A2033
Title: Fast Bayesian analysis of mixture of Gaussian structural equation models
Authors: Luca Maestrini - The Australian National University (Australia) [presenting]
Khue-Dung Dang - University of Western Australia (Australia)
Francis Hui - The Australian National University (Australia)
Abstract: Structural equation models (SEMs) are widely used in social and behavioral sciences to study the structural relationship between measured outcomes and latent constructs. Recently, Bayesian fitting procedures for SEMs have gained increasing popularity due to their potential to facilitate more flexible model structures. Variational Bayes approximations, in particular, have been shown to provide fast and accurate inference for Bayesian analysis of SEMs, although to date their application has been limited to simple forms involving no covariates and assuming normality for all measured outcomes. Motivated by a study assessing the impact of prenatal alcohol exposure on child cognitive function, mean field variational Bayes for a SEM formulation is developed where measured outcomes exhibit non-Gaussian features such as skewness and multimodality. The proposed SEMMIX model utilizes finite mixtures of Gaussian distributions to accommodate such features; covariates are incorporated into the modeling of the latent traits, and an automated approach is developed to account for missing at random outcomes. Two variational information criteria for model selection are also proposed that are straightforward to compute in the variational inference framework. Simulations and application to the motivating child cognitive function dataset demonstrate that SEMMIX fitted using fast variational Bayes methods captures key non-Gaussian features of the data.
