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Statistical method modeling correlations among observed variables with fewer latent factors to reveal underlying structure.
DESCRIPTION
Factor analysis uncovers latent constructs that explain patterns of correlation in observed variables. It reduces dimensionality while preserving common variance, aiding interpretation and measurement. Exploratory factor analysis identifies factor structure; confirmatory factor analysis tests hypothesized structures within structural equation modeling. Key steps include extraction, determining factor count, rotation, and interpretation. Assumptions include linearity, adequate sample size, and sufficient correlations. It is widely used in psychology, marketing research, and social sciences for scale development and construct validation.
ALTERNATIVE DEFINITIONS
Wikipedia
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.
Highlights modeling correlated observed variables with fewer unobserved factors.
Encyclopaedia Britannica
Factor analysis, in statistics, a method for analyzing the correlations among variables in terms of a smaller number of underlying factors.
Emphasizes correlation analysis and reduction to underlying factors.
UCLA Statistical Consulting
Factor analysis is a method for investigating whether a number of variables of interest are linearly related to a smaller number of unobserved factors.
Stresses linear relationships and investigating latent factors in practice.
Penn State Online STAT 505
Factor analysis is a technique that seeks to explain the correlations among multiple observed variables by a smaller number of latent variables called factors.
Focuses on explaining observed correlations using latent variables.
RELATED TERMS
Exploratory Factor Analysis Confirmatory Factor Analysis Latent Variable Model Structural Equation Modeling Feature Reduction Eigenvalues Rotation (Varimax/Oblimin) Communality Loadings
COMPETING TERMS
Principal Component Analysis Independent Component Analysis
KNOWLEDGE AREAS
Mathematics Data Science Data Modeling
TARGET AUDIENCE
Data Scientist Data Analyst Information Analyst Data Modeler
EXTERNAL SOURCES
- Wikipedia - Factor analysis
- UCLA Statistical Consulting - Applied overview and guidance
- Penn State STAT 505 - Course notes on factor analysis
- scikit-learn - API for FactorAnalysis
- IBM SPSS Documentation - SPSS factor analysis procedure
TOP QUESTIONS
When should Factor Analysis be used?
Use factor analysis when you suspect multiple observed variables reflect a smaller number of latent constructs. It’s common for scale development, questionnaire validation, and dimensionality reduction for interpretation.
Category: Requirements
How does Factor Analysis differ from PCA?
PCA decomposes total variance to maximize variance explained, while factor analysis models common variance via latent factors. PCA is algebraic; factor analysis is a statistical model with assumptions.
Category: Misunderstanding
What are the main assumptions in Factor Analysis?
Assumptions include linear relationships, sufficient correlations, and adequate sample size. Multivariate normality is desirable for inference; factors are assumed to cause observed covariation.
Category: Requirements
How many factors should be retained in Factor Analysis?
Use multiple criteria: eigenvalues (>1), scree plot, parallel analysis, and interpretability. No single rule suffices; triangulate statistical and substantive judgment.
Category: Opinion
What is rotation in Factor Analysis and why use it?
Rotation reorients factor loadings to enhance interpretability. Orthogonal (e.g., Varimax) preserves independence; oblique (e.g., Oblimin) allows correlated factors, often more realistic in social sciences.
Category: Example
What’s a common mistake in Factor Analysis?
Extracting too many or too few factors without using parallel analysis and ignoring cross-loadings. Poorly measured items and low communalities also lead to unstable solutions.
Category: Mistakes
How is Factor Analysis validated?
Split-sample validation with EFA then CFA, goodness-of-fit indices in SEM, and replication across cohorts. Loadings’ stability and reliability indicators (e.g., omega) support validity.
Category: Testing
What are risks of misusing Factor Analysis?
Misinterpreting statistical artifacts as real constructs can misguide decisions. Overfitting to sample idiosyncrasies reduces generalizability and can invalidate downstream analyses.
Category: Risks
What are alternatives to Factor Analysis?
Alternatives include PCA for descriptive reduction, ICA for independent sources, and non-linear embeddings (t-SNE, UMAP) for visualization, depending on goals and assumptions.
Category: Alternatives