0.6691 0.8495 0.3647
## A1 0.0000 0.0231 0.0136 0.0000 0.1106 0.5017 0.6691 0.0000 0.0000
## A2 0.0000 0.0000 0.0000 0.0000 0.0102 0.0127 0.8495 0.0000 0.0000
## A3 0.0023 0.4290 0.0959 0.0000 0.0429 0.3520 0.3647 0.0000 0.0000
## A5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0541 0.0000 0.0000 0.0000
## A6 0.0000 0.0000 0.0000 0.0000 0.1330 0.2889 0.0491 0.0000 0.0000 0.0000
## A10 0.5838 0.0916 0.0222 0.2862 0.0006 0.1577 0.8995 0.0023 0.1215 0.0014
## C1 0.0009 0.2490 0.5325 0.2186 0.8055 0.0290 0.0810 0.6336 0.9646 0.2327
## C3 0.0000 0.0000 0.0005 0.0000 0.8623 0.0218 0.2242 0.0000 0.0000 0.0099
## C4 0.0062 0.0008 0.0352 0.0003 0.4516 0.1518 0.1207 0.4567 0.0004 0.6205
## C6 0.2594 0.2446 0.3766 0.3898 0.0451 0.0000 0.4607 0.0137 0.0212 0.0433
## C8 0.0000 0.0084 0.0173 0.1955 0.9365 0.0006 0.0116 0.4398 0.3207 0.1009
## C9 0.1596 0.9555 0.7914 0.5228 0.1337 0.0024 0.8642 0.9177 0.6967 0.1729
## N1 0.0000 0.0000 0.0000 0.1799 0.0099 0.0000 0.9301 0.0226 0.0000 0.3761
## N2 0.0013 0.0023 0.0000 0.8214 0.0084 0.0000 0.0226 0.7687 0.3225 0.1077
## N4 0.0000 0.0000 0.0000 0.3343 0.0094 0.0000 0.0009 0.5109 0.1032 0.8253
## N5 0.0000 0.0000 0.0000 0.5209 0.0304 0.0000 0.0021 0.5169 0.1039 0.7176
## N6 0.0001 0.0002 0.0000 0.6739 0.0034 0.0000 0.0169 0.6108 0.4078 0.0264
## N7 0.0000 0.0000 0.0000 0.0018 0.0321 0.0000 0.0147 0.0160 0.0000 0.2296
## O3 0.1023 0.0259 0.0794 0.0000 0.6129 0.1853 0.2632 0.0000 0.0000 0.0050
## O4 0.0271 0.0293 0.2045 0.0770 0.0010 0.0581 0.2124 0.0159 0.0064 0.0134
## O7 0.4783 0.7911 0.7669 0.1138 0.7446 0.1170 0.8659 0.4925 0.1228 0.1835
## O8 0.0293 0.1947 0.5721 0.0294 0.9588 0.0136 0.6887 0.0338 0.3911 0.8716
## O9 0.2474 0.7180 0.7038 0.1173 0.1452 0.1159 0.1546 0.9410 0.2090 0.0770
## O10 0.0110 0.0954 0.4578 0.0213 0.5176 0.0001 0.4204 0.9156 0.5071 0.8137
## A5 A6 A10 C1 C3 C4 C6 C8 C9 N1
## E1 0.0000 0.0000 0.5838 0.0009 0.0000 0.0062 0.2594 0.0000 0.1596 0.0000
## E2 0.0000 0.0000 0.0916 0.2490 0.0000 0.0008 0.2446 0.0084 0.9555 0.0000
## E4 0.0000 0.0000 0.0222 0.5325 0.0005 0.0352 0.3766 0.0173 0.7914 0.0000
## E5 0.0000 0.0000 0.2862 0.2186 0.0000 0.0003 0.3898 0.1955 0.5228 0.1799
## E7 0.0000 0.1330 0.0006 0.8055 0.8623 0.4516 0.0451 0.9365 0.1337 0.0099
## E8 0.0000 0.2889 0.1577 0.0290 0.0218 0.1518 0.0000 0.0006 0.0024 0.0000
## E10 0.0541 0.0491 0.8995 0.0810 0.2242 0.1207 0.4607 0.0116 0.8642 0.9301
## A1 0.0000 0.0000 0.0023 0.6336 0.0000 0.4567 0.0137 0.4398 0.9177 0.0226
## A2 0.0000 0.0000 0.1215 0.9646 0.0000 0.0004 0.0212 0.3207 0.6967 0.0000
## A3 0.0000 0.0000 0.0014 0.2327 0.0099 0.6205 0.0433 0.1009 0.1729 0.3761
## A5 0.0000 0.0030 0.0030 0.0012 0.0082 0.0480 0.0094 0.0730 0.0000
## A6 0.0000 0.1764 0.0028 0.0000 0.0000 0.0552 0.0003 0.0038 0.0000
## A10 0.0030 0.1764 0.8723 0.7487 0.3573 0.3780 0.2291 0.0073 0.0380
## C1 0.0030 0.0028 0.8723 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024
## C3 0.0012 0.0000 0.7487 0.0000 0.0000 0.0078 0.0000 0.0000 0.0006
## C4 0.0082 0.0000 0.3573 0.0000 0.0000 0.0000 0.0000 0.0000 0.0183
## C6 0.0480 0.0552 0.3780 0.0000 0.0078 0.0000 0.0000 0.0000 0.0000
## C8 0.0094 0.0003 0.2291 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## C9 0.0730 0.0038 0.0073 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## N1 0.0000 0.0000 0.0380 0.0024 0.0006 0.0183 0.0000 0.0000 0.0000
## N2 0.0266 0.5945 0.0653 0.0848 0.3096 0.6396 0.0000 0.0216 0.0006 0.0000
## N4 0.0009 0.9486 0.1439 0.0587 0.4392 0.4524 0.0000 0.1303 0.0671 0.0000
## N5 0.0724 0.4246 0.1294 0.6848 0.3978 0.0542 0.0843 0.4115 0.0381 0.0000
## N6 0.0013 0.6638 0.8674 0.4567 0.0561 0.0010 0.1391 0.8157 0.3863 0.0000
## N7 0.0000 0.0003 0.2812 0.1074 0.0736 0.1525 0.1195 0.0930 0.2264 0.0000
## O3 0.0341 0.0000 0.5889 0.0248 0.0008 0.1844 0.5390 0.0127 0.2845 0.1593
## O4 0.0664 0.0049 0.1692 0.6493 0.0026 0.9674 0.4450 0.3391 0.2915 0.0716
## O7 0.8227 0.2837 0.0403 0.9371 0.2026 0.0000 0.1715 0.0955 0.1272 0.7761
## O8 0.1695 0.2483 0.0039 0.0404 0.0977 0.1107 0.0004 0.0143 0.0000 0.0023
## O9 0.3861 0.7737 0.0166 0.0233 0.2717 0.1308 0.0000 0.0574 0.0001 0.1124
## O10 0.0759 0.8476 0.0001 0.3447 0.0031 0.8437 0.0086 0.0059 0.0007 0.0068
## N2 N4 N5 N6 N7 O3 O4 O7 O8 O9
## E1 0.0013 0.0000 0.0000 0.0001 0.0000 0.1023 0.0271 0.4783 0.0293 0.2474
## E2 0.0023 0.0000 0.0000 0.0002 0.0000 0.0259 0.0293 0.7911 0.1947 0.7180
## E4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0794 0.2045 0.7669 0.5721 0.7038
## E5 0.8214 0.3343 0.5209 0.6739 0.0018 0.0000 0.0770 0.1138 0.0294 0.1173
## E7 0.0084 0.0094 0.0304 0.0034 0.0321 0.6129 0.0010 0.7446 0.9588 0.1452
## E8 0.0000 0.0000 0.0000 0.0000 0.0000 0.1853 0.0581 0.1170 0.0136 0.1159
## E10 0.0226 0.0009 0.0021 0.0169 0.0147 0.2632 0.2124 0.8659 0.6887 0.1546
## A1 0.7687 0.5109 0.5169 0.6108 0.0160 0.0000 0.0159 0.4925 0.0338 0.9410
## A2 0.3225 0.1032 0.1039 0.4078 0.0000 0.0000 0.0064 0.1228 0.3911 0.2090
## A3 0.1077 0.8253 0.7176 0.0264 0.2296 0.0050 0.0134 0.1835 0.8716 0.0770
## A5 0.0266 0.0009 0.0724 0.0013 0.0000 0.0341 0.0664 0.8227 0.1695 0.3861
## A6 0.5945 0.9486 0.4246 0.6638 0.0003 0.0000 0.0049 0.2837 0.2483 0.7737
## A10 0.0653 0.1439 0.1294 0.8674 0.2812 0.5889 0.1692 0.0403 0.0039 0.0166
## C1 0.0848 0.0587 0.6848 0.4567 0.1074 0.0248 0.6493 0.9371 0.0404 0.0233
## C3 0.3096 0.4392 0.3978 0.0561 0.0736 0.0008 0.0026 0.2026 0.0977 0.2717
## C4 0.6396 0.4524 0.0542 0.0010 0.1525 0.1844 0.9674 0.0000 0.1107 0.1308
## C6 0.0000 0.0000 0.0843 0.1391 0.1195 0.5390 0.4450 0.1715 0.0004 0.0000
## C8 0.0216 0.1303 0.4115 0.8157 0.0930 0.0127 0.3391 0.0955 0.0143 0.0574
## C9 0.0006 0.0671 0.0381 0.3863 0.2264 0.2845 0.2915 0.1272 0.0000 0.0001
## N1 0.0000 0.0000 0.0000 0.0000 0.0000 0.1593 0.0716 0.7761 0.0023 0.1124
## N2 0.0000 0.0000 0.0000 0.0000 0.0294 0.0000 0.2151 0.0616 0.5226
## N4 0.0000 0.0000 0.0000 0.0000 0.0074 0.0015 0.7454 0.0415 0.1623
## N5 0.0000 0.0000 0.0000 0.0000 0.1922 0.0157 0.0133 0.0333 0.2436
## N6 0.0000 0.0000 0.0000 0.0000 0.0045 0.0000 0.3436 0.5737 0.9381
## N7 0.0000 0.0000 0.0000 0.0000 0.0142 0.0556 0.1840 0.5635 0.7748
## O3 0.0294 0.0074 0.1922 0.0045 0.0142 0.0000 0.0000 0.0000 0.0000
## O4 0.0000 0.0015 0.0157 0.0000 0.0556 0.0000 0.0000 0.0000 0.0000
## O7 0.2151 0.7454 0.0133 0.3436 0.1840 0.0000 0.0000 0.0000 0.0000
## O8 0.0616 0.0415 0.0333 0.5737 0.5635 0.0000 0.0000 0.0000 0.0000
## O9 0.5226 0.1623 0.2436 0.9381 0.7748 0.0000 0.0000 0.0000 0.0000
## O10 0.1892 0.0120 0.0769 0.3345 0.7842 0.2722 0.0097 0.0000 0.0000 0.0000
## O10
## E1 0.0110
## E2 0.0954
## E4 0.4578
## E5 0.0213
## E7 0.5176
## E8 0.0001
## E10 0.4204
## A1 0.9156
## A2 0.5071
## A3 0.8137
## A5 0.0759
## A6 0.8476
## A10 0.0001
## C1 0.3447
## C3 0.0031
## C4 0.8437
## C6 0.0086
## C8 0.0059
## C9 0.0007
## N1 0.0068
## N2 0.1892
## N4 0.0120
## N5 0.0769
## N6 0.3345
## N7 0.7842
## O3 0.2722
## O4 0.0097
## O7 0.0000
## O8 0.0000
## O9 0.0000
## O10###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(sData)
ggcorrplot::ggcorrplot(sMatrix, title = "Correlation matrix for s data")
#Showing Xs for non-significant correlations
ggcorrplot::ggcorrplot(sMatrix, title = "Correlation matrix for s data", p.mat = p.mat, sig.level = .05)
#Showing lower diagonal
ggcorrplot::ggcorrplot(sMatrix, title = "Correlation matrix for s 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(sMatrix, sig.level=0.05, lab_size = 1.5, p.mat = NULL,
insig = c("pch", "blank"), pch = 1, pch.col = "black", pch.cex =1,
tl.cex = 1) +
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=5)) +
geom_tile(fill="white") +
geom_tile(height=0.8, width=0.8)
#Showing the co-coefficients (this will be messy given the number of variables)
ggcorrplot::ggcorrplot(sMatrix, lab=TRUE, title = "Correlation matrix for s 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(sMatrix, method="circle")
corrplot::corrplot(sMatrix, method="circle", type="upper")
#Visualization using numbers
corrplot::corrplot(sMatrix, method="number")
#Visualization of significance levels at 0.05
res1 <- corrplot::cor.mtest(sMatrix, conf.level = .95)
corrplot::corrplot(sMatrix, p.mat = res1$p, type="lower", sig.level = .05)
#Showing p-value for non-significant results
corrplot(sMatrix, p.mat = res1$p, type="lower",insig = "p-value")
##Step 2: Check if data is suitable - look at the relevant Statistics ###Bartlett’s test
psych::cortest.bartlett(sData)## R was not square, finding R from data## $chisq
## [1] 4005.796
##
## $p.value
## [1] 0
##
## $df
## [1] 465psych::cortest.bartlett(sMatrix, n=nrow(sData))## $chisq
## [1] 4005.796
##
## $p.value
## [1] 0
##
## $df
## [1] 465###KMO
#KMO (execute one of these):
REdaS::KMOS(sData)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: REdaS::KMOS(x = sData)
##
## Measures of Sampling Adequacy (MSA):
## E1 E2 E4 E5 E7 E8 E10 A1
## 0.8641884 0.8407491 0.8385573 0.7917548 0.6765679 0.8673551 0.7046220 0.8019284
## A2 A3 A5 A6 A10 C1 C3 C4
## 0.8648503 0.7601020 0.8576180 0.8622363 0.7057069 0.8319078 0.8381345 0.8067884
## C6 C8 C9 N1 N2 N4 N5 N6
## 0.7859700 0.8037283 0.7973788 0.8830593 0.8695670 0.8603581 0.8870846 0.8212266
## N7 O3 O4 O7 O8 O9 O10
## 0.8863330 0.7351661 0.7821279 0.7408812 0.7561814 0.7837176 0.7913902
##
## KMO-Criterion: 0.8243515psych::KMO(sData)## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = sData)
## Overall MSA = 0.82
## MSA for each item =
## E1 E2 E4 E5 E7 E8 E10 A1 A2 A3 A5 A6 A10 C1 C3 C4
## 0.86 0.84 0.84 0.79 0.68 0.87 0.70 0.80 0.86 0.76 0.86 0.86 0.71 0.83 0.84 0.81
## C6 C8 C9 N1 N2 N4 N5 N6 N7 O3 O4 O7 O8 O9 O10
## 0.79 0.80 0.80 0.88 0.87 0.86 0.89 0.82 0.89 0.74 0.78 0.74 0.76 0.78 0.79###Determinant
#Determinant (execute one of these):
det(sMatrix)## [1] 1.976978e-05det(cor(sData))## [1] 1.976978e-05##Step 3: Do the Dimension Reduction (PRINCIPAL COMPONENTS ANALYSIS)
#pcModel<-principal(dataframe/R-matrix, nfactors = number of factors, rotate = "method of rotation", scores = TRUE)
#On raw data using principal components analysis
#For PCA we know how many factors if is possible to find
#principal will work out our loadings of each variable onto each component, the proportion each component explained and the cumulative proportion of variance explained
pc1 <- principal(sData, nfactors = 31, rotate = "none")
pc1 <- principal(sData, nfactors = length(sData), rotate = "none")
pc1#output all details of the PCA## Principal Components Analysis
## Call: principal(r = sData, nfactors = length(sData), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12
## E1 -0.70 0.11 0.08 -0.07 0.28 0.02 -0.03 -0.10 0.24 -0.20 0.04 -0.04
## E2 -0.64 -0.02 0.16 -0.13 0.53 -0.06 -0.03 -0.10 0.01 0.08 -0.01 0.12
## E4 -0.62 -0.04 0.23 -0.13 0.48 -0.12 -0.01 -0.07 -0.04 0.18 0.03 -0.02
## E5 -0.44 0.49 0.25 -0.01 -0.05 -0.13 0.34 0.01 0.09 -0.25 -0.13 -0.02
## E7 0.25 0.03 -0.17 -0.04 0.35 0.52 -0.37 0.11 -0.20 -0.07 0.35 0.24
## E8 0.62 0.34 -0.05 0.06 -0.24 0.28 0.09 0.02 -0.11 -0.18 -0.17 0.02
## E10 0.16 0.24 -0.16 0.23 -0.18 0.50 0.15 -0.43 0.38 0.30 -0.12 0.00
## A1 -0.37 0.54 0.12 -0.21 -0.32 0.06 -0.15 0.05 -0.10 -0.01 0.22 -0.29
## A2 -0.52 0.47 0.26 -0.13 -0.03 0.05 -0.05 -0.07 -0.06 0.13 -0.17 0.26
## A3 -0.25 0.55 0.20 -0.20 -0.34 0.03 -0.21 0.01 -0.12 0.27 0.17 -0.10
## A5 -0.57 0.30 0.10 -0.08 -0.23 -0.12 0.04 0.30 0.15 0.01 0.06 0.04
## A6 -0.50 0.56 0.02 0.09 -0.17 0.14 0.01 0.12 -0.12 0.11 -0.05 0.02
## A10 0.15 -0.01 0.15 0.13 0.55 0.31 0.17 0.32 -0.15 0.15 -0.24 -0.44
## C1 -0.27 0.01 -0.33 0.37 0.01 0.12 0.26 0.36 0.32 -0.09 0.33 0.20
## C3 -0.41 0.36 -0.27 0.29 0.17 0.04 -0.22 -0.18 0.02 -0.34 0.02 -0.28
## C4 -0.28 0.26 -0.17 0.60 0.14 -0.12 -0.07 0.03 -0.11 0.09 -0.26 0.21
## C6 0.32 0.24 0.43 -0.42 0.10 0.10 -0.11 -0.21 0.03 -0.35 0.02 0.01
## C8 0.41 -0.04 0.45 -0.46 -0.08 -0.05 -0.02 0.27 0.03 0.15 -0.12 0.13
## C9 0.33 0.09 0.51 -0.44 0.15 0.17 0.05 0.05 0.30 -0.03 -0.07 0.08
## N1 0.65 0.29 -0.01 -0.12 0.18 -0.29 0.10 0.05 0.00 -0.11 0.06 0.03
## N2 0.42 0.48 -0.09 -0.06 0.25 -0.14 -0.14 0.02 0.28 0.07 0.04 -0.11
## N4 0.55 0.49 -0.17 0.07 0.08 -0.14 0.02 -0.08 -0.16 -0.10 -0.10 0.08
## N5 0.42 0.43 -0.13 0.18 0.03 -0.04 -0.08 0.27 0.26 -0.06 -0.06 -0.06
## N6 0.41 0.53 -0.27 0.11 0.15 -0.23 -0.17 -0.04 -0.14 0.08 -0.05 0.14
## N7 0.50 0.21 -0.23 -0.04 0.17 -0.30 0.07 -0.15 0.15 0.33 0.29 -0.15
## O3 -0.15 0.43 -0.34 -0.28 0.13 0.05 0.48 -0.10 -0.22 -0.04 0.13 0.10
## O4 -0.03 0.41 -0.33 -0.32 0.32 0.19 0.02 0.11 0.06 0.09 -0.09 0.09
## O7 0.07 0.12 0.51 0.51 0.01 -0.02 -0.34 0.17 0.12 -0.01 -0.05 0.02
## O8 0.24 0.11 0.64 0.43 0.11 -0.04 0.06 -0.08 0.01 -0.03 0.13 0.14
## O9 0.15 0.13 0.64 0.39 0.04 0.01 0.05 -0.23 -0.03 0.07 0.15 0.02
## O10 0.24 0.14 0.50 0.30 0.05 0.08 0.40 0.07 -0.22 0.02 0.22 -0.08
## PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24
## E1 -0.05 0.02 0.05 -0.18 0.16 -0.01 0.23 -0.12 -0.17 0.08 0.08 -0.03
## E2 0.05 0.11 -0.05 -0.01 0.14 0.00 -0.03 -0.01 0.01 0.05 -0.04 0.03
## E4 0.09 0.12 -0.04 -0.13 -0.08 0.13 -0.03 0.02 0.04 -0.15 0.07 0.08
## E5 -0.02 -0.07 0.04 0.09 0.37 -0.15 0.06 0.11 -0.01 0.01 -0.19 0.06
## E7 0.11 -0.21 -0.01 0.00 0.22 -0.08 -0.04 0.02 -0.03 0.00 -0.06 0.00
## E8 -0.06 0.02 0.07 0.11 0.05 0.08 0.27 -0.02 -0.13 -0.01 0.16 0.06
## E10 0.10 0.03 0.05 -0.12 0.13 0.01 -0.10 -0.03 0.12 -0.07 -0.08 0.04
## A1 0.06 0.05 -0.08 -0.02 0.12 -0.05 -0.01 -0.11 0.33 -0.03 -0.06 0.04
## A2 0.12 -0.08 0.07 0.07 -0.15 0.22 0.11 -0.04 -0.14 -0.16 -0.12 -0.08
## A3 -0.04 0.23 0.05 0.00 -0.07 -0.23 0.15 -0.06 -0.16 -0.09 0.08 -0.12
## A5 -0.02 -0.45 0.15 -0.12 -0.06 0.08 -0.05 -0.05 0.14 0.09 0.07 -0.09
## A6 0.12 -0.07 0.02 -0.04 -0.03 0.05 -0.23 0.12 -0.25 0.10 0.08 0.23
## A10 0.15 -0.06 0.18 0.02 -0.08 -0.05 0.12 -0.07 0.02 0.03 -0.11 -0.06
## C1 0.09 0.31 0.24 0.03 -0.17 0.00 0.05 -0.06 0.02 0.03 -0.04 0.04
## C3 0.01 0.11 0.07 0.08 -0.12 -0.03 -0.17 0.30 -0.08 0.03 0.06 -0.03
## C4 0.11 -0.02 -0.10 0.22 0.06 -0.21 -0.03 -0.23 0.14 0.08 0.25 0.06
## C6 0.14 0.03 0.05 0.11 -0.17 0.21 0.03 -0.22 0.12 0.11 0.02 0.17
## C8 0.06 0.21 0.06 0.11 0.08 -0.04 -0.13 0.18 -0.01 0.17 -0.12 0.13
## C9 0.09 0.05 -0.05 -0.05 0.01 -0.19 -0.08 0.09 0.02 0.06 0.30 -0.25
## N1 0.16 -0.01 0.13 -0.13 0.03 -0.21 -0.01 -0.05 0.00 -0.37 0.05 0.20
## N2 -0.24 -0.05 0.01 0.29 -0.03 -0.01 -0.27 -0.29 -0.17 -0.01 -0.13 -0.07
## N4 0.09 0.00 0.26 -0.29 -0.07 0.05 -0.19 0.05 0.08 0.02 0.01 -0.15
## N5 0.20 -0.01 -0.55 -0.20 -0.09 0.08 0.09 0.04 -0.07 -0.01 -0.07 0.02
## N6 -0.09 0.21 0.05 -0.21 0.12 0.05 0.13 -0.03 0.05 0.23 -0.14 -0.10
## N7 0.17 -0.18 0.10 0.18 0.12 0.16 0.19 0.17 -0.03 0.12 0.15 0.07
## O3 0.11 0.06 -0.21 0.26 -0.11 0.01 0.00 0.09 0.12 -0.01 -0.03 -0.19
## O4 -0.55 -0.05 -0.03 -0.05 -0.13 -0.02 0.09 0.16 0.17 -0.06 0.07 0.17
## O7 -0.04 0.13 0.06 0.19 0.12 0.23 0.05 0.17 0.21 -0.15 0.05 -0.07
## O8 -0.11 -0.18 -0.01 0.04 -0.07 -0.08 0.06 0.12 -0.07 -0.12 -0.13 -0.10
## O9 -0.05 -0.07 -0.04 -0.07 -0.29 -0.22 0.08 0.03 0.07 0.22 -0.07 0.14
## O10 -0.23 0.12 -0.11 -0.13 0.18 0.23 -0.18 -0.13 -0.07 0.00 0.15 0.00
## PC25 PC26 PC27 PC28 PC29 PC30 PC31 h2 u2 com
## E1 0.14 0.09 0.04 -0.08 0.16 -0.08 -0.22 1 -2.2e-16 3.8
## E2 -0.04 -0.14 0.20 0.01 0.04 0.35 0.08 1 -2.4e-15 3.8
## E4 0.12 0.10 -0.10 0.21 0.06 -0.18 0.20 1 -1.3e-15 4.7
## E5 -0.02 -0.08 -0.11 -0.07 -0.06 -0.10 0.18 1 -2.2e-16 7.4
## E7 0.03 0.03 0.01 -0.04 -0.02 -0.08 0.07 1 2.6e-15 7.3
## E8 0.10 -0.01 0.18 0.24 0.10 0.05 0.12 1 -8.9e-16 5.5
## E10 0.02 0.13 0.00 -0.01 -0.01 0.04 0.00 1 -2.2e-16 7.3
## A1 -0.12 -0.12 0.07 0.17 0.12 -0.05 -0.11 1 -2.2e-16 7.3
## A2 -0.21 -0.07 0.17 -0.04 -0.10 -0.14 -0.07 1 2.2e-16 7.1
## A3 0.01 0.09 -0.09 -0.17 0.01 0.09 0.14 1 -6.7e-16 7.7
## A5 0.08 0.21 0.09 0.04 -0.07 0.10 0.08 1 -4.4e-16 5.8
## A6 0.13 -0.15 -0.18 0.06 -0.02 0.07 -0.13 1 -6.7e-16 5.5
## A10 -0.02 0.01 -0.04 -0.03 -0.03 0.02 -0.03 1 5.6e-16 6.3
## C1 -0.09 -0.06 -0.02 0.03 0.02 -0.01 0.03 1 1.8e-15 10.7
## C3 -0.14 0.17 0.13 0.03 -0.08 -0.01 0.02 1 2.2e-16 11.0
## C4 -0.12 0.09 -0.02 -0.03 0.06 -0.05 -0.01 1 1.3e-15 6.3
## C6 -0.06 0.07 -0.19 -0.09 -0.03 0.09 0.04 1 1.2e-15 9.4
## C8 -0.02 0.24 0.13 -0.02 0.14 -0.06 -0.05 1 6.7e-16 7.8
## C9 -0.07 -0.14 -0.04 0.10 -0.12 -0.05 -0.02 1 1.3e-15 7.1
## N1 0.06 0.06 0.09 0.00 -0.14 0.06 -0.11 1 2.2e-16 4.7
## N2 0.11 -0.05 0.04 0.06 0.03 -0.05 0.03 1 2.0e-15 8.3
## N4 0.01 -0.13 0.02 -0.13 0.26 -0.03 0.07 1 0.0e+00 6.0
## N5 -0.03 0.02 0.02 -0.07 0.05 0.02 0.07 1 8.9e-16 5.8
## N6 0.01 0.07 -0.10 0.16 -0.21 0.02 -0.06 1 1.1e-16 7.7
## N7 -0.11 -0.05 -0.01 -0.04 0.03 -0.03 0.00 1 6.7e-16 9.7
## O3 0.22 0.08 0.00 -0.03 0.01 0.03 -0.09 1 -2.2e-16 8.3
## O4 -0.09 -0.03 -0.04 -0.08 0.03 -0.01 -0.02 1 0.0e+00 6.3
## O7 0.23 -0.07 -0.02 -0.11 -0.04 0.02 -0.05 1 -2.2e-16 6.3
## O8 -0.15 0.11 -0.18 0.17 0.18 0.12 -0.08 1 5.6e-16 4.7
## O9 0.16 -0.10 0.17 -0.04 -0.07 -0.10 0.03 1 6.7e-16 4.8
## O10 -0.12 0.07 0.08 -0.09 -0.07 -0.02 0.00 1 6.7e-16 8.5
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 5.36 3.40 2.95 2.33 1.79 1.16 1.10 0.93 0.88 0.84 0.78
## Proportion Var 0.17 0.11 0.10 0.08 0.06 0.04 0.04 0.03 0.03 0.03 0.03
## Cumulative Var 0.17 0.28 0.38 0.45 0.51 0.55 0.58 0.61 0.64 0.67 0.69
## Proportion Explained 0.17 0.11 0.10 0.08 0.06 0.04 0.04 0.03 0.03 0.03 0.03
## Cumulative Proportion 0.17 0.28 0.38 0.45 0.51 0.55 0.58 0.61 0.64 0.67 0.69
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.73 0.70 0.66 0.63 0.62 0.60 0.53 0.52 0.52 0.48 0.44
## Proportion Var 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01
## Cumulative Var 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90
## Proportion Explained 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01
## Cumulative Proportion 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31
## SS loadings 0.43 0.40 0.38 0.35 0.34 0.32 0.30 0.28 0.26
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.92 0.93 0.94 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 0.01
## Cumulative Proportion 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 6.9
## Test of the hypothesis that 31 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 5.3620195 3.3966708 2.94746733 2.3274522 1.79040792
## Proportion Var 0.1729684 0.1095700 0.09507959 0.0750791 0.05775509
## Cumulative Var 0.1729684 0.2825384 0.37761799 0.4526971 0.51045219
## Proportion Explained 0.1729684 0.1095700 0.09507959 0.0750791 0.05775509
## Cumulative Proportion 0.1729684 0.2825384 0.37761799 0.4526971 0.51045219
## PC6 PC7 PC8 PC9 PC10
## SS loadings 1.15931750 1.09850937 0.93342698 0.88231360 0.83605728
## Proportion Var 0.03739734 0.03543579 0.03011055 0.02846173 0.02696959
## Cumulative Var 0.54784953 0.58328531 0.61339586 0.64185759 0.66882718
## Proportion Explained 0.03739734 0.03543579 0.03011055 0.02846173 0.02696959
## Cumulative Proportion 0.54784953 0.58328531 0.61339586 0.64185759 0.66882718
## PC11 PC12 PC13 PC14 PC15
## SS loadings 0.77524848 0.73171304 0.69842929 0.65968066 0.63242960
## Proportion Var 0.02500802 0.02360365 0.02252998 0.02128002 0.02040095
## Cumulative Var 0.69383519 0.71743884 0.73996882 0.76124884 0.78164979
## Proportion Explained 0.02500802 0.02360365 0.02252998 0.02128002 0.02040095
## Cumulative Proportion 0.69383519 0.71743884 0.73996882 0.76124884 0.78164979
## PC16 PC17 PC18 PC19 PC20
## SS loadings 0.61833110 0.59641435 0.53346260 0.5230507 0.51641237
## Proportion Var 0.01994616 0.01923917 0.01720847 0.0168726 0.01665846
## Cumulative Var 0.80159596 0.82083513 0.83804360 0.8549162 0.87157467
## Proportion Explained 0.01994616 0.01923917 0.01720847 0.0168726 0.01665846
## Cumulative Proportion 0.80159596 0.82083513 0.83804360 0.8549162 0.87157467
## PC21 PC22 PC23 PC24 PC25
## SS loadings 0.48424207 0.43712456 0.42510769 0.39936926 0.3848867
## Proportion Var 0.01562071 0.01410079 0.01371315 0.01288288 0.0124157
## Cumulative Var 0.88719538 0.90129617 0.91500932 0.92789220 0.9403079
## Proportion Explained 0.01562071 0.01410079 0.01371315 0.01288288 0.0124157
## Cumulative Proportion 0.88719538 0.90129617 0.91500932 0.92789220 0.9403079
## PC26 PC27 PC28 PC29 PC30
## SS loadings 0.35449104 0.34192245 0.31667258 0.301706982 0.277745193
## Proportion Var 0.01143519 0.01102976 0.01021524 0.009732483 0.008959522
## Cumulative Var 0.95174310 0.96277285 0.97298810 0.982720582 0.991680104
## Proportion Explained 0.01143519 0.01102976 0.01021524 0.009732483 0.008959522
## Cumulative Proportion 0.95174310 0.96277285 0.97298810 0.982720582 0.991680104
## PC31
## SS loadings 0.257916776
## Proportion Var 0.008319896
## Cumulative Var 1.000000000
## Proportion Explained 0.008319896
## Cumulative Proportion 1.000000000#Print the Eigenvalues
pc1$values## [1] 5.3620195 3.3966708 2.9474673 2.3274522 1.7904079 1.1593175 1.0985094
## [8] 0.9334270 0.8823136 0.8360573 0.7752485 0.7317130 0.6984293 0.6596807
## [15] 0.6324296 0.6183311 0.5964144 0.5334626 0.5230507 0.5164124 0.4842421
## [22] 0.4371246 0.4251077 0.3993693 0.3848867 0.3544910 0.3419225 0.3166726
## [29] 0.3017070 0.2777452 0.2579168#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(sData)
factoextra::get_eigenvalue(pcf)## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 7.2229760 17.7878083 17.78781
## Dim.2 4.3563605 10.7282794 28.51609
## Dim.3 3.9367435 9.6949011 38.21099
## Dim.4 3.3455339 8.2389470 46.44994
## Dim.5 2.3524408 5.7932860 52.24322
## Dim.6 1.4998321 3.6935919 55.93681
## Dim.7 1.3479400 3.3195317 59.25635
## Dim.8 1.2595122 3.1017631 62.35811
## Dim.9 1.1506612 2.8336990 65.19181
## Dim.10 1.1015688 2.7128008 67.90461
## Dim.11 0.9793638 2.4118500 70.31646
## Dim.12 0.9292927 2.2885414 72.60500
## Dim.13 0.9193765 2.2641212 74.86912
## Dim.14 0.8626665 2.1244632 76.99358
## Dim.15 0.7965352 1.9616035 78.95519
## Dim.16 0.7770077 1.9135138 80.86870
## Dim.17 0.7609949 1.8740795 82.74278
## Dim.18 0.6853564 1.6878068 84.43059
## Dim.19 0.6535380 1.6094486 86.04004
## Dim.20 0.6261561 1.5420161 87.58205
## Dim.21 0.6058311 1.4919622 89.07401
## Dim.22 0.5769480 1.4208326 90.49485
## Dim.23 0.5486778 1.3512125 91.84606
## Dim.24 0.5448046 1.3416740 93.18773
## Dim.25 0.5000232 1.2313923 94.41913
## Dim.26 0.4594281 1.1314198 95.55055
## Dim.27 0.4415621 1.0874219 96.63797
## Dim.28 0.3924032 0.9663597 97.60433
## Dim.29 0.3564223 0.8777506 98.48208
## Dim.30 0.3260599 0.8029780 99.28506
## Dim.31 0.2903126 0.7149441 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 = sData, nfactors = length(sData), rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## E1 1 -0.70
## N1 20 0.65
## E2 2 -0.64 0.53
## E4 3 -0.62 0.48
## E8 6 0.62 0.34
## A5 11 -0.57 0.30
## N4 22 0.55 0.49
## A2 9 -0.52 0.47
## N7 25 0.50 0.33
## C3 15 -0.41 0.36 -0.34
## A6 12 -0.50 0.56
## A3 10 0.55 -0.34
## A1 8 -0.37 0.54 -0.32
## N6 24 0.41 0.53
## E5 4 -0.44 0.49 0.34
## N2 21 0.42 0.48
## O9 30 0.64 0.39
## O8 29 0.64 0.43
## C9 19 0.33 0.51 -0.44 0.30
## O7 28 0.51 0.51 -0.34
## O10 31 0.50 0.40
## C6 17 0.32 0.43 -0.42 -0.35
## C4 16 0.60
## C8 18 0.41 0.45 -0.46
## C1 14 -0.33 0.37 0.36 0.32 0.33
## A10 13 0.55 0.31 0.32
## E7 5 0.35 0.52 -0.37 0.35
## E10 7 0.50 -0.43 0.38 0.30
## O3 26 0.43 -0.34 0.48
## O4 27 0.41 -0.33 -0.32 0.32
## N5 23 0.42 0.43
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23
## E1
## N1 -0.37
## E2
## E4
## E8
## A5 -0.45
## N4
## A2
## N7
## C3
## A6
## A3
## A1 0.33
## N6
## E5 0.37
## N2
## O9
## O8
## C9
## O7
## O10
## C6
## C4
## C8
## C1 0.31
## A10 -0.44
## E7
## E10
## O3
## O4 -0.55
## N5 -0.55
## PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31 h2 u2 com
## E1 1 -2.2e-16 3.8
## N1 1 2.2e-16 4.7
## E2 0.35 1 -2.4e-15 3.8
## E4 1 -1.3e-15 4.7
## E8 1 -8.9e-16 5.5
## A5 1 -4.4e-16 5.8
## N4 1 0.0e+00 6.0
## A2 1 2.2e-16 7.1
## N7 1 6.7e-16 9.7
## C3 1 2.2e-16 11.0
## A6 1 -6.7e-16 5.5
## A3 1 -6.7e-16 7.7
## A1 1 -2.2e-16 7.3
## N6 1 1.1e-16 7.7
## E5 1 -2.2e-16 7.4
## N2 1 2.0e-15 8.3
## O9 1 6.7e-16 4.8
## O8 1 5.6e-16 4.7
## C9 1 1.3e-15 7.1
## O7 1 -2.2e-16 6.3
## O10 1 6.7e-16 8.5
## C6 1 1.2e-15 9.4
## C4 1 1.3e-15 6.3
## C8 1 6.7e-16 7.8
## C1 1 1.8e-15 10.7
## A10 1 5.6e-16 6.3
## E7 1 2.6e-15 7.3
## E10 1 -2.2e-16 7.3
## O3 1 -2.2e-16 8.3
## O4 1 0.0e+00 6.3
## N5 1 8.9e-16 5.8
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## SS loadings 5.36 3.40 2.95 2.33 1.79 1.16 1.10 0.93 0.88 0.84 0.78
## Proportion Var 0.17 0.11 0.10 0.08 0.06 0.04 0.04 0.03 0.03 0.03 0.03
## Cumulative Var 0.17 0.28 0.38 0.45 0.51 0.55 0.58 0.61 0.64 0.67 0.69
## Proportion Explained 0.17 0.11 0.10 0.08 0.06 0.04 0.04 0.03 0.03 0.03 0.03
## Cumulative Proportion 0.17 0.28 0.38 0.45 0.51 0.55 0.58 0.61 0.64 0.67 0.69
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## SS loadings 0.73 0.70 0.66 0.63 0.62 0.60 0.53 0.52 0.52 0.48 0.44
## Proportion Var 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01
## Cumulative Var 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90
## Proportion Explained 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01
## Cumulative Proportion 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.85 0.87 0.89 0.90
## PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31
## SS loadings 0.43 0.40 0.38 0.35 0.34 0.32 0.30 0.28 0.26
## Proportion Var 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
## Cumulative Var 0.92 0.93 0.94 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 0.01
## Cumulative Proportion 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
##
## Mean item complexity = 6.9
## Test of the hypothesis that 31 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
## E1 -0.704 0.107 0.280 -0.104 0.238 -0.202
## N1 0.647 0.292 -0.122 0.181 -0.287 -0.107
## E2 -0.638 0.164 -0.129 0.533
## E4 -0.624 0.229 -0.126 0.477 -0.116 0.184
## E8 0.616 0.344 -0.242 0.280 -0.109 -0.179
## A5 -0.573 0.302 -0.233 -0.122 0.299 0.149
## N4 0.548 0.486 -0.166 -0.139 -0.160
## A2 -0.519 0.473 0.256 -0.134 0.127
## N7 0.499 0.208 -0.234 0.168 -0.298 -0.147 0.146 0.328
## C3 -0.407 0.361 -0.265 0.294 0.167 -0.217 -0.182 -0.338
## A6 -0.504 0.564 -0.175 0.144 0.124 -0.121 0.112
## A3 -0.246 0.550 0.195 -0.200 -0.343 -0.213 -0.117 0.274
## A1 -0.370 0.537 0.123 -0.209 -0.316 -0.155
## N6 0.408 0.532 -0.273 0.114 0.149 -0.230 -0.167 -0.136
## E5 -0.437 0.487 0.246 -0.134 0.336 -0.248
## N2 0.424 0.479 0.254 -0.137 -0.136 0.281
## O9 0.152 0.126 0.640 0.388 -0.234
## O8 0.240 0.109 0.638 0.434 0.115
## C9 0.326 0.514 -0.437 0.152 0.169 0.303
## O7 0.123 0.509 0.508 -0.337 0.167 0.116
## O10 0.235 0.139 0.505 0.299 0.405 -0.224
## C6 0.316 0.239 0.432 -0.423 0.102 -0.109 -0.208 -0.354
## C4 -0.282 0.265 -0.166 0.596 0.145 -0.121 -0.113
## C8 0.406 0.449 -0.460 0.267 0.155
## C1 -0.271 -0.325 0.368 0.117 0.260 0.359 0.318
## A10 0.153 0.147 0.131 0.551 0.310 0.169 0.320 -0.153 0.147
## E7 0.252 -0.173 0.352 0.521 -0.366 0.111 -0.202
## E10 0.158 0.236 -0.162 0.227 -0.183 0.503 0.152 -0.427 0.379 0.303
## O3 -0.147 0.425 -0.341 -0.281 0.127 0.480 -0.216
## O4 0.414 -0.329 -0.324 0.316 0.186 0.105
## N5 0.416 0.433 -0.126 0.178 0.269 0.256
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## E1 -0.181 0.157 0.227 -0.123
## N1 0.161 0.126 -0.127 -0.210
## E2 0.117 0.111 0.138
## E4 0.123 -0.131 0.129
## E8 -0.173 0.112 0.270
## A5 -0.447 0.148 -0.123
## N4 -0.102 0.262 -0.291 -0.190
## A2 -0.167 0.262 0.122 -0.150 0.223 0.113
## N7 0.291 -0.153 0.169 -0.183 0.104 0.179 0.122 0.156 0.186 0.170
## C3 -0.280 0.107 -0.117 -0.174 0.300
## A6 0.123 -0.231 0.120
## A3 0.170 -0.102 0.227 -0.228 0.153
## A1 0.215 -0.288 0.117 -0.106
## N6 0.137 0.209 -0.211 0.122 0.134
## E5 -0.132 0.365 -0.145 0.107
## N2 -0.111 -0.239 0.292 -0.268 -0.293
## O9 0.155 -0.290 -0.221
## O8 0.129 0.136 -0.107 -0.185 0.121
## C9 -0.186
## O7 0.135 0.185 0.116 0.226 0.171
## O10 0.221 -0.227 0.115 -0.113 -0.127 0.185 0.232 -0.176 -0.133
## C6 0.141 0.111 -0.168 0.207 -0.220
## C4 -0.261 0.210 0.113 -0.102 0.216 -0.212 -0.225
## C8 -0.119 0.130 0.209 0.110 -0.129 0.176
## C1 0.327 0.204 0.313 0.235 -0.168
## A10 -0.243 -0.442 0.152 0.178 0.117
## E7 0.352 0.242 0.110 -0.213 0.223
## E10 -0.122 -0.115 0.127
## O3 0.131 0.103 0.114 -0.214 0.263 -0.110
## O4 -0.550 -0.133 0.159
## N5 0.197 -0.552 -0.201
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## E1 -0.170 0.145 0.162
## N1 -0.372 0.203 -0.137
## E2 -0.139 0.197 0.348
## E4 -0.152 0.121 0.101 0.211 -0.181
## E8 -0.133 0.163 0.104 0.177 0.237
## A5 0.144 0.206 0.101
## N4 -0.154 -0.132 -0.132 0.262
## A2 -0.137 -0.158 -0.121 -0.209 0.167 -0.141
## N7 0.119 0.154 -0.114
## C3 -0.141 0.175 0.128
## A6 -0.250 0.229 0.131 -0.148 -0.184
## A3 -0.164 -0.116 -0.172
## A1 0.326 -0.121 -0.123 0.174 0.117
## N6 0.230 -0.138 -0.101 0.163 -0.215
## E5 -0.188 -0.107
## N2 -0.168 -0.130 0.110
## O9 0.220 0.141 0.156 0.175
## O8 -0.117 -0.129 -0.100 -0.149 0.108 -0.181 0.171 0.179 0.123
## C9 0.295 -0.246 -0.139 0.102 -0.115
## O7 0.214 -0.151 0.234 -0.109
## O10 0.154 -0.120
## C6 0.119 0.110 0.166 -0.194
## C4 0.138 0.249 -0.118
## C8 0.169 -0.121 0.132 0.245 0.129 0.141
## C1
## A10 -0.106
## E7
## E10 0.119 0.129
## O3 0.122 -0.188 0.220
## O4 0.165 0.170
## N5
## PC31
## E1 -0.219
## N1 -0.110
## E2
## E4 0.200
## E8 0.124
## A5
## N4
## A2
## N7
## C3
## A6 -0.131
## A3 0.135
## A1 -0.111
## N6
## E5 0.183
## N2
## O9
## O8
## C9
## O7
## O10
## C6
## C4
## C8
## C1
## A10
## E7
## E10
## O3
## O4
## N5
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## SS loadings 5.362 3.397 2.947 2.327 1.790 1.159 1.099 0.933 0.882 0.836
## Proportion Var 0.173 0.110 0.095 0.075 0.058 0.037 0.035 0.030 0.028 0.027
## Cumulative Var 0.173 0.283 0.378 0.453 0.510 0.548 0.583 0.613 0.642 0.669
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## SS loadings 0.775 0.732 0.698 0.660 0.632 0.618 0.596 0.533 0.523 0.516
## Proportion Var 0.025 0.024 0.023 0.021 0.020 0.020 0.019 0.017 0.017 0.017
## Cumulative Var 0.694 0.717 0.740 0.761 0.782 0.802 0.821 0.838 0.855 0.872
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## SS loadings 0.484 0.437 0.425 0.399 0.385 0.354 0.342 0.317 0.302 0.278
## Proportion Var 0.016 0.014 0.014 0.013 0.012 0.011 0.011 0.010 0.010 0.009
## Cumulative Var 0.887 0.901 0.915 0.928 0.940 0.952 0.963 0.973 0.983 0.992
## PC31
## SS loadings 0.258
## Proportion Var 0.008
## Cumulative Var 1.000#Output the communalities of variables across components (will be one for PCA since all the variance is used)
pc1$communality ## E1 E2 E4 E5 E7 E8 E10 A1 A2 A3 A5 A6 A10 C1 C3 C4 C6 C8 C9 N1
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## N2 N4 N5 N6 N7 O3 O4 O7 O8 O9 O10
## 1 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(sData, nfactors = 5, rotate = "varimax")#Extracting 4 factors
#output the components
psych::print.psych(pc2, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = sData, nfactors = 5, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item RC1 RC2 RC4 RC3 RC5 h2 u2 com
## N6 24 0.72 0.56 0.44 1.2
## N4 22 0.70 0.57 0.43 1.3
## N2 21 0.69 0.49 0.51 1.1
## N1 20 0.63 0.31 0.55 0.45 1.8
## N5 23 0.57 0.41 0.59 1.5
## N7 25 0.55 0.38 0.62 1.5
## O4 27 0.48 -0.39 0.49 0.51 2.9
## E7 5 0.35 0.22 0.78 2.4
## A1 8 0.76 0.58 0.42 1.0
## A3 10 0.73 0.56 0.44 1.1
## A6 12 0.72 0.61 0.39 1.3
## A2 9 0.70 0.58 0.42 1.3
## E5 4 0.65 0.49 0.51 1.3
## A5 11 0.63 0.49 0.51 1.4
## C8 18 0.75 0.59 0.41 1.1
## C9 19 0.72 0.59 0.41 1.3
## C4 16 -0.67 0.55 0.45 1.5
## C6 17 0.65 0.53 0.47 1.6
## C1 14 -0.56 0.32 0.68 1.0
## C3 15 0.31 -0.55 0.48 0.52 2.2
## O8 29 0.81 0.68 0.32 1.1
## O9 30 0.76 0.60 0.40 1.1
## O7 28 0.72 0.54 0.46 1.0
## O10 31 0.63 0.42 0.58 1.2
## O3 26 0.35 0.31 -0.40 0.41 0.59 3.3
## E2 2 0.81 0.73 0.27 1.2
## E4 3 0.77 0.69 0.31 1.3
## E1 1 0.37 0.60 0.60 0.40 2.3
## E8 6 0.48 -0.54 0.56 0.44 2.3
## A10 13 0.39 0.37 0.63 3.5
## E10 7 -0.31 0.19 0.81 2.9
##
## RC1 RC2 RC4 RC3 RC5
## SS loadings 3.68 3.66 2.98 2.78 2.72
## Proportion Var 0.12 0.12 0.10 0.09 0.09
## Cumulative Var 0.12 0.24 0.33 0.42 0.51
## Proportion Explained 0.23 0.23 0.19 0.18 0.17
## Cumulative Proportion 0.23 0.46 0.65 0.83 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 5 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.05
## with the empirical chi square 961.55 with prob < 2.2e-65
##
## Fit based upon off diagonal values = 0.93#output the communalities
pc2$communality## E1 E2 E4 E5 E7 E8 E10 A1
## 0.5950986 0.7340796 0.6870828 0.4906798 0.2197046 0.5624587 0.1921658 0.5833365
## A2 A3 A5 A6 A10 C1 C3 C4
## 0.5785891 0.5586902 0.4898214 0.6109292 0.3654486 0.3153426 0.4805751 0.5535264
## C6 C8 C9 N1 N2 N4 N5 N6
## 0.5322111 0.5865772 0.5929027 0.5510816 0.4860990 0.5744249 0.4090745 0.5596758
## N7 O3 O4 O7 O8 O9 O10
## 0.3777081 0.4140158 0.4853921 0.5366989 0.6790055 0.6002451 0.4213765#NOTE: you can do all the other things done for the model created in pc1##Step 3: Do the dimension reduction and Step 4: Decide which factors/components to retain (FACTOR ANALYSIS)
#Factor Analysis - the default here is principal axis factoring fm=pa
#If we know our data going in is normally distributed we use maximum likelihood
facsol <- psych::fa(sMatrix, nfactors=5, obs=NA, n.iter=1, rotate="varimax", fm="pa")
#Create your scree plot
plot(facsol$values, type = "b") #scree plot
#Print the Variance accounted for by each factor/component
facsol$Vaccounted## PA2 PA1 PA4 PA3 PA5
## SS loadings 3.1242347 3.1129711 2.42967385 2.24229110 2.21900146
## Proportion Var 0.1007818 0.1004184 0.07837658 0.07233197 0.07158069
## Cumulative Var 0.1007818 0.2012002 0.27957676 0.35190873 0.42348943
## Proportion Explained 0.2379794 0.2371214 0.18507328 0.17079995 0.16902593
## Cumulative Proportion 0.2379794 0.4751009 0.66017413 0.83097407 1.00000000#Output the Eigenvalues
facsol$values ## [1] 4.852945576 2.844349777 2.405285652 1.767867218 1.257723978
## [6] 0.466286721 0.434095835 0.299373252 0.290345985 0.205915199
## [11] 0.158279258 0.102028578 0.086714067 0.054795845 0.019749853
## [16] 0.001157938 -0.014060215 -0.027338985 -0.040157756 -0.049978343
## [21] -0.063822217 -0.100939952 -0.108816615 -0.134368997 -0.161522477
## [26] -0.178654131 -0.210469246 -0.227316507 -0.234606308 -0.264508730
## [31] -0.303063955#Print the components with loadings
psych::print.psych(facsol,cut=0.3, sort=TRUE)## Factor Analysis using method = pa
## Call: psych::fa(r = sMatrix, nfactors = 5, n.iter = 1, rotate = "varimax",
## fm = "pa", obs = NA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA2 PA1 PA4 PA3 PA5 h2 u2 com
## A1 8 0.70 0.50 0.50 1.0
## A6 12 0.70 0.56 0.44 1.3
## A2 9 0.66 0.51 0.49 1.3
## A3 10 0.66 0.45 0.55 1.1
## E5 4 0.59 0.40 0.60 1.3
## A5 11 0.58 0.41 0.59 1.5
## N6 24 0.69 0.50 0.50 1.1
## N4 22 0.68 0.52 0.48 1.3
## N2 21 0.62 0.40 0.60 1.1
## N1 20 0.60 0.50 0.50 1.8
## N5 23 0.51 0.32 0.68 1.5
## N7 25 0.49 0.31 0.69 1.6
## O4 27 0.40 -0.33 0.34 0.66 2.9
## E7 5 0.11 0.89 2.1
## C8 18 0.69 0.50 0.50 1.1
## C9 19 0.67 0.51 0.49 1.3
## C4 16 -0.59 0.44 0.56 1.5
## C6 17 0.58 0.42 0.58 1.6
## C3 15 -0.49 0.38 0.62 2.2
## C1 14 -0.45 0.21 0.79 1.1
## O8 29 0.79 0.64 0.36 1.1
## O9 30 0.70 0.51 0.49 1.1
## O7 28 0.63 0.40 0.60 1.0
## O10 31 0.52 0.30 0.70 1.2
## O3 26 -0.34 0.30 0.70 3.3
## E2 2 0.80 0.72 0.28 1.3
## E4 3 0.73 0.63 0.37 1.4
## E1 1 0.36 0.55 0.53 0.47 2.5
## E8 6 0.47 -0.49 0.49 0.51 2.3
## A10 13 0.16 0.84 3.9
## E10 7 0.11 0.89 2.9
##
## PA2 PA1 PA4 PA3 PA5
## SS loadings 3.12 3.11 2.43 2.24 2.22
## Proportion Var 0.10 0.10 0.08 0.07 0.07
## Cumulative Var 0.10 0.20 0.28 0.35 0.42
## Proportion Explained 0.24 0.24 0.19 0.17 0.17
## Cumulative Proportion 0.24 0.48 0.66 0.83 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 5 factors are sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 10.83
## The degrees of freedom for the model are 320 and the objective function was 1.55
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA2 PA1 PA4 PA3 PA5
## Correlation of (regression) scores with factors 0.92 0.91 0.89 0.90 0.90
## Multiple R square of scores with factors 0.84 0.82 0.80 0.81 0.81
## Minimum correlation of possible factor scores 0.68 0.65 0.60 0.63 0.62#Print sorted list of loadings
fa.sort(facsol$loading)##
## Loadings:
## PA2 PA1 PA4 PA3 PA5
## A1 0.704
## A6 0.695 -0.273
## A2 0.661 0.262
## A3 0.659 0.110
## E5 0.589 0.120 0.194
## A5 0.577 -0.219 -0.129 0.113
## N6 0.688 -0.136
## N4 0.680 -0.233
## N2 0.622 0.111
## N1 -0.167 0.601 0.297 -0.138
## N5 0.511 0.120 -0.214
## N7 -0.194 0.493 -0.130
## O4 0.185 0.402 -0.329 0.194
## E7 -0.192 0.259
## C8 0.693 0.104
## C9 0.141 0.668 0.176 0.108
## C4 0.148 0.114 -0.594 0.202 0.107
## C6 0.120 0.231 0.579 0.139
## C3 0.294 0.128 -0.491 0.194
## C1 -0.445
## O8 0.107 0.792
## O9 0.108 0.703
## O7 0.627
## O10 0.131 0.524
## O3 0.283 0.293 -0.336 0.121
## E2 0.183 -0.191 0.802
## E4 0.192 -0.248 0.725
## E1 0.360 -0.228 -0.202 0.546
## E8 0.466 0.159 0.119 -0.488
## A10 -0.190 0.176 0.196 0.223
## E10 0.193 -0.138 -0.220
##
## PA2 PA1 PA4 PA3 PA5
## SS loadings 3.124 3.113 2.430 2.242 2.219
## Proportion Var 0.101 0.100 0.078 0.072 0.072
## Cumulative Var 0.101 0.201 0.280 0.352 0.423#create a diagram showing the factors and how the manifest variables load
fa.diagram(facsol)
#Note: you can apply rotation as you did for PCA##Step 5: Apply rotation
#Apply rotation to try to refine the component structure
facsolrot <- principal(sMatrix, rotate = "varimax")
#output the components
psych::print.psych(facsolrot, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = sMatrix, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PC1 h2 u2 com
## E1 1 -0.70 0.4949 0.51 1
## N1 20 0.65 0.4182 0.58 1
## E2 2 -0.64 0.4066 0.59 1
## E4 3 -0.62 0.3895 0.61 1
## E8 6 0.62 0.3793 0.62 1
## A5 11 -0.57 0.3287 0.67 1
## N4 22 0.55 0.3000 0.70 1
## A2 9 -0.52 0.2695 0.73 1
## A6 12 -0.50 0.2538 0.75 1
## N7 25 0.50 0.2492 0.75 1
## E5 4 -0.44 0.1906 0.81 1
## N2 21 0.42 0.1798 0.82 1
## N5 23 0.42 0.1732 0.83 1
## N6 24 0.41 0.1668 0.83 1
## C3 15 -0.41 0.1654 0.83 1
## C8 18 0.41 0.1648 0.84 1
## A1 8 -0.37 0.1366 0.86 1
## C9 19 0.33 0.1061 0.89 1
## C6 17 0.32 0.1002 0.90 1
## C4 16 0.0793 0.92 1
## C1 14 0.0736 0.93 1
## E7 5 0.0634 0.94 1
## A3 10 0.0605 0.94 1
## O8 29 0.0578 0.94 1
## O10 31 0.0552 0.94 1
## E10 7 0.0250 0.97 1
## A10 13 0.0233 0.98 1
## O9 30 0.0230 0.98 1
## O3 26 0.0217 0.98 1
## O7 28 0.0049 1.00 1
## O4 27 0.0011 1.00 1
##
## PC1
## SS loadings 5.36
## Proportion Var 0.17
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.14
##
## Fit based upon off diagonal values = 0.53#output the communalities
facsolrot$communality## E1 E2 E4 E5 E7 E8
## 0.494926381 0.406647063 0.389467986 0.190572844 0.063369993 0.379281993
## E10 A1 A2 A3 A5 A6
## 0.025049575 0.136626173 0.269473040 0.060537662 0.328688668 0.253826408
## A10 C1 C3 C4 C6 C8
## 0.023294309 0.073642526 0.165388951 0.079304631 0.100155772 0.164808128
## C9 N1 N2 N4 N5 N6
## 0.106117618 0.418150978 0.179774377 0.299967255 0.173172585 0.166793188
## N7 O3 O4 O7 O8 O9
## 0.249211928 0.021689535 0.001102876 0.004935733 0.057837081 0.022970963
## O10
## 0.055233310##Step 6: Reliability Analysis
#If you know that variables are grouped, test each group as a separate scale
Extraversion <-sData[,c('E1','E2','E4','E5','E7','E8','E10')]
Agreeableness <- sData[, c('A1','A2','A3','A5','A6','A10')]
Conscientiousness <- sData[, c('C1','C3','C4','C6','C8','C9')]
Neuroticism <- sData[, c('N1','N2','N4','N5','N6','N7')]
Openness <- sData[, c('O3','O4','O7','O8','O9','O10')]
#Output our Cronbach Alpha values
psych::alpha(Extraversion,check.keys=TRUE)## Warning in psych::alpha(Extraversion, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = Extraversion, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.73 0.72 0.74 0.27 2.6 0.02 2.8 0.73 0.22
##
## lower alpha upper 95% confidence boundaries
## 0.69 0.73 0.77
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## E1 0.67 0.65 0.68 0.24 1.9 0.025 0.039 0.20
## E2 0.64 0.64 0.65 0.23 1.8 0.028 0.029 0.20
## E4 0.64 0.64 0.66 0.23 1.8 0.027 0.032 0.20
## E5 0.73 0.71 0.72 0.29 2.5 0.021 0.047 0.22
## E7- 0.76 0.75 0.75 0.33 2.9 0.018 0.041 0.28
## E8- 0.67 0.66 0.69 0.25 2.0 0.025 0.042 0.20
## E10- 0.75 0.74 0.76 0.32 2.8 0.019 0.044 0.28
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## E1 382 0.72 0.72 0.68 0.58 2.6 1.17
## E2 382 0.78 0.76 0.76 0.64 2.9 1.33
## E4 382 0.78 0.76 0.75 0.65 2.7 1.25
## E5 382 0.47 0.52 0.40 0.31 3.9 0.95
## E7- 382 0.37 0.40 0.22 0.16 2.9 1.11
## E8- 382 0.71 0.69 0.63 0.55 1.9 1.25
## E10- 382 0.43 0.43 0.25 0.22 2.7 1.17
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## E1 0.01 0.20 0.31 0.27 0.15 0.06 0
## E2 0.01 0.16 0.23 0.19 0.28 0.13 0
## E4 0.01 0.20 0.27 0.21 0.24 0.07 0
## E5 0.02 0.01 0.04 0.13 0.54 0.25 0
## E7 0.01 0.35 0.37 0.12 0.12 0.03 0
## E8 0.01 0.08 0.28 0.22 0.25 0.16 0
## E10 0.01 0.27 0.39 0.15 0.12 0.05 0#Some items were negatively correlated with the total scale and probably
## should be reversed.
psych::alpha(Agreeableness,check.keys = TRUE)## Warning in psych::alpha(Agreeableness, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = Agreeableness, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.75 0.75 0.74 0.33 3 0.02 3.6 0.67 0.42
##
## lower alpha upper 95% confidence boundaries
## 0.71 0.75 0.79
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## A1 0.68 0.69 0.67 0.31 2.2 0.026 0.0300 0.37
## A2 0.70 0.70 0.68 0.32 2.3 0.024 0.0290 0.36
## A3 0.69 0.69 0.67 0.31 2.3 0.025 0.0309 0.41
## A5 0.70 0.71 0.69 0.32 2.4 0.024 0.0348 0.41
## A6 0.69 0.69 0.67 0.31 2.2 0.025 0.0260 0.35
## A10- 0.80 0.80 0.77 0.44 3.9 0.016 0.0045 0.44
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## A1 382 0.76 0.74 0.69 0.59 3.7 1.13
## A2 382 0.71 0.71 0.64 0.54 3.9 1.00
## A3 382 0.74 0.72 0.66 0.57 3.8 1.08
## A5 382 0.67 0.69 0.60 0.52 3.9 0.87
## A6 382 0.72 0.73 0.67 0.57 3.7 0.92
## A10- 382 0.41 0.40 0.19 0.17 2.6 1.05
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## A1 0.01 0.03 0.12 0.14 0.47 0.23 0
## A2 0.01 0.02 0.06 0.18 0.48 0.26 0
## A3 0.01 0.03 0.08 0.15 0.47 0.25 0
## A5 0.00 0.01 0.05 0.17 0.52 0.25 0
## A6 0.01 0.02 0.05 0.25 0.49 0.18 0
## A10 0.01 0.17 0.43 0.21 0.15 0.03 0psych::alpha(Conscientiousness,check.keys = TRUE)## Warning in psych::alpha(Conscientiousness, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = Conscientiousness, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.75 0.75 0.73 0.33 2.9 0.02 2.2 0.79 0.33
##
## lower alpha upper 95% confidence boundaries
## 0.71 0.75 0.79
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## C1- 0.74 0.74 0.71 0.36 2.8 0.021 0.0112 0.36
## C3- 0.73 0.73 0.70 0.35 2.7 0.022 0.0073 0.33
## C4- 0.72 0.72 0.69 0.34 2.5 0.022 0.0134 0.31
## C6 0.71 0.71 0.68 0.33 2.5 0.023 0.0079 0.32
## C8 0.68 0.68 0.64 0.29 2.1 0.026 0.0080 0.30
## C9 0.69 0.69 0.65 0.30 2.2 0.025 0.0078 0.31
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## C1- 382 0.59 0.59 0.45 0.39 2.2 1.2
## C3- 382 0.58 0.61 0.49 0.41 1.6 1.0
## C4- 382 0.64 0.65 0.53 0.46 1.6 1.1
## C6 382 0.68 0.65 0.56 0.48 2.9 1.3
## C8 382 0.76 0.75 0.70 0.60 2.4 1.2
## C9 382 0.73 0.73 0.67 0.58 2.3 1.2
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## C1 0.01 0.12 0.30 0.26 0.23 0.09 0
## C3 0.01 0.03 0.13 0.26 0.47 0.10 0
## C4 0.02 0.05 0.18 0.20 0.44 0.12 0
## C6 0.01 0.14 0.30 0.21 0.21 0.13 0
## C8 0.00 0.31 0.30 0.20 0.12 0.08 0
## C9 0.01 0.27 0.37 0.15 0.15 0.05 0psych::alpha(Neuroticism,check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = Neuroticism, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.8 0.8 0.78 0.4 4 0.016 3.5 0.8 0.39
##
## lower alpha upper 95% confidence boundaries
## 0.77 0.8 0.83
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## N1 0.76 0.76 0.73 0.39 3.2 0.019 0.0057 0.38
## N2 0.77 0.77 0.74 0.40 3.4 0.018 0.0078 0.38
## N4 0.75 0.75 0.71 0.38 3.1 0.020 0.0021 0.39
## N5 0.79 0.79 0.76 0.43 3.7 0.017 0.0049 0.41
## N6 0.76 0.76 0.72 0.38 3.1 0.020 0.0045 0.37
## N7 0.78 0.78 0.75 0.42 3.6 0.018 0.0053 0.40
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## N1 382 0.74 0.74 0.67 0.59 2.8 1.22
## N2 382 0.70 0.70 0.60 0.54 3.6 1.17
## N4 382 0.76 0.76 0.71 0.62 3.3 1.16
## N5 382 0.66 0.65 0.53 0.48 3.7 1.21
## N6 382 0.74 0.74 0.68 0.61 3.7 1.10
## N7 382 0.63 0.66 0.55 0.49 4.1 0.95
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## N1 0.01 0.12 0.33 0.23 0.21 0.10 0
## N2 0.02 0.02 0.17 0.20 0.36 0.23 0
## N4 0.01 0.05 0.17 0.28 0.34 0.15 0
## N5 0.01 0.04 0.15 0.12 0.39 0.29 0
## N6 0.01 0.03 0.10 0.19 0.42 0.24 0
## N7 0.01 0.01 0.06 0.12 0.43 0.38 0psych::alpha(Openness,check.keys = TRUE) #for illustrative proposes## Warning in psych::alpha(Openness, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: psych::alpha(x = Openness, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.73 0.73 0.72 0.31 2.7 0.02 2.6 0.79 0.29
##
## lower alpha upper 95% confidence boundaries
## 0.69 0.73 0.77
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## O3- 0.73 0.72 0.70 0.34 2.6 0.021 0.022 0.34
## O4- 0.74 0.73 0.71 0.35 2.7 0.020 0.025 0.37
## O7 0.68 0.67 0.66 0.29 2.0 0.025 0.028 0.23
## O8 0.64 0.64 0.62 0.26 1.8 0.029 0.014 0.25
## O9 0.66 0.66 0.64 0.28 1.9 0.027 0.018 0.26
## O10 0.71 0.71 0.69 0.32 2.4 0.023 0.018 0.29
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## O3- 382 0.52 0.56 0.42 0.34 1.4 1.0
## O4- 382 0.52 0.54 0.38 0.32 1.5 1.1
## O7 382 0.70 0.70 0.61 0.52 2.9 1.2
## O8 382 0.79 0.77 0.74 0.64 3.1 1.4
## O9 382 0.75 0.73 0.68 0.58 3.1 1.3
## O10 382 0.61 0.61 0.49 0.42 3.5 1.2
##
## Non missing response frequency for each item
## 0 1 2 3 4 5 miss
## O3 0.01 0.03 0.10 0.20 0.52 0.13 0
## O4 0.01 0.04 0.15 0.26 0.37 0.18 0
## O7 0.01 0.12 0.33 0.18 0.29 0.07 0
## O8 0.01 0.13 0.21 0.16 0.31 0.17 0
## O9 0.01 0.12 0.25 0.15 0.34 0.13 0
## O10 0.01 0.05 0.16 0.14 0.47 0.17 0