R Programming Assignment on Factor Analysis

In this R programming assignment, we performed factor analysis on a given dataset and interpreted the results to identify underlying factors. 

Please note that the code provided here assumes you have the dataset in the correct format and that you have appropriately preprocessed the data (e.g., handling missing values, scaling variables) before performing factor analysis. This solution is plagiarism-free and should serve as a helpful guide for R Programming assignment.


Personality <- read.csv("Personality.txt", sep="")
head(Personality)
summary(Personality)
library(corrplot)
corrplot(cor(Personality), order = "hclust", tl.col='black', tl.cex=.75)

d_stan = as.data.frame(scale(Personality))
### Factor analysis with no rotation
res1b = factanal(d_stan, factors = 10, rotation = "none", na.action = na.omit)
res1b$loadings

# Compute eigenvalues from factor loadings

# Compute eigenvalue of factor 1
loadings_fac1 = res1b$loadings[,1]
eigenv_fac1 = sum(loadings_fac1^2); eigenv_fac1
# Compute proportion variance
eigenv_fac1/32

# Uniqueness & Communality
res1b$uniquenesses
# Calculate uniqueness
loadings_distant = res1b$loadings[1,]
communality_distant = sum(loadings_distant^2); communality_distant
uniqueness_distant = 1-communality_distant; uniqueness_distant

### Plot loadings against one another
load = res1b$loadings[,1:2]
plot(load, type="n") # set up plot 
text(load,labels=names(d_stan),cex=.7) # add variable names

# Rotation of Factors

### Factor analysis with rotation
res1a = factanal(d_stan, factors = 10, rotation = "varimax", na.action = na.omit)
res1a$loadings
### Plot loadings against one another
load = res1a$loadings[,1:2]
plot(load, type="n") # set up plot 
text(load,labels=names(d_stan),cex=.7) # add variable names

# Creating composite variables

k = 2
p = 5
yes = 'yes! lets extract k factors!'
no = 'no! we need more data or fewer factors!'
ifelse(((p-k)^2 > p+k), yes, no)

#Let’s try combining some synonyms and then look at the extracted Factors!
  shy = rowMeans(cbind(d_stan$distant, d_stan$shy, d_stan$withdrw, d_stan$quiet))
outgoing = rowMeans(cbind(d_stan$talkatv, d_stan$outgoin, d_stan$sociabl))
hardworking = rowMeans(cbind(d_stan$hardwrk, d_stan$persevr, d_stan$discipl))

friendly = rowMeans(cbind(d_stan$friendl, d_stan$kind, d_stan$coopera, d_stan$agreebl, d_stan$approvn, 
                          d_stan$sociabl))
anxious = rowMeans(cbind(d_stan$tense, d_stan$anxious, d_stan$worryin))
#etc, you guys choose what you want to combine
combined_data = cbind(shy,outgoing,hardworking,friendly,anxious)
combined_data = as.data.frame(combined_data)
res2 = factanal(combined_data, factors = 2, na.action=na.omit)
res2$loadings

### Plot loadings against one another
load = res2$loadings[,1:2]
plot(load, type="n") # set up plot 
text(load,labels=names(combined_data),cex=.7) # add variable names

Please note that the code provided here is for illustrative purposes and assumes you have the necessary dataset and target variable for training and evaluation. This solution is plagiarism-free and should serve as a helpful guide for your homework.