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Bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic
Xin-Yuan Song1, Sik-Yum Lee, Maggie C Y Ng
1Department of Statistics, The Chinese University of Hong Kong, Shatin NT, Hong Kong. xysong@sta.cuhk.edu.hk
Statistics in Medicine
|October 4, 2006
Summary
This study introduces a new nonlinear structural equation model to analyze complex diseases influenced by genetic and observable traits. The model effectively handles mixed data types and interactions, offering insights into disease mechanisms.
Area of Science:
- Biostatistics
- Genetics
- Epidemiology
Background:
- Complex diseases are influenced by correlated phenotype and genotype variables and their interactions.
- Assessing these influences is challenging due to the large number of variables and the multinomial distribution of genotype data.
- Missing data further complicates analysis.
Purpose of the Study:
- To develop a novel nonlinear structural equation model for analyzing mixed continuous and multinomial data with missing values.
- To assess linear and interaction effects of latent variables on disease outcomes.
- To apply the methodology to a type 2 diabetes cohort.
Main Methods:
- A confirmatory factor analysis model using Kronecker products to group manifest variables into latent variables.
- A nonlinear structural equation formulation to model variable effects and interactions.
- Bayesian estimation and model comparison using Markov chain Monte Carlo and path sampling.
Main Results:
- The developed model successfully analyzes mixed continuous and multinomial data, accounting for missingness.
- It effectively identifies linear and interaction effects between latent variables.
- The application to type 2 diabetic patients with nephropathy demonstrates its utility.
Conclusions:
- The novel nonlinear structural equation model provides a robust framework for analyzing complex diseases with genetic and phenotypic data.
- This approach enhances understanding of disease etiology by incorporating variable interactions.
- The methodology is applicable to real-world epidemiological studies.
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