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Biostatistics Advance Access originally published online on February 17, 2006
Biostatistics 2006 7(4):551-568; doi:10.1093/biostatistics/kxj025
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Published by Oxford University Press 2006.

Bayesian dynamic modeling of latent trait distributions

David B. Dunson

Biostatistics Branch, National Institute of Environmental Health Sciences, MD A3-03, PO Box 12233, Research Triangle Park, NC 27709, USA dunson1{at}niehs.nih.gov

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.

Keywords: Dynamic Dirichlet process; Factor analysis; Hierarchical model; Latent variables; Measurement error; Random effect; Surrogate data


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