12 Workshop 15: Factor Analysis (and Reliability Analysis)

Aims:

• To practice using factor analysis to determine the number of factors in a data set.
• To conduct a reliability analysis using Cronbach’s Alpha.

12.1 Exercise 1: Import and Prepare Data

# Set the working directory -WD- so R knows where the data lives. Do this by going Session > Set working directory > Choose directory

# You can check the working directory...

getwd()

#Before doing anything, need to make sure the right packages are installed and open. We will use all of these......

library(tidyverse)
library(psych)

#Import the data
mydata <- read_csv("study_perception.csv")

12.2 Exercise Two

#### Understanding your data
str(mydata) #we can use this to check all of the variables in the file are numeric
#any categorical/factor variables would need to be removed.

### A quick summary of the data
summary(mydata)

# Let's create a correlation matrix just to get an understanding of our data file
# we also need to create the correlation matrix to use later
corr_matrix <- round(cor(mydata, use = "pairwise.complete.obs"), 3)
view(corr_matrix)

12.3 Exercise Three

#### Assess the need for factor analysis
### assumptions
# Kaiser-Meyer-Olkin (KMO) Test - Measures Sampling Adequacy
kmo_result <- KMO(corr_matrix)
print(kmo_result)  # KMO should be > 0.6 for FA to be appropriate

# Bartlett’s Test of Sphericity - Checks if correlation matrix is an identity matrix
bartlett_result <- cortest.bartlett(corr_matrix, n = nrow(mydata))
print(bartlett_result)  # p-value should be < 0.05 for FA to be suitable

12.4 Exercise Four

#### Determine the number of factors.
# Compute Eigenvalues
eigen_values <- eigen(corr_matrix)$values
print(eigen_values)  # Kaiser’s criterion: Keep factors with eigenvalues > 1

# Scree Plot
fa.parallel(mydata, fa = "fa", n.iter = 100, show.legend = TRUE)

12.5 Exercise Five

##### Interpretation of factors.
# Perform Factor Analysis with Varimax Rotation
fa_result <- fa(mydata, nfactors = 2, rotate = "varimax", fm = "ml")  # Adjust nfactors
# Print Factor Loadings (Rotated Component Matrix)
print(fa_result$loadings, cutoff = 0.3)  # Show only loadings > 0.3

# Visualizing Loadings
fa.diagram(fa_result)  # Shows factor structure in a diagram

12.6 Exercise Six

####  Reliability Analysis
# select items and put them onto a scale.
# Group items based on factor loadings
colnames(mydata)
scale_1 <- mydata %>% select(starts_with("s1_"))
scale_2  <- mydata %>% select(starts_with("s2_"))

# Compute Cronbach's Alpha
alpha(scale_1)  # For Factor 1
alpha(scale_2)  # For Factor 2

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Well Done. You have reached the end of the workshop

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