Chap8.R

library(psych)
#library(psychTools)
test<-read.table("test_score.csv", sep=",", header=T) 
lowerCor(test)

##    Y1    Y2    Y3    Y4    Y5    Y6   
## Y1  1.00                              
## Y2  0.65  1.00                        
## Y3  0.70  0.57  1.00                  
## Y4 -0.56 -0.50 -0.38  1.00            
## Y5 -0.46 -0.35 -0.27  0.81  1.00      
## Y6 -0.44 -0.46 -0.24  0.83  0.82  1.00

pairs.panels(test,pch='.')

cor.plot(test,numbers=TRUE,main="6 variables from Test Score")

uls <- fa(test,2,rotate="varimax")
print(uls,sort=TRUE)

## Factor Analysis using method =  minres
## Call: fa(r = test, nfactors = 2, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
##    item   MR1   MR2   h2   u2 com
## Y6    6  0.90 -0.20 0.86 0.14 1.1
## Y5    5  0.86 -0.20 0.78 0.22 1.1
## Y4    4  0.85 -0.36 0.85 0.15 1.3
## Y1    1 -0.32  0.82 0.77 0.23 1.3
## Y3    3 -0.11  0.81 0.66 0.34 1.0
## Y2    2 -0.31  0.67 0.54 0.46 1.4
## 
##                        MR1  MR2
## SS loadings           2.49 1.98
## Proportion Var        0.41 0.33
## Cumulative Var        0.41 0.75
## Proportion Explained  0.56 0.44
## Cumulative Proportion 0.56 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  15  and the objective function was  4.28 with Chi Square of  205.97
## The degrees of freedom for the model are 4  and the objective function was  0.08 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.04 
## 
## The harmonic number of observations is  52 with the empirical chi square  0.58  with prob <  0.96 
## The total number of observations was  52  with Likelihood Chi Square =  3.72  with prob <  0.45 
## 
## Tucker Lewis Index of factoring reliability =  1.006
## RMSEA index =  0  and the 90 % confidence intervals are  0 0.205
## BIC =  -12.09
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    MR1  MR2
## Correlation of (regression) scores with factors   0.96 0.91
## Multiple R square of scores with factors          0.91 0.83
## Minimum correlation of possible factor scores     0.82 0.66

fa.diagram(uls,digits = 2,main="Test Score Factors")

plot(uls)

#add factor scores
f <- factanal(test, factors=2, rotation="promax", scores="regression")
data <- cbind(test, f$scores)  #add two variables
#another solution
fs <- factor.scores(test,uls)     #obtain factor scores
fs <- fs$scores                   #get the columns of factor scores for each case
bfi <- cbind(test,fs)              #append factor scores to dataset  

#library(ggfortify)
#autoplot(f,label = TRUE, label.size = 3,
#        loadings = TRUE, loadings.label = TRUE, loadings.label.size  = 3)