Frequentist Model Averaging in Structure Equation Model With Ordinal Data

Area of Science:

• Statistics
• Psychometrics
• Econometrics

Background:

• Structural Equation Modeling (SEM) often involves selecting a single best-fitting model from candidates.
• Inference based on a selected model ignores model selection uncertainty, leading to overly optimistic results.
• Existing frequentist model averaging methods for SEM are primarily designed for continuous data.

Purpose of the Study:

• To adapt frequentist model averaging for SEM with ordinal data.
• To address the limitations of applying continuous data methods to ordinal SEM.
• To develop valid statistical inference techniques that account for model selection uncertainty in ordinal SEM.

Main Methods:

• Proving consistency and asymptotic normality of polychoric correlation estimators under a local asymptotic framework.
• Developing a novel frequentist model averaging estimator for ordinal SEM.
• Deriving valid confidence intervals and goodness-of-fit test statistics for the proposed estimator.

Main Results:

• Demonstrated that existing frequentist model averaging results are not directly applicable to ordinal SEM.
• Established theoretical properties (consistency, asymptotic normality) of polychoric correlation estimators in the local asymptotic framework.
• Proposed a new model averaging estimator and valid inferential tools specifically for ordinal data.

Conclusions:

• The proposed frequentist model averaging approach provides a statistically sound method for SEM with ordinal data.
• This method effectively handles model selection uncertainty, offering a compromise between selecting a single model and using the full model.
• The developed techniques enhance the accuracy and reliability of statistical inference in ordinal SEM.