1. Load + Organize Data

# Load data 
pmeans <- read.csv("/Users/linde/Downloads/LavBen_Germany.csv")

# Keep just the numeric columns subset so I can run fa.parallel
pmeans_num <- pmeans[, c("Mean1", "Mean2", "Mean5", "Mean12",
                         "Mean17", "Mean19", "Mean23", "Mean24")]

pmeans_num <- as.data.frame(sapply(pmeans_num, as.numeric)) 

2. Descriptions of Select Mean Positions

4. Scree Plot + Eigenvalues

parallel <- fa.parallel(pmeans_num, fm = 'minres', fa = 'fa')

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA

In conclusion:

5. Factor Analysis Model (3 factors)

threefactor <- fa(pmeans_num, nfactors=3, rotate="oblimin", fm="minres")
print(threefactor)
## Factor Analysis using method =  minres
## Call: fa(r = pmeans_num, nfactors = 3, rotate = "oblimin", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
##          MR1   MR2   MR3   h2      u2 com
## Mean1   0.29 -0.93  0.21 0.98  0.0178 1.3
## Mean2   1.00 -0.02 -0.03 0.95  0.0514 1.0
## Mean5  -0.04 -0.01  1.02 1.00  0.0043 1.0
## Mean12  0.16  0.89  0.16 0.91  0.0855 1.1
## Mean17  0.45  0.69  0.03 0.84  0.1581 1.7
## Mean19  0.99 -0.05  0.03 1.00 -0.0015 1.0
## Mean23  0.92 -0.07  0.10 0.97  0.0300 1.0
## Mean24  0.70  0.41  0.13 0.94  0.0577 1.7
## 
##                        MR1  MR2  MR3
## SS loadings           3.89 2.38 1.32
## Proportion Var        0.49 0.30 0.17
## Cumulative Var        0.49 0.78 0.95
## Proportion Explained  0.51 0.31 0.17
## Cumulative Proportion 0.51 0.83 1.00
## 
##  With factor correlations of 
##      MR1   MR2   MR3
## MR1 1.00  0.22  0.73
## MR2 0.22  1.00 -0.07
## MR3 0.73 -0.07  1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 3 factors are sufficient.
## 
## df null model =  28  with the objective function =  21.77 with Chi Square =  119.74
## df of  the model are 7  and the objective function was  6.84 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.05 
## 
## The harmonic n.obs is  10 with the empirical chi square  0.15  with prob <  1 
## The total n.obs was  10  with Likelihood Chi Square =  23.93  with prob <  0.0012 
## 
## Tucker Lewis Index of factoring reliability =  -0.405
## RMSEA index =  0.48  and the 90 % confidence intervals are  0.3 0.753
## BIC =  7.81
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    MR1  MR2  MR3
## Correlation of (regression) scores with factors   0.99 0.99 0.99
## Multiple R square of scores with factors          0.98 0.98 0.99
## Minimum correlation of possible factor scores     0.96 0.96 0.97

6. Factor Analysis Interpretations

7. Plotting

plot(threefactor$scores[,1], threefactor$scores[,2], pch=16, col="red", xlab="Factor 1", ylab="Factor 2", main="Factor Analysis of German Political Parties in 2002", xlim=c(-2.5, 2.5), ylim=c(-2.5, 2.5)) 
text(threefactor$scores[,1], threefactor$scores[,2], labels=c("CDU-CSU", "DKP", "DVU", "FDP", "GRÜ", "NPD", "PDS", "Rep", "SPD", "Schill"),, pos = 4)
mtext("Plot by Linden James using data from Laver and Benoit", side = 3, line = 0.5, cex = 0.8)

8. Interpretations + Comparisons