Bayesian Modeling For Multivariate Mixed Outcomes With Applications To Cognitive Testing Data
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This dissertation studies parametric and semiparametric approaches to latent variable models, multivariate regression and model-based clustering for mixed outcomes. We use the term mixed outcomes to refer to binary, ordered categorical, count, continuous and other ordered outcomes in combination. Such data structures are common in social, behavioral, and medical sciences. We first review existing parametric approaches to mixed outcomes in latent variable models before developing extensions to accommodate outcome types specific to cognitive testing data. We subsequently develop two new regression approaches for mixed outcome data, the semiparametric Bayesian latent variable model and the semiparametric reduced rank multivariate regression model. In contrast to the existing parametric approaches, these models allow us to avoid specification of distributions for each outcome type. We apply the latent variable and multivariate regression models to investigate the association between cognitive outcomes and MRI-measured regional brain volumes using data from a study of dementia and compare results from the different models. Finally, we develop a new semiparametric correlated partial membership model for model-based clustering of mixed outcome data that also allows us to avoid specification of outcome distributions. We demonstrate our semiparametric approach to model-based clustering on NBA player data from the 2010-2011 season as well as on cognitive testing data from a study of dementia.
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