Show Me Some ID: A Universal Identification Program for Structural Equation Models

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Increasing complexity in statistical models and research designs necessitates robust methods for model identification.
• Model identification, determining if a model can be estimated, is fundamental to valid statistical inference.

Purpose of the Study:

• To extend existing data-independent model identification techniques for structural equation models.
• To introduce data-dependent empirical model identification methods.
• To provide a practical solution for complex model identification challenges.

Main Methods:

• Leveraging previously published work on data-independent identification for structural equation models.
• Extending methods to accommodate flexible exogenous covariate effects.
• Developing and applying data-dependent empirical identification criteria.
• Implementing the solution within the OpenMx package in R.

Main Results:

• The proposed methods successfully address model identification for complex structural equation models.
• The approach is validated on known examples and a real-world dataset (National Longitudinal Survey of Youth).
• The extended framework enhances the applicability of model identification to a broader range of models.

Conclusions:

• The developed methods provide a comprehensive solution for model identification in complex structural equation models.
• The implementation in OpenMx facilitates practical application for researchers.
• This work advances the foundational understanding and practical assessment of model identifiability.