A General Theorem and Proof for the Identification of Composed CFA Models

Area of Science:

• Psychometrics
• Statistical Modeling
• Structural Equation Modeling

Background:

• Composed Confirmatory Factor Analysis (CFA) models integrate multiple identified submodels linked by latent factor covariances.
• These models are widely applied in analyzing multimethod, longitudinal, and multidimensional psychometric data.

Purpose of the Study:

• To present a general theorem and proof for the global identification of composed CFA models.
• To establish conditions under which composed CFA models can be reliably identified.

Main Methods:

• Development of a general theorem for composed CFA model identification.
• Analysis of identification conditions based on the nature of primary submodels (reduced vs. non-reduced).
• Provision of Python code for checking model identification status.

Main Results:

• The theorem simplifies composed model identification to submodel identification and condition verification.
• Composed CFA models with reduced primary models (e.g., CT-C[Formula: see text]) are generally globally identified.
• Composed CFA models with non-reduced primary models may be globally underidentified depending on covariance assumptions.

Conclusions:

• The study offers a theoretical framework and practical tools for assessing the global identification of complex composed CFA models.
• Understanding identification conditions is critical for accurate analysis of multimethod, longitudinal, and multidimensional data.
• The provided Python code facilitates the application of these identification principles to real-world research scenarios.