Bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic nephropathy.

There is now increasing evidence proving that many complex diseases can be significantly influenced by correlated phenotype and genotype variables, as well as their interactions. Effective and rigorous assessment of such influence is difficult, because the number of phenotype and genotype variables of interest may not be small, and a genotype variable is an unordered categorical variable that follows a multinomial distribution. To address the problem, we establish a novel nonlinear structural equation model for analysing mixed continuous and multinomial data that can be missing at random. A confirmatory factor analysis model with Kronecker product is proposed for grouping the manifest continuous and multinomial variables into latent variables according to their functions; and a nonlinear structural equation is formulated to assess the linear and interaction effects of the independent latent variables to the dependent latent variables. Bayesian methods for estimation and model comparison are developed through Markov chain Monte Carlo techniques and path sampling. The newly developed methodologies are applied to a case-control cohort of type 2 diabetic patients with nephropathy.