Module factor_analysis 

Factor Analysis module Factor Analysis for dimensionality reduction and latent variable modeling

Factor Analysis is a statistical method that describes variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. It differs from PCA in that it models noise separately for each observed variable (uniquenesses/specific variances).

Algorithm (EM-based)

The factor model is: x = W * z + mu + epsilon where z ~ N(0, I) are the latent factors, W is the loading matrix, and epsilon_i ~ N(0, psi_i) are the uniquenesses.

The EM algorithm alternates between:

• E-step: Compute expected sufficient statistics of latent factors given observed data
• M-step: Update loadings (W) and uniquenesses (psi) to maximize expected log-likelihood

Rotation Methods

• Varimax: Orthogonal rotation maximizing variance of squared loadings
• Promax: Oblique rotation based on raised varimax solution

Structs

FactorAnalysis

Factor Analysis for dimensionality reduction

FactorAnalysisResult

Factor Analysis results

ScreePlotData

Scree plot data for selecting the number of factors

Enums

RotationMethod

Rotation method for factor loadings

Functions

factor_analysis

Convenience function for factor analysis

scree_plot_data

Convenience function to compute scree plot data for factor selection