Initial Extraction of the Components
Jogglew01NeupsyPCA<-principal(Jogglew01Neupsy,nfactors=20,rotate="none")
principal(r=Jogglew01Neupsy,nfactors=20,rotate="none")
Eigen Values
ev <- eigen(cor(Jogglew01Neupsy))
ev$values
## [1] 5.724e+00 2.812e+00 1.826e+00 1.577e+00 1.101e+00 9.140e-01
## [7] 7.005e-01 6.977e-01 6.360e-01 6.075e-01 5.429e-01 5.030e-01
## [13] 4.766e-01 4.181e-01 3.897e-01 3.328e-01 2.823e-01 2.703e-01
## [19] 1.885e-01 -4.196e-16
Scree Plot
ap <- parallel(subject=nrow(Jogglew01Neupsy),var=ncol(Jogglew01Neupsy), rep=100,cent=.05)
nS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)
plotnScree(nS)
Rotation to Final Solution - 5 Factors
Jogglew01NeupsyPCA.r<-principal(Jogglew01Neupsy,nfactors=5,rotate="promax",scores=T)
principal(r=Jogglew01Neupsy,nfactors=5,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew01Neupsy, nfactors = 5, rotate = "promax",
## scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC5 PC4 h2 u2
## BARTaccuracy1 0.70 0.06 0.19 0.16 -0.14 0.51 0.493
## DSSTefficiency1 0.78 -0.03 -0.06 -0.03 0.33 0.81 0.192
## LOTefficiency1 0.31 -0.01 -0.08 0.03 0.68 0.59 0.408
## PVTefficiency1 0.04 0.78 -0.17 0.09 0.30 0.60 0.396
## AMefficiency1 0.21 -0.58 0.38 -0.08 0.27 0.58 0.423
## NBACKaccuracy1 0.84 0.01 -0.07 -0.06 -0.13 0.70 0.302
## VOLTefficiency1 -0.19 0.18 -0.26 0.00 0.83 0.63 0.374
## MPTspeed1 0.38 0.21 0.14 0.00 0.36 0.46 0.539
## BVRtot1 -0.70 -0.32 -0.14 -0.04 0.05 0.68 0.322
## CrdRot1 0.05 -0.15 0.85 -0.15 -0.12 0.74 0.259
## IdentPicScore 0.79 0.13 0.16 -0.03 0.00 0.76 0.239
## CVLtca1 0.26 0.55 0.24 -0.06 -0.15 0.58 0.421
## DigitSpanFwd1 -0.64 0.42 0.26 -0.14 0.10 0.65 0.352
## DigitSpanBck1 0.44 0.71 -0.19 -0.09 -0.09 0.68 0.324
## FluencyWord1 0.79 -0.08 -0.18 -0.08 0.10 0.68 0.319
## TrailsAtestSec1 0.03 0.00 -0.24 -0.05 -0.43 0.27 0.725
## TrailsBtestSec1 -0.04 -0.01 -0.03 0.95 -0.03 0.97 0.026
## TrailsBminusA1 -0.04 -0.01 0.01 0.99 0.05 0.98 0.024
## Attention1 -0.23 0.57 0.33 -0.01 0.09 0.59 0.413
## ClockTotal1 -0.04 0.01 0.84 0.16 -0.15 0.59 0.409
##
## PC1 PC2 PC3 PC5 PC4
## SS loadings 4.68 2.47 2.04 2.05 1.81
## Proportion Var 0.23 0.12 0.10 0.10 0.09
## Cumulative Var 0.23 0.36 0.46 0.56 0.65
## Proportion Explained 0.36 0.19 0.16 0.16 0.14
## Cumulative Proportion 0.36 0.55 0.70 0.86 1.00
##
## With component correlations of
## PC1 PC2 PC3 PC5 PC4
## PC1 1.00 0.06 0.19 -0.31 0.19
## PC2 0.06 1.00 0.34 -0.17 0.01
## PC3 0.19 0.34 1.00 -0.42 0.27
## PC5 -0.31 -0.17 -0.42 1.00 -0.22
## PC4 0.19 0.01 0.27 -0.22 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 30.05
## The degrees of freedom for the model are 100 and the objective function was 20.02
## The total number of observations was 1972 with MLE Chi Square = 39239 with prob < 0
##
## Fit based upon off diagonal values = 0.97
Rotation to Final Solution - 6 Factors
Jogglew01NeupsyPCA.r<-principal(Jogglew01Neupsy,nfactors=6,rotate="promax",scores=T)
principal(r=Jogglew01Neupsy,nfactors=6,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew01Neupsy, nfactors = 6, rotate = "promax",
## scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC5 PC3 PC4 PC6 h2 u2
## BARTaccuracy1 0.70 0.07 0.15 0.22 -0.10 0.10 0.51 0.487
## DSSTefficiency1 0.78 -0.03 -0.03 -0.05 0.30 -0.06 0.81 0.192
## LOTefficiency1 0.28 -0.01 0.02 0.03 0.71 0.06 0.65 0.350
## PVTefficiency1 0.02 0.79 0.08 -0.09 0.36 0.13 0.63 0.367
## AMefficiency1 0.20 -0.58 -0.08 0.37 0.23 -0.11 0.58 0.422
## NBACKaccuracy1 0.85 0.00 -0.06 -0.09 -0.14 0.01 0.70 0.299
## VOLTefficiency1 -0.21 0.18 -0.01 -0.17 0.82 -0.03 0.66 0.345
## MPTspeed1 0.37 0.21 0.00 0.16 0.34 -0.05 0.47 0.534
## BVRtot1 -0.71 -0.33 -0.04 -0.12 0.05 0.01 0.68 0.322
## CrdRot1 0.04 -0.13 -0.15 0.81 -0.11 -0.05 0.74 0.255
## IdentPicScore 0.81 0.12 -0.03 0.09 -0.06 -0.14 0.78 0.224
## CVLtca1 0.27 0.56 -0.06 0.20 -0.16 -0.03 0.58 0.419
## DigitSpanFwd1 -0.63 0.43 -0.14 0.22 0.07 -0.10 0.65 0.351
## DigitSpanBck1 0.46 0.70 -0.09 -0.23 -0.11 -0.02 0.69 0.313
## FluencyWord1 0.79 -0.09 -0.08 -0.16 0.10 0.04 0.68 0.318
## TrailsAtestSec1 -0.09 0.04 -0.09 0.14 0.01 1.02 0.93 0.068
## TrailsBtestSec1 -0.05 -0.01 0.96 0.02 0.00 0.05 0.98 0.023
## TrailsBminusA1 -0.03 -0.02 1.01 -0.01 0.00 -0.15 0.99 0.014
## Attention1 -0.22 0.58 -0.01 0.28 0.06 -0.12 0.59 0.411
## ClockTotal1 -0.07 0.04 0.14 0.91 -0.04 0.18 0.67 0.333
##
## PC1 PC2 PC5 PC3 PC4 PC6
## SS loadings 4.70 2.49 2.08 1.91 1.66 1.12
## Proportion Var 0.23 0.12 0.10 0.10 0.08 0.06
## Cumulative Var 0.23 0.36 0.46 0.56 0.64 0.70
## Proportion Explained 0.34 0.18 0.15 0.14 0.12 0.08
## Cumulative Proportion 0.34 0.51 0.66 0.80 0.92 1.00
##
## With component correlations of
## PC1 PC2 PC5 PC3 PC4 PC6
## PC1 1.00 0.06 -0.31 0.21 0.21 -0.07
## PC2 0.06 1.00 -0.18 0.32 -0.05 -0.17
## PC5 -0.31 -0.18 1.00 -0.43 -0.17 0.29
## PC3 0.21 0.32 -0.43 1.00 0.15 -0.35
## PC4 0.21 -0.05 -0.17 0.15 1.00 -0.24
## PC6 -0.07 -0.17 0.29 -0.35 -0.24 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 30.05
## The degrees of freedom for the model are 85 and the objective function was 19.37
## The total number of observations was 1972 with MLE Chi Square = 37960 with prob < 0
##
## Fit based upon off diagonal values = 0.97
Rotation to Final Solution - 7 Factors
Jogglew01NeupsyPCA.r<-principal(Jogglew01Neupsy,nfactors=7,rotate="promax",scores=T)
principal(r=Jogglew01Neupsy,nfactors=7,rotate="promax",scores=T)
## Principal Components Analysis
## Call: principal(r = Jogglew01Neupsy, nfactors = 7, rotate = "promax",
## scores = T)
##
## Warning: A Heywood case was detected.
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC3 PC2 PC5 PC4 PC7 PC6 h2 u2
## BARTaccuracy1 0.70 0.02 0.19 0.16 -0.03 -0.06 0.11 0.52 0.482
## DSSTefficiency1 0.77 -0.03 -0.06 -0.03 0.23 0.25 -0.06 0.81 0.192
## LOTefficiency1 0.29 0.14 0.22 0.00 0.23 0.86 -0.01 0.82 0.181
## PVTefficiency1 0.04 0.77 -0.06 0.08 0.31 0.21 0.12 0.64 0.365
## AMefficiency1 0.18 -0.61 0.32 -0.08 0.24 0.14 -0.09 0.59 0.410
## NBACKaccuracy1 0.86 0.01 -0.08 -0.06 -0.15 0.00 0.01 0.70 0.298
## VOLTefficiency1 -0.24 0.12 -0.26 -0.01 0.85 0.31 0.01 0.70 0.299
## MPTspeed1 0.35 0.04 -0.04 0.01 0.64 -0.14 0.03 0.66 0.343
## BVRtot1 -0.73 -0.31 -0.15 -0.04 0.07 -0.05 0.02 0.68 0.319
## CrdRot1 0.05 -0.19 0.82 -0.15 -0.07 -0.03 -0.04 0.74 0.255
## IdentPicScore 0.82 0.07 0.06 -0.02 0.01 -0.05 -0.13 0.78 0.220
## CVLtca1 0.28 0.40 0.07 -0.05 0.17 -0.39 0.03 0.67 0.327
## DigitSpanFwd1 -0.61 0.43 0.29 -0.14 0.01 0.08 -0.13 0.67 0.332
## DigitSpanBck1 0.50 0.75 -0.12 -0.09 -0.23 0.09 -0.07 0.74 0.258
## FluencyWord1 0.80 -0.02 -0.09 -0.09 -0.09 0.28 0.01 0.71 0.288
## TrailsAtestSec1 -0.11 0.03 0.11 -0.09 0.03 -0.02 1.02 0.95 0.055
## TrailsBtestSec1 -0.05 -0.01 0.03 0.97 0.00 0.00 0.05 0.98 0.023
## TrailsBminusA1 -0.03 -0.01 0.01 1.01 0.00 0.00 -0.15 0.99 0.014
## Attention1 -0.19 0.52 0.28 -0.01 0.13 -0.04 -0.12 0.59 0.411
## ClockTotal1 -0.04 0.07 1.05 0.13 -0.22 0.24 0.13 0.73 0.273
##
## PC1 PC3 PC2 PC5 PC4 PC7 PC6
## SS loadings 4.75 2.29 1.93 2.09 1.41 1.08 1.10
## Proportion Var 0.24 0.11 0.10 0.10 0.07 0.05 0.06
## Cumulative Var 0.24 0.35 0.45 0.55 0.62 0.68 0.73
## Proportion Explained 0.32 0.16 0.13 0.14 0.10 0.07 0.08
## Cumulative Proportion 0.32 0.48 0.61 0.75 0.85 0.92 1.00
##
## With component correlations of
## PC1 PC3 PC2 PC5 PC4 PC7 PC6
## PC1 1.00 0.05 0.22 -0.33 0.28 -0.05 -0.06
## PC3 0.05 1.00 0.32 -0.14 0.17 -0.33 -0.14
## PC2 0.22 0.32 1.00 -0.43 0.43 -0.38 -0.32
## PC5 -0.33 -0.14 -0.43 1.00 -0.30 0.11 0.28
## PC4 0.28 0.17 0.43 -0.30 1.00 -0.06 -0.32
## PC7 -0.05 -0.33 -0.38 0.11 -0.06 1.00 0.05
## PC6 -0.06 -0.14 -0.32 0.28 -0.32 0.05 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 30.05
## The degrees of freedom for the model are 71 and the objective function was 19.66
## The total number of observations was 1972 with MLE Chi Square = 38508 with prob < 0
##
## Fit based upon off diagonal values = 0.97