Assessment of generalised Bayesian structural equation models for continuous and binary data.

Area of Science:

• Statistics
• Psychometrics
• Computational Statistics

Background:

• Current Bayesian structural equation modeling (BSEM) relies heavily on posterior predictive p-values, which have limitations in assessing model fit.
• The approximate zero approach, using informative priors, offers an alternative to explicitly setting parameters to zero.

Purpose of the Study:

• To propose a novel model assessment paradigm for BSEM that addresses the shortcomings of posterior predictive p-values.
• To introduce tools that monitor out-of-sample predictive performance for evaluating hypothesized models.
• To enhance BSEM for continuous and binary data, including categorical and non-normally distributed data.

Main Methods:

• Utilizing the approximate zero approach with informative priors for parameters like factor loadings.
• Implementing scoring rules and cross-validation for model assessment.
• Introducing an item-individual random effect for modeling complex data types.

Main Results:

• The proposed methodology demonstrates effective monitoring of out-of-sample predictive performance.
• Simulation experiments and real-data analyses (Big-5 personality, Fagerstrom test) validate the approach.
• The tools are applicable to both continuous and binary data models.

Conclusions:

• The novel paradigm offers a robust method for assessing BSEM, supplementing existing metrics.
• The approach provides guidelines for determining data support for hypothesized models.
• The enhanced tools improve the flexibility and applicability of BSEM for diverse data structures.