What Are the Differences Between Principal Component Analysis and Factor Analysis?
Principal Component Analysis (PCA) and Factor Analysis are widely used multivariate techniques for reducing data dimensionality and extracting underlying structures. While they share certain similarities, they differ in key theoretical and methodological aspects:
Principal Component Analysis (PCA)
1. Objective
PCA aims to transform the original variables into a set of new, uncorrelated components through linear transformation. These components, known as principal components, are constructed to capture the maximum variance in the dataset.
2. Interpretation of Variables
PCA explains data variability by identifying directions of maximum variance. The first principal component captures the highest variance, followed by the second, and so on.
3. Inter-Variable Relationships
PCA assumes linear correlations among variables and seeks to derive new variables (principal components) that are mutually uncorrelated.
4. Component Weights
Each principal component is associated with a set of weights (loadings), indicating the contribution of each original variable to the component.
5. Interpretability
PCA quantifies the proportion of total variance explained by each component, enhancing interpretability of the data structure.
Factor Analysis
1. Objective
Factor Analysis seeks to uncover latent (unobserved) factors that account for the correlations among observed variables.
2. Interpretation of Variables
It attempts to identify a smaller number of underlying factors that explain the common variance shared among observed variables. Each factor reflects shared variability across a subset of variables.
3. Inter-Variable Relationships
Factor Analysis assumes linear relationships among variables and estimates latent factors that account for their shared variance, typically assuming orthogonal or minimally correlated factors.
4. Factor Loadings
Each variable is associated with a set of factor loadings, representing the extent to which the variable contributes to each underlying factor.
5. Interpretability
Factor Analysis provides the proportion of variance in the observed data explained by each extracted factor.
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