Modular item response and structural equation modelling via measurement and uncertainty preserving parametric...

Area of Science:

• Statistical modeling
• Psychometrics
• Quantitative psychology

Background:

• Latent variable models like structural equation modeling (SEM) and item response theory (IRT) are crucial for research and operational assessments.
• Current multistage estimation practices have limitations, particularly from a Bayesian viewpoint.

Purpose of the Study:

• To extend 2-Stage Bayesian approaches in SEM to a general multistage framework.
• To develop a modular approach for assembling model fragments in complex analyses.
• To offer an alternative with improved alignment with Bayesian principles.

Main Methods:

• Developed a general multistage Bayesian approach for structural equation modeling.
• Applied the framework to diverse modeling scenarios, including advanced SEM and operational assessment calibration/scoring.
• Provided R functions interfacing with Mplus for practical implementation.

Main Results:

• The proposed multistage Bayesian approach accommodates a wider range of SEM situations than existing methods.
• Demonstrated effectiveness in calibration and scoring within item response theory contexts.
• The modular framework enhances flexibility and adherence to Bayesian principles.

Conclusions:

• The novel multistage Bayesian approach provides a flexible and principled framework for complex latent variable modeling.
• This method offers significant advantages over traditional single-stage and multistage estimation techniques.
• The provided R functions facilitate the application of this advanced methodology.