Random Effect and Latent Variable Model Selection
Random effects and latent variable models are broadly used in analyses of multivariate data. These models can accommodate high dimensional data having a variety of measurement scales. Methods for model selection and comparison are needed in conducting hyp
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David B. Dunson Editor
Random Effect and Latent Variable Model Selection
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Editor David B. Dunson National Institute of Environmental Health Sciences Research Triangle Park, NC USA [email protected]
ISBN: 978-0-387-76720-8 e-ISBN: 978-0-387-76721-5 DOI: 10.1007/978-0-387-76721-5 Library of Congress Control Number: 2008928920 c 2008 Springer Science+Business Media, LLC ° All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Cover illustration: Follicles of colloid in thyroid Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
Preface Random Effect and Latent Variable Model Selection
In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of fields. For example, it is now standard practice to routinely collect many response variables on each individual in a study. The different variables may correspond to repeated measurements over time, to a battery of surrogates for one or more latent traits, or to multiple types of outcomes having an unknown dependence structure. Hierarchical models that incorporate subjectspecific parameters are one of the most widely-used tools for analyzing multivariate and correlated data. Such subject-specific parameters are commonly referred to as random effects, latent variables or frailties. There are two modeling frameworks that have been particularly widely used as hierarchical generalizations of linear regression models. The first is the linear mixed effects model (Laird and Ware , 1982) and the second is the structural equation model (Bollen , 1989). Linear mixed effects (LME) models extend linear regression to incorporate two components, with the first corresponding to fixed effects describing the impact of predictors on the mean and the second to random effects characterizing the impact on the covariance. LMEs have also been increasingly used for function estimation. In implementing LME analyses, model selection problems are unavoidable. For example, there may be interest in comparing models with and without a predictor in the fixed and/or random effects component. In addition, there is typically uncertainty in the subset of predictors to be included in the model, with the number of candidate predictors large in many applications. To address problems of this type, it is not appropriate to rely on classical methods developed for mo
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