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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data
1Department of Statistics, The Chinese University of Hong Kong, Shatin. sylee@sparc2.sta.cuhk.edu.hk
Summary
This study introduces a Bayesian approach for structural equation models with non-normal, ordered categorical data, common in behavioral research. The new method enhances analysis for complex datasets, offering improved model evaluation.
Area of Science:
- Statistics
- Psychometrics
- Behavioral Sciences
Background:
- Structural equation models (SEMs) are widely used but primarily assume data normality.
- Existing SEM software struggles with non-normal and ordered categorical data prevalent in social and psychological research.
- This limitation hinders the accurate analysis of complex relationships in these fields.
Purpose of the Study:
- To develop a flexible Bayesian framework for SEMs accommodating non-normal and ordered categorical variables.
- To enable the analysis of models with mixed data types, including binomial, ordered categorical, and normal variables.
- To provide robust parameter estimation and model fit assessment for complex data structures.
Main Methods:
- A Bayesian approach utilizing the Gibbs sampler and Metropolis-Hastings algorithm for parameter estimation.
- Development of goodness-of-fit statistics tailored for the proposed model.
- Application to simulated data and a real-world dataset on patient adherence to hypertension treatment.
Main Results:
- The Bayesian approach successfully estimates parameters in SEMs with non-normal and mixed data types.
- The proposed goodness-of-fit statistics effectively evaluate model fit for these complex models.
- Demonstrated utility through simulation studies and a practical example in medical adherence research.
Conclusions:
- The developed Bayesian methodology offers a powerful and flexible tool for SEM analysis with non-normal and ordered categorical data.
- This approach expands the applicability of SEMs in behavioral, social, and psychological research.
- The method provides reliable parameter estimates and model evaluation for complex, real-world datasets.
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