##Commands for Joggle Data and w03Neupsy Data PCA Analyses on 1/24/14
##Packages Used: “psych”, “GPArotation”, “nFactors”
##load(file='/Users/meganwilliams/Desktop/Joggle/Joggle Data/Joggle.rdata')
load(file='/Users/meganwilliams/Desktop/HANDLS/Joggle/Joggle PCA/JoggleData.rdata')
#install.packages("psych")
library("psych")
#install.packages("GPArotation")
library("GPArotation")
#install.packages("nFactors")
library("nFactors")
#JoggleDataVARS = c("BARTaccuracy","DSSTefficiency","LOTefficiency","PVTefficiency","AMefficiency","NBACKaccuracy","VOLTefficiency","MPTspeed")
#JoggleData=Joggle[JoggleDataVARS]
#save(JoggleData,file='/Users/meganwilliams/Desktop/HANDLS/Joggle/Joggle PCA/JoggleData.rdata')
Initial Extraction of the Components
JogglePCA<-principal(JoggleData,nfactors=8,rotate="none")
principal(r=JoggleData,nfactors=8,rotate="none")
## Principal Components Analysis
## Call: principal(r = JoggleData, nfactors = 8, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 h2 u2
## BARTaccuracy 0.30 0.20 0.92 -0.11 0.08 -0.02 -0.04 -0.04 1 0.0e+00
## DSSTefficiency 0.82 -0.08 -0.12 -0.02 -0.07 0.24 -0.15 -0.48 1 1.9e-15
## LOTefficiency 0.80 -0.07 -0.06 -0.04 -0.01 0.29 -0.36 0.38 1 8.9e-16
## PVTefficiency 0.19 0.85 -0.10 0.13 -0.02 0.33 0.32 0.04 1 0.0e+00
## AMefficiency 0.58 -0.54 0.05 -0.29 -0.09 0.09 0.51 0.09 1 5.6e-16
## NBACKaccuracy 0.48 -0.21 0.10 0.83 0.03 -0.13 0.11 0.04 1 8.9e-16
## VOLTefficiency 0.60 0.18 -0.20 -0.16 0.66 -0.31 0.04 0.00 1 6.7e-16
## MPTspeed 0.61 0.33 -0.09 -0.12 -0.52 -0.47 -0.02 0.04 1 0.0e+00
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## SS loadings 2.72 1.26 0.94 0.84 0.73 0.59 0.53 0.39
## Proportion Var 0.34 0.16 0.12 0.11 0.09 0.07 0.07 0.05
## Cumulative Var 0.34 0.50 0.62 0.72 0.81 0.89 0.95 1.00
## Proportion Explained 0.34 0.16 0.12 0.11 0.09 0.07 0.07 0.05
## Cumulative Proportion 0.34 0.50 0.62 0.72 0.81 0.89 0.95 1.00
##
## Test of the hypothesis that 8 components are sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 1.44
## The degrees of freedom for the model are -8 and the objective function was 0
## The total number of observations was 1793 with MLE Chi Square = 0 with prob < NA
##
## Fit based upon off diagonal values = 1
Eigen Values
ev <- eigen(cor(JoggleData))
ev$values
## [1] 2.7241 1.2642 0.9379 0.8403 0.7325 0.5872 0.5281 0.3856
Scree Plot
ap <- parallel(subject=nrow(JoggleData),var=ncol(JoggleData), rep=100,cent=.05)
nS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)
plotnScree(nS)
Rotation to Final Solution - 3 Factors
JogglePCA.r<-principal(JoggleData,nfactors=3,rotate="promax",scores=T)
principal(r=JoggleData,nfactors=3,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = JoggleData, nfactors = 3, rotate = "promax", scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 h2 u2
## BARTaccuracy -0.01 0.08 0.98 0.98 0.023
## DSSTefficiency 0.81 0.07 -0.05 0.69 0.310
## LOTefficiency 0.78 0.07 0.01 0.64 0.357
## PVTefficiency -0.20 0.91 0.06 0.77 0.228
## AMefficiency 0.77 -0.46 0.02 0.63 0.371
## NBACKaccuracy 0.52 -0.16 0.12 0.29 0.714
## VOLTefficiency 0.51 0.32 -0.10 0.44 0.563
## MPTspeed 0.42 0.45 0.03 0.49 0.507
##
## PC1 PC2 PC3
## SS loadings 2.57 1.35 1.00
## Proportion Var 0.32 0.17 0.13
## Cumulative Var 0.32 0.49 0.62
## Proportion Explained 0.52 0.27 0.20
## Cumulative Proportion 0.52 0.80 1.00
##
## With component correlations of
## PC1 PC2 PC3
## PC1 1.00 0.26 0.18
## PC2 0.26 1.00 0.05
## PC3 0.18 0.05 1.00
##
## Test of the hypothesis that 3 components are sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 1.44
## The degrees of freedom for the model are 7 and the objective function was 0.4
## The total number of observations was 1793 with MLE Chi Square = 717 with prob < 1.5e-150
##
## Fit based upon off diagonal values = 0.87
Rotation to Final Solution - 4 Factors
JogglePCA.r<-principal(JoggleData,nfactors=4,rotate="promax",scores=T)
principal(r=JoggleData,nfactors=4,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = JoggleData, nfactors = 4, rotate = "promax", scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 h2 u2
## BARTaccuracy -0.04 0.02 1.00 0.00 0.99 0.01
## DSSTefficiency 0.80 -0.07 -0.04 0.13 0.69 0.31
## LOTefficiency 0.77 -0.07 0.02 0.10 0.64 0.36
## PVTefficiency 0.18 0.86 0.04 0.00 0.79 0.21
## AMefficiency 0.60 -0.61 0.06 -0.09 0.71 0.29
## NBACKaccuracy 0.11 0.04 0.00 0.96 0.97 0.03
## VOLTefficiency 0.68 0.15 -0.08 -0.10 0.46 0.54
## MPTspeed 0.64 0.29 0.05 -0.08 0.51 0.49
##
## PC1 PC2 PC3 PC4
## SS loadings 2.53 1.23 1.01 0.99
## Proportion Var 0.32 0.15 0.13 0.12
## Cumulative Var 0.32 0.47 0.60 0.72
## Proportion Explained 0.44 0.21 0.18 0.17
## Cumulative Proportion 0.44 0.65 0.83 1.00
##
## With component correlations of
## PC1 PC2 PC3 PC4
## PC1 1.00 0.02 0.23 0.21
## PC2 0.02 1.00 0.03 -0.12
## PC3 0.23 0.03 1.00 0.08
## PC4 0.21 -0.12 0.08 1.00
##
## Test of the hypothesis that 4 components are sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 1.44
## The degrees of freedom for the model are 2 and the objective function was 0.55
## The total number of observations was 1793 with MLE Chi Square = 989.1 with prob < 1.6e-215
##
## Fit based upon off diagonal values = 0.89
Rotation to Final Solution - 5 Factors
JogglePCA.r<-principal(JoggleData,nfactors=5,rotate="promax",scores=T)
principal(r=JoggleData,nfactors=5,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = JoggleData, nfactors = 5, rotate = "promax", scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC5 PC2 PC4 PC3 h2 u2
## BARTaccuracy -0.03 -0.01 0.03 0.01 1.01 1.00 0.0035
## DSSTefficiency 0.64 0.19 -0.06 0.14 -0.05 0.70 0.3048
## LOTefficiency 0.56 0.25 -0.06 0.11 0.02 0.64 0.3550
## PVTefficiency 0.29 0.19 0.90 0.00 0.04 0.79 0.2123
## AMefficiency 0.45 0.03 -0.63 -0.10 0.05 0.72 0.2776
## NBACKaccuracy -0.02 -0.09 0.04 1.02 0.01 0.97 0.0295
## VOLTefficiency -0.14 1.07 0.17 -0.08 -0.01 0.90 0.0967
## MPTspeed 1.05 -0.30 0.31 -0.11 -0.01 0.78 0.2216
##
## PC1 PC5 PC2 PC4 PC3
## SS loadings 1.99 1.21 1.23 1.06 1.01
## Proportion Var 0.25 0.15 0.15 0.13 0.13
## Cumulative Var 0.25 0.40 0.55 0.69 0.81
## Proportion Explained 0.31 0.19 0.19 0.16 0.16
## Cumulative Proportion 0.31 0.49 0.68 0.84 1.00
##
## With component correlations of
## PC1 PC5 PC2 PC4 PC3
## PC1 1.00 0.58 -0.24 0.37 0.23
## PC5 0.58 1.00 -0.25 0.35 0.17
## PC2 -0.24 -0.25 1.00 -0.21 -0.04
## PC4 0.37 0.35 -0.21 1.00 0.12
## PC3 0.23 0.17 -0.04 0.12 1.00
##
## Test of the hypothesis that 5 components are sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 1.44
## The degrees of freedom for the model are -2 and the objective function was 1.09
## The total number of observations was 1793 with MLE Chi Square = 1940 with prob < NA
##
## Fit based upon off diagonal values = 0.9