What is Factor Analysis ?

Factor Analysis (FA) is a statistical technique used to identify underlying relationships among a large set of variables. It helps in data reduction by grouping correlated variables into factors, making it easier to interpret complex datasets. This method is widely used in psychology, social sciences, finance, and marketing research.

Types of Factor Analysis

1. Exploratory Factor Analysis (EFA)

Used when the researcher does not have prior assumptions about the number of factors in the dataset.
Helps discover the underlying structure in the data.
Identifies groups of variables that move together.

2. Confirmatory Factor Analysis (CFA)

Used to test hypotheses and confirm whether specific variables load onto predefined factors.
Requires prior theoretical knowledge or assumptions about the data structure.

Key Concepts in Factor Analysis

1. Factors

Latent (hidden) variables that influence observed variables.
Represented as dimensions that explain common variance among variables.

2. Factor Loadings

Measure how strongly each observed variable is associated with a factor.
Values range from -1 to 1. Higher absolute values indicate a strong relationship.

3. Communalities

The proportion of each variable’s variance explained by the extracted factors.
A high communality value suggests that the variable is well represented by the factors.

4. Eigenvalues

Indicate the amount of variance explained by each factor.
Factors with eigenvalues greater than 1 are considered significant.

5. Rotation Techniques

Used to improve interpretability by making factor loadings clearer.
Two main types:
Orthogonal Rotation (Varimax): Assumes factors are uncorrelated.
Oblique Rotation (Promax, Oblimin): Allows factors to be correlated.

Steps in Conducting Factor Analysis

Data Collection : Gather a dataset with multiple observed variables.
Check Data Suitability : Kaiser-Meyer-Olkin (KMO) Test, Bartlett’s Test of Sphericity.
Choose Extraction Method : Principal Component Analysis (PCA), Principal Axis Factoring (PAF).
Decide the Number of Factors: Based on eigenvalues (>1 rule), scree plot (elbow method), and variance explained.
Rotate Factors (if needed): Helps in better interpretation of results.
Interpret and Label Factors: Assign meaningful labels based on the grouped variables.
Validate the Factor Model: Conduct reliability testing (Cronbach’s Alpha) and cross-validation.

Applications of Factor Analysis

Psychology: Identifies personality traits, intelligence factors, and behavioral patterns.
Marketing: Segments customers based on buying behavior.
Finance: Identifies economic indicators affecting stock markets.
Education: Analyzes student performance based on multiple criteria.
Healthcare: Identifies symptoms that group into specific diseases.

Advantages of Factor Analysis

Reduces data complexity.
Identifies hidden relationships among variables.
Improves data interpretation.
Helps in questionnaire development by identifying redundant questions.

Limitations of Factor Analysis

Requires large sample sizes for reliable results.
Interpretation of factors can be subjective.
Sensitive to outliers and missing data.
Assumes linear relationships among variables.

Frequently Asked Questions (FAQs)

1. What is the main purpose of factor analysis ?

Factor analysis helps identify underlying relationships between observed variables by reducing them into smaller groups of factors.

2. How is factor analysis different from Principal Component Analysis (PCA) ?

While both methods reduce data dimensionality, PCA focuses on maximizing variance, whereas factor analysis identifies latent constructs that explain correlations among variables.

3. How do I determine the number of factors to retain ?

You can use:

Kaiser’s Criterion (Eigenvalues > 1)
Scree Plot (Elbow method)
Parallel Analysis

4. Can factor analysis be applied to categorical data ?

Traditional factor analysis works best with continuous data, but categorical data can be analyzed using Correspondence Analysis or Latent Class Analysis.

5. What sample size is required for factor analysis ?

A common rule is at least 5–10 observations per variable, but larger samples (e.g., 300+ observations) produce more reliable results.

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What is Factor Analysis ?