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Title: Using chain graph models for structural inference for multi-level data with an application to linguistic data Authors:  Craig Alexander - University of Glasgow (United Kingdom) [presenting]
Ludger Evers - University of Glasgow (United Kingdom)
Tereza Neocleous - University of Glasgow (United Kingdom)
Jane Stuart-Smith - University of Glasgow (United Kingdom)
Abstract: Graphical models provide a visualisation of the conditional dependence structure between variables, making them an attractive tool for inference. We discuss the use of a chain graph model as an alternative to a standard multi-level regression analysis with a multivariate response. The improved readability of the model output makes this an appealing alternative for those not with a strong statistical background. The chain graph can be inferred from three parts. The dependency structure of the covariates can be modelled independently using standard methods for structural inference in graphical models such as log-linear models in the case of categorical covariates. The directed edges between the explanatory and response variables and the undirected edges between the response variables are jointly inferred using a multivariate Bayesian multi-level model in which the precision matrix of residuals and random effects is assumed to conform to a undirected graphical model, which is to be inferred. We present an application of this model using linguistic data obtained from the Sounds of the City corpus which consists of a real time corpus of Glaswegian speech. From the data, we look to recover the underlying chain graph model detailing which factors affect vowel quality.