Understanding Factors Through Factor Loadings

In real-world data, patterns often exist—but the underlying reasons behind those patterns are not always obvious. When analyzing survey or behavioral datasets, responses are typically shaped by hidden influences that cannot be observed directly.
For example, consider a demographic survey:
Married individuals without children may spend more than single individuals
Married individuals with children may spend more than married individuals without children
Here, the observable variable is expenses, but the invisible driving variables may include:
Economic condition
Education level
Salary
Location
Mapping responses directly to manually defined categories often introduces bias, guesswork, and loss of insight. This is where Factor Analysis provides a much more powerful and systematic approach.

What Is Factor Analysis?
Factor Analysis is a statistical technique that identifies latent (hidden) variables that explain patterns in observed data.
Instead of manually categorizing variables, factor analysis:
Automatically groups variables into meaningful hidden factors
Assigns weights (loadings) to variables based on their influence
Reduces noise and redundancy
Preserves as much information as possible
The technique uses:
Eigenvalues → How much variance each factor explains
Eigenvectors → The directions along which the data is transformed
Any factor with an eigenvalue > 1 is usually considered meaningful.

Creating Meaningful Factors
Factor analysis transforms your original variables into a new set of variables (factors) where:
Each factor is a weighted combination of original variables
Factors are ordered by importance
Later factors can often be discarded without losing much information
Typically, analysts retain enough factors to explain 90%–99% of total variance.

Understanding Factors Through Factor Loadings
The key to interpreting factor analysis lies in factor loadings.
Factor loadings:
Show the relationship between original variables and factors
Help us label what each factor represents
Airline Survey Example (Conceptual)
Let’s assume an airline customer satisfaction survey. Factor loadings might reveal:
Factor 1: Customer Experience
Factor 2: Booking & Loyalty Experience
Factor 3: Competitive Advantage
Negative loadings can also provide deep insights, such as customers remaining loyal despite worsening perks.
This interpretability makes factor analysis extremely valuable.

Exploratory vs Confirmatory Factor Analysis
Confirmatory Factor Analysis (CFA)
Used when:
You already have strong expectations of factor structure
You want to confirm existing business or psychological theories
Exploratory Factor Analysis (EFA)
Used when:
You don’t know the structure in advance
You want the data to guide you
To decide the number of factors, analysts use the scree plot, which shows eigenvalues vs factors and reveals an “elbow point”.

Hands-On: Factor Analysis in R Using the Psych Package
We’ll now perform factor analysis in R using the built-in bfi dataset from the psych package.
Step 1 – Install and Load Package
install.packages("psych")
library(psych)

Step 2 – Load Dataset
bfi_data = bfi

Step 3 – Remove Missing Values
bfi_data = bfi_data[complete.cases(bfi_data), ]

Step 4 – Create Correlation Matrix
bfi_cor <- cor(bfi_data)

Step 5 – Perform Factor Analysis
factors_data <- fa(r = bfi_cor, nfactors = 6)
factors_data

This generates:
Factor loadings
Variance explained
Factor correlations
Model adequacy metrics
From your results:
First dominant factor represented Neuroticism
Followed by Conscientiousness, Extraversion, Agreeableness, and Openness
This confirms that the dataset behaves as designed.

Key Guidelines When Using Factor Analysis
✅ Healthy Factor Loadings
Loadings > 0.5 → Strong relationship
0.3 to 0.5 → Moderate
Below 0.3 → Weak (consider dropping or reducing factors)
✅ Avoid Too Many Factors
If loadings are consistently low, reduce the number of factors.
✅ Maintain Interpretability
Every factor should be logically explainable.
If it's too abstract → Too many factors.
If it's too broad → Too few factors.
✅ Dynamic Monitoring
Factor structures can change over time, especially in evolving datasets.

Why Factor Analysis Matters
Factor analysis helps you:
✅ Discover hidden patterns
✅ Reduce dimensionality
✅ Improve model simplicity
✅ Eliminate redundancy
✅ Create more powerful features for machine learning

Full R Code (As Promised)
install.packages("psych")
library(psych)

bfi_data = bfi
bfi_data = bfi_data[complete.cases(bfi_data), ]

bfi_cor <- cor(bfi_data)

factors_data <- fa(r = bfi_cor, nfactors = 6)
factors_data

Final Thoughts
Factor analysis offers a powerful way to look at your data through a different lens. Instead of guessing patterns, you let the data reveal its hidden structure.
If the factors make sense — you’ve unlocked meaningful insight.
If not — refine and rerun.
That iterative learning is what makes factor analysis such an important tool in advanced analytics.
At Perceptive Analytics, our mission is “to enable businesses to unlock value in data.” For two decades, we’ve supported 100+ organizations worldwide in building high-impact analytics systems. Our offerings span ai consulting services and tableau consulting companies, helping organizations turn raw data into meaningful, decision-ready insights. We would love to talk to you. Do reach out to us.