Initial Extraction of the Components
Jogglew03NeupsyPCA<-principal(Jogglew03Neupsy,nfactors=20,rotate="none")
principal(r=Jogglew03Neupsy,nfactors=20,rotate="none")
Eigen Values
ev <- eigen(cor(Jogglew03Neupsy))
ev$values
## [1] 7.723e+00 2.560e+00 1.690e+00 1.265e+00 1.119e+00 8.035e-01 7.101e-01
## [8] 6.672e-01 5.524e-01 4.466e-01 4.352e-01 3.834e-01 3.221e-01 2.962e-01
## [15] 2.725e-01 2.474e-01 1.911e-01 1.632e-01 1.532e-01 5.540e-17
Scree Plot
ap <- parallel(subject=nrow(Jogglew03Neupsy),var=ncol(Jogglew03Neupsy), rep=100,cent=.05)
nS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)
plotnScree(nS)
Rotation to Final Solution - 5 Factors
Jogglew03NeupsyPCA.r<-principal(Jogglew03Neupsy,nfactors=5,rotate="promax",scores=T)
principal(r=Jogglew03Neupsy,nfactors=5,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew03Neupsy, nfactors = 5, rotate = "promax",
## scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC4 PC2 PC3 PC5 h2 u2
## BARTaccuracy3 0.05 -0.14 -0.20 0.73 0.27 0.51 0.49
## DSSTefficiency3 0.94 -0.27 0.05 -0.18 0.11 0.75 0.25
## LOTefficiency3 0.83 0.03 0.13 0.06 -0.01 0.76 0.24
## PVTefficiency3 0.15 0.80 0.13 -0.16 0.19 0.74 0.26
## AMefficiency3 0.45 -0.94 0.41 0.14 0.09 0.79 0.21
## NBACKaccuracy3 -0.04 -0.12 0.29 0.74 0.11 0.56 0.44
## VOLTefficiency3 0.76 0.18 0.02 -0.44 0.02 0.69 0.31
## MPTspeed3 0.78 -0.05 -0.02 -0.22 0.21 0.60 0.40
## BVRtot3 -0.86 -0.06 -0.04 -0.02 0.07 0.81 0.19
## StroopInterference -0.37 -0.09 0.71 -0.03 -0.15 0.70 0.30
## StroopWords3 0.73 0.09 -0.50 0.01 0.11 0.84 0.16
## CVLtca3 0.85 -0.09 -0.22 0.09 -0.14 0.82 0.18
## DigitSpanFwd3 -0.12 0.08 0.05 0.29 1.01 0.84 0.16
## DigitSpanBck3 0.47 0.40 -0.04 0.39 0.21 0.73 0.27
## FluencyWord3 -0.07 -0.07 0.83 0.09 0.18 0.64 0.36
## TrailsAtestSec3 -0.55 0.20 0.14 -0.06 0.21 0.37 0.63
## TrailsBtestSec3 -0.81 0.06 0.17 -0.22 0.18 0.87 0.13
## TrailsBminusA3 -0.76 0.02 0.16 -0.23 0.14 0.79 0.21
## Attention3 0.46 0.43 0.27 0.06 -0.07 0.74 0.26
## ClockTotal3 0.26 0.28 0.39 0.23 -0.32 0.81 0.19
##
## PC1 PC4 PC2 PC3 PC5
## SS loadings 7.22 2.03 2.10 1.65 1.36
## Proportion Var 0.36 0.10 0.10 0.08 0.07
## Cumulative Var 0.36 0.46 0.57 0.65 0.72
## Proportion Explained 0.50 0.14 0.15 0.12 0.09
## Cumulative Proportion 0.50 0.64 0.79 0.91 1.00
##
## With component correlations of
## PC1 PC4 PC2 PC3 PC5
## PC1 1.00 0.33 -0.01 0.27 -0.10
## PC4 0.33 1.00 0.27 0.20 -0.25
## PC2 -0.01 0.27 1.00 0.08 -0.22
## PC3 0.27 0.20 0.08 1.00 -0.40
## PC5 -0.10 -0.25 -0.22 -0.40 1.00
##
## Test of the hypothesis that 5 components are sufficient.
##
## The degrees of freedom for the null model are 190 and the objective function was 33.72
## The degrees of freedom for the model are 100 and the objective function was 22.02
## The total number of observations was 1752 with MLE Chi Square = 38319 with prob < 0
##
## Fit based upon off diagonal values = 0.98
Rotation to Final Solution - 6 Factors
Jogglew03NeupsyPCA.r<-principal(Jogglew03Neupsy,nfactors=6,rotate="promax",scores=T)
principal(r=Jogglew03Neupsy,nfactors=6,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew03Neupsy, nfactors = 6, rotate = "promax",
## scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC3 PC1 PC2 PC4 PC6 PC5 h2 u2
## BARTaccuracy3 -0.22 0.05 -0.22 -0.06 0.94 0.00 0.75 0.246
## DSSTefficiency3 0.16 0.82 0.04 -0.26 -0.05 0.05 0.76 0.242
## LOTefficiency3 0.37 0.56 0.13 0.01 0.08 -0.04 0.76 0.239
## PVTefficiency3 -0.10 0.30 0.14 0.77 -0.03 0.10 0.76 0.237
## AMefficiency3 0.05 0.39 0.42 -0.92 0.06 0.09 0.79 0.213
## NBACKaccuracy3 0.33 -0.31 0.31 -0.14 0.48 0.09 0.56 0.439
## VOLTefficiency3 -0.03 0.81 0.01 0.18 -0.19 -0.05 0.70 0.295
## MPTspeed3 -0.16 0.88 -0.04 -0.01 0.10 0.05 0.67 0.325
## BVRtot3 -0.48 -0.52 -0.04 -0.03 0.00 0.06 0.81 0.187
## StroopInterference -0.21 -0.16 0.76 -0.11 -0.14 -0.11 0.70 0.301
## StroopWords3 0.46 0.38 -0.53 0.08 0.03 0.11 0.84 0.159
## CVLtca3 0.63 0.37 -0.23 -0.11 0.01 -0.09 0.83 0.171
## DigitSpanFwd3 0.05 -0.02 0.04 0.01 0.02 0.98 0.92 0.078
## DigitSpanBck3 0.80 -0.03 -0.03 0.31 0.04 0.30 0.80 0.200
## FluencyWord3 -0.12 0.11 0.87 -0.12 -0.05 0.16 0.64 0.357
## TrailsAtestSec3 -0.99 0.10 0.13 0.29 0.39 -0.07 0.64 0.364
## TrailsBtestSec3 -0.69 -0.27 0.18 0.08 -0.10 0.12 0.87 0.128
## TrailsBminusA3 -0.53 -0.32 0.17 0.02 -0.20 0.15 0.80 0.204
## Attention3 0.44 0.21 0.29 0.37 -0.08 -0.02 0.74 0.261
## ClockTotal3 0.48 -0.06 0.42 0.22 0.03 -0.25 0.81 0.194
##
## PC3 PC1 PC2 PC4 PC6 PC5
## SS loadings 4.44 4.14 2.21 1.87 1.27 1.23
## Proportion Var 0.22 0.21 0.11 0.09 0.06 0.06
## Cumulative Var 0.22 0.43 0.54 0.63 0.70 0.76
## Proportion Explained 0.29 0.27 0.15 0.12 0.08 0.08
## Cumulative Proportion 0.29 0.57 0.71 0.83 0.92 1.00
##
## With component correlations of
## PC3 PC1 PC2 PC4 PC6 PC5
## PC3 1.00 0.55 0.14 0.28 0.47 -0.27
## PC1 0.55 1.00 -0.12 0.21 0.19 -0.05
## PC2 0.14 -0.12 1.00 0.30 0.15 -0.21
## PC4 0.28 0.21 0.30 1.00 0.07 -0.16
## PC6 0.47 0.19 0.15 0.07 1.00 -0.10
## PC5 -0.27 -0.05 -0.21 -0.16 -0.10 1.00
##
## Test of the hypothesis that 6 components are sufficient.
##
## The degrees of freedom for the null model are 190 and the objective function was 33.72
## The degrees of freedom for the model are 85 and the objective function was 22.28
## The total number of observations was 1752 with MLE Chi Square = 38753 with prob < 0
##
## Fit based upon off diagonal values = 0.98
Rotation to Final Solution - 7 Factors
Jogglew03NeupsyPCA.r<-principal(Jogglew03Neupsy,nfactors=7,rotate="promax",scores=T)
principal(r=Jogglew03Neupsy,nfactors=7,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew03Neupsy, nfactors = 7, rotate = "promax",
## scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC4 PC2 PC3 PC7 PC5 PC6 h2 u2
## BARTaccuracy3 0.05 0.10 -0.12 0.05 -0.06 -0.01 0.96 0.96 0.040
## DSSTefficiency3 0.95 -0.11 0.02 -0.25 -0.03 0.05 -0.01 0.76 0.241
## LOTefficiency3 0.71 0.22 0.10 0.02 -0.05 -0.04 0.08 0.76 0.236
## PVTefficiency3 0.30 -0.04 0.14 0.80 0.13 0.10 0.06 0.77 0.226
## AMefficiency3 0.45 0.06 0.39 -0.93 -0.07 0.09 0.00 0.79 0.211
## NBACKaccuracy3 -0.24 0.92 0.21 -0.20 0.23 0.10 0.13 0.62 0.384
## VOLTefficiency3 0.89 -0.30 0.02 0.20 0.05 -0.05 -0.08 0.71 0.293
## MPTspeed3 0.96 -0.23 -0.03 0.01 0.14 0.05 0.13 0.68 0.322
## BVRtot3 -0.68 -0.23 -0.01 -0.04 0.09 0.07 0.00 0.81 0.186
## StroopInterference -0.24 -0.04 0.76 -0.08 -0.08 -0.12 -0.03 0.72 0.285
## StroopWords3 0.52 0.14 -0.56 0.05 -0.03 0.12 -0.03 0.85 0.150
## CVLtca3 0.55 0.31 -0.27 -0.13 -0.11 -0.08 -0.05 0.83 0.166
## DigitSpanFwd3 -0.07 0.09 0.01 0.01 -0.05 0.99 -0.01 0.92 0.077
## DigitSpanBck3 0.10 0.65 -0.10 0.29 -0.14 0.31 -0.05 0.81 0.195
## FluencyWord3 0.08 0.21 0.81 -0.12 0.10 0.16 -0.09 0.64 0.356
## TrailsAtestSec3 0.00 0.18 0.02 0.15 1.08 -0.05 -0.05 0.93 0.074
## TrailsBtestSec3 -0.46 -0.50 0.24 0.12 0.05 0.12 0.03 0.89 0.110
## TrailsBminusA3 -0.51 -0.60 0.26 0.09 -0.20 0.14 0.05 0.87 0.129
## Attention3 0.31 0.30 0.26 0.39 -0.11 -0.02 -0.03 0.74 0.256
## ClockTotal3 0.04 0.51 0.38 0.23 -0.09 -0.25 0.01 0.81 0.193
##
## PC1 PC4 PC2 PC3 PC7 PC5 PC6
## SS loadings 5.50 2.79 2.27 1.88 1.22 1.24 0.98
## Proportion Var 0.27 0.14 0.11 0.09 0.06 0.06 0.05
## Cumulative Var 0.27 0.41 0.53 0.62 0.68 0.74 0.79
## Proportion Explained 0.35 0.18 0.14 0.12 0.08 0.08 0.06
## Cumulative Proportion 0.35 0.52 0.67 0.78 0.86 0.94 1.00
##
## With component correlations of
## PC1 PC4 PC2 PC3 PC7 PC5 PC6
## PC1 1.00 0.51 -0.22 0.29 -0.54 -0.08 -0.05
## PC4 0.51 1.00 -0.04 0.27 -0.55 -0.29 0.06
## PC2 -0.22 -0.04 1.00 0.18 0.16 -0.10 -0.05
## PC3 0.29 0.27 0.18 1.00 -0.24 -0.15 -0.23
## PC7 -0.54 -0.55 0.16 -0.24 1.00 0.22 0.07
## PC5 -0.08 -0.29 -0.10 -0.15 0.22 1.00 0.09
## PC6 -0.05 0.06 -0.05 -0.23 0.07 0.09 1.00
##
## Test of the hypothesis that 7 components are sufficient.
##
## The degrees of freedom for the null model are 190 and the objective function was 33.72
## The degrees of freedom for the model are 71 and the objective function was 21.92
## The total number of observations was 1752 with MLE Chi Square = 38116 with prob < 0
##
## Fit based upon off diagonal values = 0.99