Title: Bayesian covariance structure modeling of high-dimensional dependence structures
Authors: Jean-Paul Fox - University of Twente (Netherlands) [presenting]
Abstract: The covariance structure of response data represents interesting phenomena such as the inter and intra-individual variability, and response dependencies due to higher-level clusters. The well-known psychometric modeling frameworks (e.g., structural equation modeling, item response theory, multilevel modeling), use latent variables (random effects) to model the covariance structures. However, latent variables have several disadvantages. They demand larger sample sizes, increase the number of model parameters, and limit the flexibility of the model to describe high-dimensional data. To avoid the problems associated with latent variables, the covariance structure is modeled directly by defining conjugate priors for the (co)variance parameters, where a multivariate distribution is defined for the response data. The priors include restrictions on the parameter space of the covariance parameters such that any combination of covariance parameters leads to a positive definite covariance matrix. The priors give support to testing the presence of random effects, reduce boundary effects by allowing non-positive (co)variance parameters, and support accurate estimation even for very small true variance parameters. The priors lead to efficient posterior computation using Gibbs sampling. The advantages of Bayesian Covariance Structure Modeling (BCSM) are illustrated through the joint modeling of high-dimensional response data and process data.