Factor Analysis Procedures Revisited from the Comprehensive Model with Unique Factors Decomposed into Specific...

Area of Science:

• Statistics
• Computational Statistics
• Multivariate Analysis

Background:

• Factor Analysis (FA) encompasses various procedures, including latent variable FA (LVFA), matrix decomposition FA (MDFA), and completely decomposed FA (CDFA).
• These methods are often analyzed through the lens of the Comprehensive FA (CompFA) model, which decomposes observations into common factor, specific factor, and error components.

Purpose of the Study:

• To revisit and compare LVFA, MDFA, and CDFA procedures within the framework of the CompFA model.
• To evaluate how well each FA procedure satisfies CompFA model assumptions and estimates its parameters.
• To analyze parameter recovery in CDFA and MDFA, and unique factor estimation in LVFA.

Main Methods:

• Revisiting existing FA procedures (LVFA, MDFA, CDFA) using the CompFA model.
• Analyzing the separation of common factor, specific factor, and error parts in each FA type.
• Examining parameter estimation accuracy within the CompFA framework for each procedure.
• Subdividing the CompFA model based on error term correlation for detailed analysis.

Main Results:

• CDFA fully satisfies the assumptions of the CompFA model.
• MDFA does not completely satisfy the CompFA model assumptions.
• CDFA accurately recovers all CompFA model parameters.
• LVFA approximates the unique factor parameter, and MDFA approximates the specific factor parameter, rather than estimating them directly.

Conclusions:

• CDFA offers a more theoretically sound approach to factor analysis by fully adhering to the CompFA model.
• CDFA provides superior parameter estimation accuracy compared to MDFA and LVFA within the CompFA framework.
• The findings highlight the importance of model assumptions and parameter recovery in selecting appropriate factor analysis techniques.